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1015 lines
36 KiB
Plaintext
1015 lines
36 KiB
Plaintext
# Minimal valid case: an empty histogram.
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load 5m
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empty_histogram {{}}
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eval instant at 1m empty_histogram
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{__name__="empty_histogram"} {{}}
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eval instant at 1m histogram_count(empty_histogram)
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{} 0
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eval instant at 1m histogram_sum(empty_histogram)
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{} 0
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eval instant at 1m histogram_avg(empty_histogram)
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{} NaN
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eval instant at 1m histogram_fraction(-Inf, +Inf, empty_histogram)
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{} NaN
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eval instant at 1m histogram_fraction(0, 8, empty_histogram)
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{} NaN
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clear
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# buckets:[1 2 1] means 1 observation in the 1st bucket, 2 observations in the 2nd and 1 observation in the 3rd (total 4).
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load 5m
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single_histogram {{schema:0 sum:5 count:4 buckets:[1 2 1]}}
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# histogram_count extracts the count property from the histogram.
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eval instant at 1m histogram_count(single_histogram)
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{} 4
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# histogram_sum extracts the sum property from the histogram.
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eval instant at 1m histogram_sum(single_histogram)
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{} 5
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# histogram_avg calculates the average from sum and count properties.
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eval instant at 1m histogram_avg(single_histogram)
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{} 1.25
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# We expect half of the values to fall in the range 1 < x <= 2.
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eval instant at 1m histogram_fraction(1, 2, single_histogram)
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{} 0.5
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# We expect all values to fall in the range 0 < x <= 8.
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eval instant at 1m histogram_fraction(0, 8, single_histogram)
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{} 1
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# Median is 1.5 due to linear estimation of the midpoint of the middle bucket, whose values are within range 1 < x <= 2.
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eval instant at 1m histogram_quantile(0.5, single_histogram)
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{} 1.5
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clear
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# Repeat the same histogram 10 times.
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load 5m
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multi_histogram {{schema:0 sum:5 count:4 buckets:[1 2 1]}}x10
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eval instant at 5m histogram_count(multi_histogram)
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{} 4
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eval instant at 5m histogram_sum(multi_histogram)
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{} 5
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eval instant at 5m histogram_avg(multi_histogram)
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{} 1.25
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eval instant at 5m histogram_fraction(1, 2, multi_histogram)
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{} 0.5
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eval instant at 5m histogram_quantile(0.5, multi_histogram)
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{} 1.5
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# Each entry should look the same as the first.
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eval instant at 50m histogram_count(multi_histogram)
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{} 4
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eval instant at 50m histogram_sum(multi_histogram)
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{} 5
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eval instant at 50m histogram_avg(multi_histogram)
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{} 1.25
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eval instant at 50m histogram_fraction(1, 2, multi_histogram)
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{} 0.5
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eval instant at 50m histogram_quantile(0.5, multi_histogram)
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{} 1.5
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clear
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# Accumulate the histogram addition for 10 iterations, offset is a bucket position where offset:0 is always the bucket
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# with an upper limit of 1 and offset:1 is the bucket which follows to the right. Negative offsets represent bucket
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# positions for upper limits <1 (tending toward zero), where offset:-1 is the bucket to the left of offset:0.
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load 5m
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incr_histogram {{schema:0 sum:4 count:4 buckets:[1 2 1]}}+{{sum:2 count:1 buckets:[1] offset:1}}x10
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eval instant at 5m histogram_count(incr_histogram)
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{} 5
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eval instant at 5m histogram_sum(incr_histogram)
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{} 6
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eval instant at 5m histogram_avg(incr_histogram)
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{} 1.2
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# We expect 3/5ths of the values to fall in the range 1 < x <= 2.
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eval instant at 5m histogram_fraction(1, 2, incr_histogram)
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{} 0.6
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eval instant at 5m histogram_quantile(0.5, incr_histogram)
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{} 1.5
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eval instant at 50m incr_histogram
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{__name__="incr_histogram"} {{count:14 sum:24 buckets:[1 12 1]}}
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eval instant at 50m histogram_count(incr_histogram)
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{} 14
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eval instant at 50m histogram_sum(incr_histogram)
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{} 24
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eval instant at 50m histogram_avg(incr_histogram)
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{} 1.7142857142857142
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# We expect 12/14ths of the values to fall in the range 1 < x <= 2.
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eval instant at 50m histogram_fraction(1, 2, incr_histogram)
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{} 0.8571428571428571
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eval instant at 50m histogram_quantile(0.5, incr_histogram)
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{} 1.5
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# Per-second average rate of increase should be 1/(5*60) for count and buckets, then 2/(5*60) for sum.
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eval instant at 50m rate(incr_histogram[10m])
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{} {{count:0.0033333333333333335 sum:0.006666666666666667 offset:1 buckets:[0.0033333333333333335]}}
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# Calculate the 50th percentile of observations over the last 10m.
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eval instant at 50m histogram_quantile(0.5, rate(incr_histogram[10m]))
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{} 1.5
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clear
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# Schema represents the histogram resolution, different schema have compatible bucket boundaries, e.g.:
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# 0: 1 2 4 8 16 32 64 (higher resolution)
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# -1: 1 4 16 64 (lower resolution)
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#
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# Histograms can be merged as long as the histogram to the right is same resolution or higher.
