22### SUBSTRAIT_INCLUDE: '/extensions/functions_arithmetic.yaml'
33
44# basic: Basic examples without any special cases
5- ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp32, SAMPLE::enum) = 2.5::fp32
6- ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp64, SAMPLE::enum) = 2.5::fp64
7- ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp32, POPULATION::enum) = 2.0::fp32
8- ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp64, POPULATION::enum) = 2.0::fp64
5+ ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp32, SAMPLE::enum) = 2.5::fp32?
6+ ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp64, SAMPLE::enum) = 2.5::fp64?
7+ ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp32, POPULATION::enum) = 2.