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load 5m
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low_res_histogram {{schema:-1 sum:4 count:1 buckets:[1] offset:1}}+{{schema:0 sum:4 count:4 buckets:[2 2] offset:1}}x1
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eval instant at 5m low_res_histogram
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{__name__="low_res_histogram"} {{schema:-1 count:5 sum:8 offset:1 buckets:[5]}}
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eval instant at 5m histogram_count(low_res_histogram)
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{} 5
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eval instant at 5m histogram_sum(low_res_histogram)
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{} 8
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eval instant at 5m histogram_avg(low_res_histogram)
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{} 1.6
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# We expect all values to fall into the lower-resolution bucket with the range 1 < x <= 4.
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eval instant at 5m histogram_fraction(1, 4, low_res_histogram)
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{} 1
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clear
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# z_bucket:1 means there is one observation in the zero bucket and z_bucket_w:0.5 means the zero bucket has the range
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# 0 < x <= 0.5. Sum and count are expected to represent all observations in the histogram, including those in the zero bucket.
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load 5m
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single_zero_histogram {{schema:0 z_bucket:1 z_bucket_w:0.5 sum:0.25 count:1}}
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eval instant at 1m histogram_count(single_zero_histogram)
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{} 1
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eval instant at 1m histogram_sum(single_zero_histogram)
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{} 0.25
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eval instant at 1m histogram_avg(single_zero_histogram)
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{} 0.25
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# When only the zero bucket is populated, or there are negative buckets, the distribution is assumed to be equally
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# distributed around zero; i.e. that there are an equal number of positive and negative observations. Therefore the
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# entire distribution must lie within the full range of the zero bucket, in this case: -0.5 < x <= +0.5.
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eval instant at 1m histogram_fraction(-0.5, 0.5, single_zero_histogram)
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{} 1
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# Half of the observations are estimated to be zero, as this is the midpoint between -0.5 and +0.5.
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eval instant at 1m histogram_quantile(0.5, single_zero_histogram)
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{} 0
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clear
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# Let's turn single_histogram upside-down.
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load 5m
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negative_histogram {{schema:0 sum:-5 count:4 n_buckets:[1 2 1]}}
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eval instant at 1m histogram_count(negative_histogram)
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{} 4
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eval instant at 1m histogram_sum(negative_histogram)
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{} -5
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eval instant at 1m histogram_avg(negative_histogram)
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{} -1.25
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# We expect half of the values to fall in the range -2 < x <= -1.
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eval instant at 1m histogram_fraction(-2, -1, negative_histogram)
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{} 0.5
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eval instant at 1m histogram_quantile(0.5, negative_histogram)
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{} -1.5
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clear
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# Two histogram samples.
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load 5m
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two_samples_histogram {{schema:0 sum:4 count:4 buckets:[1 2 1]}} {{schema:0 sum:-4 count:4 n_buckets:[1 2 1]}}
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# We expect to see the newest sample.
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eval instant at 5m histogram_count(two_samples_histogram)
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{} 4
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eval instant at 5m histogram_sum(two_samples_histogram)
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{} -4
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eval instant at 5m histogram_avg(two_samples_histogram)
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{} -1
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eval instant at 5m histogram_fraction(-2, -1, two_samples_histogram)
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{} 0.5
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eval instant at 5m histogram_quantile(0.5, two_samples_histogram)
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{} -1.5
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clear
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# Add two histograms with negated data.
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load 5m
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balanced_histogram {{schema:0 sum:4 count:4 buckets:[1 2 1]}}+{{schema:0 sum:-4 count:4 n_buckets:[1 2 1]}}x1
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eval instant at 5m histogram_count(balanced_histogram)
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{} 8
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eval instant at 5m histogram_sum(balanced_histogram)
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{} 0
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eval instant at 5m histogram_avg(balanced_histogram)
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{} 0
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eval instant at 5m histogram_fraction(0, 4, balanced_histogram)
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{} 0.5
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# If the quantile happens to be located in a span of empty buckets, the actually returned value is the lower bound of
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# the first populated bucket after the span of empty buckets.
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eval instant at 5m histogram_quantile(0.5, balanced_histogram)
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{} 0.5
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clear
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# Add histogram to test sum(last_over_time) regression
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load 5m
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incr_sum_histogram{number="1"} {{schema:0 sum:0 count:0 buckets:[1]}}+{{schema:0 sum:1 count:1 buckets:[1]}}x10
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incr_sum_histogram{number="2"} {{schema:0 sum:0 count:0 buckets:[1]}}+{{schema:0 sum:2 count:1 buckets:[1]}}x10
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eval instant at 50m histogram_sum(sum(incr_sum_histogram))
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{} 30
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eval instant at 50m histogram_sum(sum(last_over_time(incr_sum_histogram[5m])))
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{} 30
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clear
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# Apply rate function to histogram.
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load 15s
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histogram_rate {{schema:1 count:12 sum:18.4 z_bucket:2 z_bucket_w:0.001 buckets:[1 2 0 1 1] n_buckets:[1 2 0 1 1]}}+{{schema:1 count:9 sum:18.4 z_bucket:1 z_bucket_w:0.001 buckets:[1 1 0 1 1] n_buckets:[1 1 0 1 1]}}x100
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eval instant at 5m rate(histogram_rate[45s])
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{} {{schema:1 count:0.6 sum:1.2266666666666652 z_bucket:0.06666666666666667 z_bucket_w:0.001 buckets:[0.06666666666666667 0.06666666666666667 0 0.06666666666666667 0.06666666666666667] n_buckets:[0.06666666666666667 0.06666666666666667 0 0.06666666666666667 0.06666666666666667]}}
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eval range from 5m to 5m30s step 30s rate(histogram_rate[45s])
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{} {{schema:1 count:0.6 sum:1.2266666666666652 z_bucket:0.06666666666666667 z_bucket_w:0.001 buckets:[0.06666666666666667 0.06666666666666667 0 0.06666666666666667 0.06666666666666667] n_buckets:[0.06666666666666667 0.06666666666666667 0 0.06666666666666667 0.06666666666666667]}}x1
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clear
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# Apply count and sum function to histogram.
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load 10m
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histogram_count_sum_2 {{schema:0 count:24 sum:100 z_bucket:4 z_bucket_w:0.001 buckets:[2 3 0 1 4] n_buckets:[2 3 0 1 4]}}x1
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eval instant at 10m histogram_count(histogram_count_sum_2)
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{} 24
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eval instant at 10m histogram_sum(histogram_count_sum_2)
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{} 100
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clear
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# Apply stddev and stdvar function to histogram with {1, 2, 3, 4} (low res).
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load 10m
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histogram_stddev_stdvar_1 {{schema:2 count:4 sum:10 buckets:[1 0 0 0 1 0 0 1 1]}}x1
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eval instant at 10m histogram_stddev(histogram_stddev_stdvar_1)
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{} 1.0787993180043811
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eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_1)
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{} 1.163807968526718
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clear
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# Apply stddev and stdvar function to histogram with {1, 1, 1, 1} (high res).
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load 10m
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histogram_stddev_stdvar_2 {{schema:8 count:10 sum:10 buckets:[1 2 3 4]}}x1
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eval instant at 10m histogram_stddev(histogram_stddev_stdvar_2)
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{} 0.0048960313898237465
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eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_2)
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{} 2.3971123370139447e-05
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clear
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# Apply stddev and stdvar function to histogram with {-50, -8, 0, 3, 8, 9}.
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load 10m
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histogram_stddev_stdvar_3 {{schema:3 count:7 sum:62 z_bucket:1 buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] n_buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]}}x1
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eval instant at 10m histogram_stddev(histogram_stddev_stdvar_3)
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{} 42.947236400258
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eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_3)
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{} 1844.4651144196398
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clear
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# Apply stddev and stdvar function to histogram with {-100000, -10000, -1000, -888, -888, -100, -50, -9, -8, -3}.
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load 10m
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histogram_stddev_stdvar_4 {{schema:0 count:10 sum:-112946 z_bucket:0 n_buckets:[0 0 1 1 1 0 1 1 0 0 3 0 0 0 1 0 0 1]}}x1
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eval instant at 10m histogram_stddev(histogram_stddev_stdvar_4)
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{} 27556.344499842
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eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_4)
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{} 759352122.1939945
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clear
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# Apply stddev and stdvar function to histogram with {-10x10}.
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load 10m
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histogram_stddev_stdvar_5 {{schema:0 count:10 sum:-100 z_bucket:0 n_buckets:[0 0 0 0 10]}}x1
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eval instant at 10m histogram_stddev(histogram_stddev_stdvar_5)
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{} 1.3137084989848
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eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_5)
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{} 1.725830020304794
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clear
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# Apply stddev and stdvar function to histogram with {-50, -8, 0, 3, 8, 9, NaN}.
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load 10m
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histogram_stddev_stdvar_6 {{schema:3 count:7 sum:NaN z_bucket:1 buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] n_buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]}}x1
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eval instant at 10m histogram_stddev(histogram_stddev_stdvar_6)
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{} NaN
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eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_6)
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{} NaN
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clear
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# Apply stddev and stdvar function to histogram with {-50, -8, 0, 3, 8, 9, Inf}.
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load 10m
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histogram_stddev_stdvar_7 {{schema:3 count:7 sum:Inf z_bucket:1 buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] n_buckets:[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]}}x1
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eval instant at 10m histogram_stddev(histogram_stddev_stdvar_7)
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{} Inf
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eval instant at 10m histogram_stdvar(histogram_stddev_stdvar_7)
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{} Inf
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clear
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# Apply quantile function to histogram with all positive buckets with zero bucket.
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load 10m
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histogram_quantile_1 {{schema:0 count:12 sum:100 z_bucket:2 z_bucket_w:0.001 buckets:[2 3 0 1 4]}}x1
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eval_warn instant at 10m histogram_quantile(1.001, histogram_quantile_1)
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{} Inf
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eval instant at 10m histogram_quantile(1, histogram_quantile_1)
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{} 16
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eval instant at 10m histogram_quantile(0.99, histogram_quantile_1)
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{} 15.759999999999998
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eval instant at 10m histogram_quantile(0.9, histogram_quantile_1)
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{} 13.600000000000001
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eval instant at 10m histogram_quantile(0.6, histogram_quantile_1)
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{} 4.799999999999997
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eval instant at 10m histogram_quantile(0.5, histogram_quantile_1)
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{} 1.6666666666666665
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eval instant at 10m histogram_quantile(0.1, histogram_quantile_1)
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{} 0.0006000000000000001
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eval instant at 10m histogram_quantile(0, histogram_quantile_1)
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{} 0
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eval_warn instant at 10m histogram_quantile(-1, histogram_quantile_1)
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{} -Inf
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clear
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# Apply quantile function to histogram with all negative buckets with zero bucket.
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load 10m
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histogram_quantile_2 {{schema:0 count:12 sum:100 z_bucket:2 z_bucket_w:0.001 n_buckets:[2 3 0 1 4]}}x1
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eval_warn instant at 10m histogram_quantile(1.001, histogram_quantile_2)
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{} Inf
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eval instant at 10m histogram_quantile(1, histogram_quantile_2)
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{} 0
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eval instant at 10m histogram_quantile(0.99, histogram_quantile_2)
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{} -6.000000000000048e-05
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eval instant at 10m histogram_quantile(0.9, histogram_quantile_2)
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{} -0.0005999999999999996
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eval instant at 10m histogram_quantile(0.5, histogram_quantile_2)
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{} -1.6666666666666667
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eval instant at 10m histogram_quantile(0.1, histogram_quantile_2)
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{} -13.6
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eval instant at 10m histogram_quantile(0, histogram_quantile_2)
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{} -16
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eval_warn instant at 10m histogram_quantile(-1, histogram_quantile_2)
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{} -Inf
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clear
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# Apply quantile function to histogram with both positive and negative buckets with zero bucket.
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load 10m
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histogram_quantile_3 {{schema:0 count:24 sum:100 z_bucket:4 z_bucket_w:0.001 buckets:[2 3 0 1 4] n_buckets:[2 3 0 1 4]}}x1
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eval_warn instant at 10m histogram_quantile(1.001, histogram_quantile_3)
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{} Inf
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eval instant at 10m histogram_quantile(1, histogram_quantile_3)
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{} 16
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eval instant at 10m histogram_quantile(0.99, histogram_quantile_3)
|
|
{} 15.519999999999996
|
|
|
|
eval instant at 10m histogram_quantile(0.9, histogram_quantile_3)
|
|
{} 11.200000000000003
|
|
|
|
eval instant at 10m histogram_quantile(0.7, histogram_quantile_3)
|
|
{} 1.2666666666666657
|
|
|
|
eval instant at 10m histogram_quantile(0.55, histogram_quantile_3)
|
|
{} 0.0006000000000000005
|
|
|
|
eval instant at 10m histogram_quantile(0.5, histogram_quantile_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_quantile(0.45, histogram_quantile_3)
|
|
{} -0.0005999999999999996
|
|
|
|
eval instant at 10m histogram_quantile(0.3, histogram_quantile_3)
|
|
{} -1.266666666666667
|
|
|
|
eval instant at 10m histogram_quantile(0.1, histogram_quantile_3)
|
|
{} -11.2
|
|
|
|
eval instant at 10m histogram_quantile(0.01, histogram_quantile_3)
|
|
{} -15.52
|
|
|
|
eval instant at 10m histogram_quantile(0, histogram_quantile_3)
|
|
{} -16
|
|
|
|
eval_warn instant at 10m histogram_quantile(-1, histogram_quantile_3)
|
|
{} -Inf
|
|
|
|
clear
|
|
|
|
# Apply fraction function to empty histogram.
|
|
load 10m
|
|
histogram_fraction_1 {{}}x1
|
|
|
|
eval instant at 10m histogram_fraction(3.1415, 42, histogram_fraction_1)
|
|
{} NaN
|
|
|
|
clear
|
|
|
|
# Apply fraction function to histogram with positive and zero buckets.
|
|
load 10m
|
|
histogram_fraction_2 {{schema:0 count:12 sum:100 z_bucket:2 z_bucket_w:0.001 buckets:[2 3 0 1 4]}}x1
|
|
|
|
eval instant at 10m histogram_fraction(0, +Inf, histogram_fraction_2)
|
|
{} 1
|
|
|
|
eval instant at 10m histogram_fraction(-Inf, 0, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-0.001, 0, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(0, 0.001, histogram_fraction_2)
|
|
{} 0.16666666666666666
|
|
|
|
eval instant at 10m histogram_fraction(0, 0.0005, histogram_fraction_2)
|
|
{} 0.08333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(0.001, inf, histogram_fraction_2)
|
|
{} 0.8333333333333334
|
|
|
|
eval instant at 10m histogram_fraction(-inf, -0.001, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(1, 2, histogram_fraction_2)
|
|
{} 0.25
|
|
|
|
eval instant at 10m histogram_fraction(1.5, 2, histogram_fraction_2)
|
|
{} 0.125
|
|
|
|
eval instant at 10m histogram_fraction(1, 8, histogram_fraction_2)
|
|
{} 0.3333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(1, 6, histogram_fraction_2)
|
|
{} 0.2916666666666667
|
|
|
|
eval instant at 10m histogram_fraction(1.5, 6, histogram_fraction_2)
|
|
{} 0.16666666666666666
|
|
|
|
eval instant at 10m histogram_fraction(-2, -1, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-2, -1.5, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-8, -1, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-6, -1, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-6, -1.5, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(42, 3.1415, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(0, 0, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(0.000001, 0.000001, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(42, 42, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-3.1, -3.1, histogram_fraction_2)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(3.1415, NaN, histogram_fraction_2)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(NaN, 42, histogram_fraction_2)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(NaN, NaN, histogram_fraction_2)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(-Inf, +Inf, histogram_fraction_2)
|
|
{} 1
|
|
|
|
# Apply fraction function to histogram with negative and zero buckets.
|
|
load 10m
|
|
histogram_fraction_3 {{schema:0 count:12 sum:100 z_bucket:2 z_bucket_w:0.001 n_buckets:[2 3 0 1 4]}}x1
|
|
|
|
eval instant at 10m histogram_fraction(0, +Inf, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-Inf, 0, histogram_fraction_3)
|
|
{} 1
|
|
|
|
eval instant at 10m histogram_fraction(-0.001, 0, histogram_fraction_3)
|
|
{} 0.16666666666666666
|
|
|
|
eval instant at 10m histogram_fraction(0, 0.001, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-0.0005, 0, histogram_fraction_3)
|
|
{} 0.08333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(0.001, inf, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-inf, -0.001, histogram_fraction_3)
|
|
{} 0.8333333333333334
|
|
|
|
eval instant at 10m histogram_fraction(1, 2, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(1.5, 2, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(1, 8, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(1, 6, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(1.5, 6, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-2, -1, histogram_fraction_3)
|
|
{} 0.25
|
|
|
|
eval instant at 10m histogram_fraction(-2, -1.5, histogram_fraction_3)
|
|
{} 0.125
|
|
|
|
eval instant at 10m histogram_fraction(-8, -1, histogram_fraction_3)
|
|
{} 0.3333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(-6, -1, histogram_fraction_3)
|
|
{} 0.2916666666666667
|
|
|
|
eval instant at 10m histogram_fraction(-6, -1.5, histogram_fraction_3)
|
|
{} 0.16666666666666666
|
|
|
|
eval instant at 10m histogram_fraction(42, 3.1415, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(0, 0, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(0.000001, 0.000001, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(42, 42, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-3.1, -3.1, histogram_fraction_3)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(3.1415, NaN, histogram_fraction_3)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(NaN, 42, histogram_fraction_3)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(NaN, NaN, histogram_fraction_3)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(-Inf, +Inf, histogram_fraction_3)
|
|
{} 1
|
|
|
|
clear
|
|
|
|
# Apply fraction function to histogram with both positive, negative and zero buckets.
|
|
load 10m
|
|
histogram_fraction_4 {{schema:0 count:24 sum:100 z_bucket:4 z_bucket_w:0.001 buckets:[2 3 0 1 4] n_buckets:[2 3 0 1 4]}}x1
|
|
|
|
eval instant at 10m histogram_fraction(0, +Inf, histogram_fraction_4)
|
|
{} 0.5
|
|
|
|
eval instant at 10m histogram_fraction(-Inf, 0, histogram_fraction_4)
|
|
{} 0.5
|
|
|
|
eval instant at 10m histogram_fraction(-0.001, 0, histogram_fraction_4)
|
|
{} 0.08333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(0, 0.001, histogram_fraction_4)
|
|
{} 0.08333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(-0.0005, 0.0005, histogram_fraction_4)
|
|
{} 0.08333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(0.001, inf, histogram_fraction_4)
|
|
{} 0.4166666666666667
|
|
|
|
eval instant at 10m histogram_fraction(-inf, -0.001, histogram_fraction_4)
|
|
{} 0.4166666666666667
|
|
|
|
eval instant at 10m histogram_fraction(1, 2, histogram_fraction_4)
|
|
{} 0.125
|
|
|
|
eval instant at 10m histogram_fraction(1.5, 2, histogram_fraction_4)
|
|
{} 0.0625
|
|
|
|
eval instant at 10m histogram_fraction(1, 8, histogram_fraction_4)
|
|
{} 0.16666666666666666
|
|
|
|
eval instant at 10m histogram_fraction(1, 6, histogram_fraction_4)
|
|
{} 0.14583333333333334
|
|
|
|
eval instant at 10m histogram_fraction(1.5, 6, histogram_fraction_4)
|
|
{} 0.08333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(-2, -1, histogram_fraction_4)
|
|
{} 0.125
|
|
|
|
eval instant at 10m histogram_fraction(-2, -1.5, histogram_fraction_4)
|
|
{} 0.0625
|
|
|
|
eval instant at 10m histogram_fraction(-8, -1, histogram_fraction_4)
|
|
{} 0.16666666666666666
|
|
|
|
eval instant at 10m histogram_fraction(-6, -1, histogram_fraction_4)
|
|
{} 0.14583333333333334
|
|
|
|
eval instant at 10m histogram_fraction(-6, -1.5, histogram_fraction_4)
|
|
{} 0.08333333333333333
|
|
|
|
eval instant at 10m histogram_fraction(42, 3.1415, histogram_fraction_4)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(0, 0, histogram_fraction_4)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(0.000001, 0.000001, histogram_fraction_4)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(42, 42, histogram_fraction_4)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(-3.1, -3.1, histogram_fraction_4)
|
|
{} 0
|
|
|
|
eval instant at 10m histogram_fraction(3.1415, NaN, histogram_fraction_4)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(NaN, 42, histogram_fraction_4)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(NaN, NaN, histogram_fraction_4)
|
|
{} NaN
|
|
|
|
eval instant at 10m histogram_fraction(-Inf, +Inf, histogram_fraction_4)
|
|
{} 1
|
|
|
|
eval instant at 10m histogram_sum(scalar(histogram_fraction(-Inf, +Inf, sum(histogram_fraction_4))) * histogram_fraction_4)
|
|
{} 100
|
|
|
|
# Apply multiplication and division operator to histogram.
|
|
load 10m
|
|
histogram_mul_div {{schema:0 count:30 sum:33 z_bucket:3 z_bucket_w:0.001 buckets:[3 3 3] n_buckets:[6 6 6]}}x1
|
|
float_series_3 3+0x1
|
|
float_series_0 0+0x1
|
|
|
|
eval instant at 10m histogram_mul_div*3
|
|
{} {{schema:0 count:90 sum:99 z_bucket:9 z_bucket_w:0.001 buckets:[9 9 9] n_buckets:[18 18 18]}}
|
|
|
|
eval instant at 10m histogram_mul_div*-1
|
|
{} {{schema:0 count:-30 sum:-33 z_bucket:-3 z_bucket_w:0.001 buckets:[-3 -3 -3] n_buckets:[-6 -6 -6]}}
|
|
|
|
eval instant at 10m -histogram_mul_div
|
|
{} {{schema:0 count:-30 sum:-33 z_bucket:-3 z_bucket_w:0.001 buckets:[-3 -3 -3] n_buckets:[-6 -6 -6]}}
|
|
|
|
eval instant at 10m histogram_mul_div*-3
|
|
{} {{schema:0 count:-90 sum:-99 z_bucket:-9 z_bucket_w:0.001 buckets:[-9 -9 -9] n_buckets:[-18 -18 -18]}}
|
|
|
|
eval instant at 10m 3*histogram_mul_div
|
|
{} {{schema:0 count:90 sum:99 z_bucket:9 z_bucket_w:0.001 buckets:[9 9 9] n_buckets:[18 18 18]}}
|
|
|
|
eval instant at 10m histogram_mul_div*float_series_3
|
|
{} {{schema:0 count:90 sum:99 z_bucket:9 z_bucket_w:0.001 buckets:[9 9 9] n_buckets:[18 18 18]}}
|
|
|
|
eval instant at 10m float_series_3*histogram_mul_div
|
|
{} {{schema:0 count:90 sum:99 z_bucket:9 z_bucket_w:0.001 buckets:[9 9 9] n_buckets:[18 18 18]}}
|
|
|
|
eval instant at 10m histogram_mul_div/3
|
|
{} {{schema:0 count:10 sum:11 z_bucket:1 z_bucket_w:0.001 buckets:[1 1 1] n_buckets:[2 2 2]}}
|
|
|
|
eval instant at 10m histogram_mul_div/-3
|
|
{} {{schema:0 count:-10 sum:-11 z_bucket:-1 z_bucket_w:0.001 buckets:[-1 -1 -1] n_buckets:[-2 -2 -2]}}
|
|
|
|
eval instant at 10m histogram_mul_div/float_series_3
|
|
{} {{schema:0 count:10 sum:11 z_bucket:1 z_bucket_w:0.001 buckets:[1 1 1] n_buckets:[2 2 2]}}
|
|
|
|
eval instant at 10m histogram_mul_div*0
|
|
{} {{schema:0 count:0 sum:0 z_bucket:0 z_bucket_w:0.001 buckets:[0 0 0] n_buckets:[0 0 0]}}
|
|
|
|
eval instant at 10m 0*histogram_mul_div
|
|
{} {{schema:0 count:0 sum:0 z_bucket:0 z_bucket_w:0.001 buckets:[0 0 0] n_buckets:[0 0 0]}}
|
|
|
|
eval instant at 10m histogram_mul_div*float_series_0
|
|
{} {{schema:0 count:0 sum:0 z_bucket:0 z_bucket_w:0.001 buckets:[0 0 0] n_buckets:[0 0 0]}}
|
|
|
|
eval instant at 10m float_series_0*histogram_mul_div
|
|
{} {{schema:0 count:0 sum:0 z_bucket:0 z_bucket_w:0.001 buckets:[0 0 0] n_buckets:[0 0 0]}}
|
|
|
|
# TODO: (NeerajGartia21) remove all the histogram buckets in case of division with zero. See: https://github.com/prometheus/prometheus/issues/13934
|
|
eval instant at 10m histogram_mul_div/0
|
|
{} {{schema:0 count:Inf sum:Inf z_bucket:Inf z_bucket_w:0.001 buckets:[Inf Inf Inf] n_buckets:[Inf Inf Inf]}}
|
|
|
|
eval instant at 10m histogram_mul_div/float_series_0
|
|
{} {{schema:0 count:Inf sum:Inf z_bucket:Inf z_bucket_w:0.001 buckets:[Inf Inf Inf] n_buckets:[Inf Inf Inf]}}
|
|
|
|
eval instant at 10m histogram_mul_div*0/0
|
|
{} {{schema:0 count:NaN sum:NaN z_bucket:NaN z_bucket_w:0.001 buckets:[NaN NaN NaN] n_buckets:[NaN NaN NaN]}}
|
|
|
|
clear
|
|
|
|
# Counter reset only noticeable in a single bucket.
|
|
load 5m
|
|
reset_in_bucket {{schema:0 count:4 sum:5 buckets:[1 2 1]}} {{schema:0 count:5 sum:6 buckets:[1 1 3]}} {{schema:0 count:6 sum:7 buckets:[1 2 3]}}
|
|
|
|
eval instant at 10m increase(reset_in_bucket[15m])
|
|
{} {{count:9 sum:10.5 buckets:[1.5 3 4.5]}}
|
|
|
|
# The following two test the "fast path" where only sum and count is decoded.
|
|
eval instant at 10m histogram_count(increase(reset_in_bucket[15m]))
|
|
{} 9
|
|
|
|
eval instant at 10m histogram_sum(increase(reset_in_bucket[15m]))
|
|
{} 10.5
|
|
|
|
clear
|
|
|
|
# Test native histograms with custom buckets.
|
|
load 5m
|
|
custom_buckets_histogram {{schema:-53 sum:5 count:4 custom_values:[5 10] buckets:[1 2 1]}}x10
|
|
|
|
eval instant at 5m histogram_fraction(5, 10, custom_buckets_histogram)
|
|
{} 0.5
|
|
|
|
eval instant at 5m histogram_quantile(0.5, custom_buckets_histogram)
|
|
{} 7.5
|
|
|
|
eval instant at 5m sum(custom_buckets_histogram)
|
|
{} {{schema:-53 sum:5 count:4 custom_values:[5 10] buckets:[1 2 1]}}
|
|
|
|
clear
|
|
|
|
# Test 'this native histogram metric is not a gauge' warning for rate
|
|
load 30s
|
|
some_metric {{schema:0 sum:1 count:1 buckets:[1] counter_reset_hint:gauge}} {{schema:0 sum:2 count:2 buckets:[2] counter_reset_hint:gauge}} {{schema:0 sum:3 count:3 buckets:[3] counter_reset_hint:gauge}}
|
|
|
|
# Test the case where we only have two points for rate
|
|
eval_warn instant at 30s rate(some_metric[1m])
|
|
{} {{count:0.03333333333333333 sum:0.03333333333333333 buckets:[0.03333333333333333]}}
|
|
|
|
# Test the case where we have more than two points for rate
|
|
eval_warn instant at 1m rate(some_metric[1m])
|
|
{} {{count:0.03333333333333333 sum:0.03333333333333333 buckets:[0.03333333333333333]}}
|
|
|
|
clear
|
|
|
|
# Test rate() over mixed exponential and custom buckets.
|
|
load 30s
|
|
some_metric {{schema:0 sum:1 count:1 buckets:[1]}} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}} {{schema:0 sum:5 count:4 buckets:[1 2 1]}} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}}
|
|
|
|
# Start and end with exponential, with custom in the middle.
|
|
eval_warn instant at 1m rate(some_metric[1m])
|
|
# Should produce no results.
|
|
|
|
# Start and end with custom, with exponential in the middle.
|
|
eval_warn instant at 1m30s rate(some_metric[1m])
|
|
# Should produce no results.
|
|
|
|
# Start with custom, end with exponential.
|
|
eval_warn instant at 1m rate(some_metric[1m])
|
|
# Should produce no results.
|
|
|
|
# Start with exponential, end with custom.
|
|
eval_warn instant at 30s rate(some_metric[1m])
|
|
# Should produce no results.
|
|
|
|
clear
|
|
|
|
# Histogram with constant buckets.
|
|
load 1m
|
|
const_histogram {{schema:0 sum:1 count:1 buckets:[1 1 1]}} {{schema:0 sum:1 count:1 buckets:[1 1 1]}} {{schema:0 sum:1 count:1 buckets:[1 1 1]}} {{schema:0 sum:1 count:1 buckets:[1 1 1]}} {{schema:0 sum:1 count:1 buckets:[1 1 1]}}
|
|
|
|
# There is no change to the bucket count over time, thus rate is 0 in each bucket.
|
|
# However native histograms do not represent empty buckets, so here the zeros are implicit.
|
|
eval instant at 5m rate(const_histogram[5m])
|
|
{} {{schema:0 sum:0 count:0}}
|
|
|
|
# Zero buckets mean no observations, thus the denominator in the average is 0
|
|
# leading to 0/0, which is NaN.
|
|
eval instant at 5m histogram_avg(rate(const_histogram[5m]))
|
|
{} NaN
|
|
|
|
# Zero buckets mean no observations, so count is 0.
|
|
eval instant at 5m histogram_count(rate(const_histogram[5m]))
|
|
{} 0.0
|
|
|
|
# Zero buckets mean no observations and empty histogram has a sum of 0 by definition.
|
|
eval instant at 5m histogram_sum(rate(const_histogram[5m]))
|
|
{} 0.0
|
|
|
|
# Zero buckets mean no observations, thus the denominator in the fraction is 0,
|
|
# leading to 0/0, which is NaN.
|
|
eval instant at 5m histogram_fraction(0.0, 1.0, rate(const_histogram[5m]))
|
|
{} NaN
|
|
|
|
# Workaround to calculate the observation count corresponding to NaN fraction.
|
|
eval instant at 5m histogram_count(rate(const_histogram[5m])) == 0.0 or histogram_fraction(0.0, 1.0, rate(const_histogram[5m])) * histogram_count(rate(const_histogram[5m]))
|
|
{} 0.0
|
|
|
|
# Zero buckets mean no observations, so there is no value that observations fall below,
|
|
# which means that any quantile is a NaN.
|
|
eval instant at 5m histogram_quantile(1.0, rate(const_histogram[5m]))
|
|
{} NaN
|
|
|
|
# Zero buckets mean no observations, so there is no standard deviation.
|
|
eval instant at 5m histogram_stddev(rate(const_histogram[5m]))
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{} NaN
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# Zero buckets mean no observations, so there is no standard variance.
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eval instant at 5m histogram_stdvar(rate(const_histogram[5m]))
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{} NaN
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clear
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# Test mixing exponential and custom buckets.
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load 6m
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metric{series="exponential"} {{sum:4 count:3 buckets:[1 2 1]}} _ {{sum:4 count:3 buckets:[1 2 1]}}
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metric{series="other-exponential"} {{sum:3 count:2 buckets:[1 1 1]}} _ {{sum:3 count:2 buckets:[1 1 1]}}
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metric{series="custom"} _ {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}}
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metric{series="other-custom"} _ {{schema:-53 sum:15 count:2 custom_values:[5 10] buckets:[0 2]}} {{schema:-53 sum:15 count:2 custom_values:[5 10] buckets:[0 2]}}
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# T=0: only exponential
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# T=6: only custom
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# T=12: mixed, should be ignored and emit a warning
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eval_warn range from 0 to 12m step 6m sum(metric)
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{} {{sum:7 count:5 buckets:[2 3 2]}} {{schema:-53 sum:16 count:3 custom_values:[5 10] buckets:[1 2]}} _
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eval_warn range from 0 to 12m step 6m avg(metric)
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{} {{sum:3.5 count:2.5 buckets:[1 1.5 1]}} {{schema:-53 sum:8 count:1.5 custom_values:[5 10] buckets:[0.5 1]}} _
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clear
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# Test incompatible custom bucket schemas.
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load 6m
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metric{series="1"} _ {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}}
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metric{series="2"} {{schema:-53 sum:1 count:1 custom_values:[2] buckets:[1]}} _ {{schema:-53 sum:1 count:1 custom_values:[2] buckets:[1]}}
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metric{series="3"} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}}
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# T=0: incompatible, should be ignored and emit a warning
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# T=6: compatible
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# T=12: incompatible followed by compatible, should be ignored and emit a warning
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eval_warn range from 0 to 12m step 6m sum(metric)
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{} _ {{schema:-53 sum:2 count:2 custom_values:[5 10] buckets:[2]}} _
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eval_warn range from 0 to 12m step 6m avg(metric)
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{} _ {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}} _
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clear
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load 1m
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metric{group="just-floats", series="1"} 2
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metric{group="just-floats", series="2"} 3
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metric{group="just-exponential-histograms", series="1"} {{sum:3 count:4 buckets:[1 2 1]}}
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metric{group="just-exponential-histograms", series="2"} {{sum:2 count:3 buckets:[1 1 1]}}
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metric{group="just-custom-histograms", series="1"} {{schema:-53 sum:1 count:1 custom_values:[2] buckets:[1]}}
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metric{group="just-custom-histograms", series="2"} {{schema:-53 sum:3 count:4 custom_values:[2] buckets:[7]}}
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metric{group="floats-and-histograms", series="1"} 2
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metric{group="floats-and-histograms", series="2"} {{sum:2 count:3 buckets:[1 1 1]}}
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metric{group="exponential-and-custom-histograms", series="1"} {{sum:2 count:3 buckets:[1 1 1]}}
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metric{group="exponential-and-custom-histograms", series="2"} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}}
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metric{group="incompatible-custom-histograms", series="1"} {{schema:-53 sum:1 count:1 custom_values:[5 10] buckets:[1]}}
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metric{group="incompatible-custom-histograms", series="2"} {{schema:-53 sum:1 count:1 custom_values:[2] buckets:[1]}}
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eval_warn instant at 0 sum by (group) (metric)
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{group="just-floats"} 5
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{group="just-exponential-histograms"} {{sum:5 count:7 buckets:[2 3 2]}}
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{group="just-custom-histograms"} {{schema:-53 sum:4 count:5 custom_values:[2] buckets:[8]}}
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clear
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# Test native histograms with sum, count, avg.
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load 10m
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histogram_sum{idx="0"} {{schema:0 count:25 sum:1234.5 z_bucket:4 z_bucket_w:0.001 buckets:[1 2 0 1 1] n_buckets:[2 4 0 0 1 9]}}x1
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histogram_sum{idx="1"} {{schema:0 count:41 sum:2345.6 z_bucket:5 z_bucket_w:0.001 buckets:[1 3 1 2 1 1 1] n_buckets:[0 1 4 2 7 0 0 0 0 5 5 2]}}x1
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histogram_sum{idx="2"} {{schema:0 count:41 sum:1111.1 z_bucket:5 z_bucket_w:0.001 buckets:[1 3 1 2 1 1 1] n_buckets:[0 1 4 2 7 0 0 0 0 5 5 2]}}x1
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histogram_sum{idx="3"} {{schema:1 count:0}}x1
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histogram_sum_float{idx="0"} 42.0x1
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eval instant at 10m sum(histogram_sum)
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{} {{schema:0 count:107 sum:4691.2 z_bucket:14 z_bucket_w:0.001 buckets:[3 8 2 5 3 2 2] n_buckets:[2 6 8 4 15 9 0 0 0 10 10 4]}}
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eval_warn instant at 10m sum({idx="0"})
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eval instant at 10m sum(histogram_sum{idx="0"} + ignoring(idx) histogram_sum{idx="1"} + ignoring(idx) histogram_sum{idx="2"} + ignoring(idx) histogram_sum{idx="3"})
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{} {{schema:0 count:107 sum:4691.2 z_bucket:14 z_bucket_w:0.001 buckets:[3 8 2 5 3 2 2] n_buckets:[2 6 8 4 15 9 0 0 0 10 10 4]}}
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eval instant at 10m count(histogram_sum)
|
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{} 4
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eval instant at 10m avg(histogram_sum)
|
|
{} {{schema:0 count:26.75 sum:1172.8 z_bucket:3.5 z_bucket_w:0.001 buckets:[0.75 2 0.5 1.25 0.75 0.5 0.5] n_buckets:[0.5 1.5 2 1 3.75 2.25 0 0 0 2.5 2.5 1]}}
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clear
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# Test native histograms with sum_over_time, avg_over_time.
|
|
load 1m
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|
histogram_sum_over_time {{schema:0 count:25 sum:1234.5 z_bucket:4 z_bucket_w:0.001 buckets:[1 2 0 1 1] n_buckets:[2 4 0 0 1 9]}} {{schema:0 count:41 sum:2345.6 z_bucket:5 z_bucket_w:0.001 buckets:[1 3 1 2 1 1 1] n_buckets:[0 1 4 2 7 0 0 0 0 5 5 2]}} {{schema:0 count:41 sum:1111.1 z_bucket:5 z_bucket_w:0.001 buckets:[1 3 1 2 1 1 1] n_buckets:[0 1 4 2 7 0 0 0 0 5 5 2]}} {{schema:1 count:0}}
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eval instant at 3m sum_over_time(histogram_sum_over_time[4m:1m])
|
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{} {{schema:0 count:107 sum:4691.2 z_bucket:14 z_bucket_w:0.001 buckets:[3 8 2 5 3 2 2] n_buckets:[2 6 8 4 15 9 0 0 0 10 10 4]}}
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eval instant at 3m avg_over_time(histogram_sum_over_time[4m:1m])
|
|
{} {{schema:0 count:26.75 sum:1172.8 z_bucket:3.5 z_bucket_w:0.001 buckets:[0.75 2 0.5 1.25 0.75 0.5 0.5] n_buckets:[0.5 1.5 2 1 3.75 2.25 0 0 0 2.5 2.5 1]}}
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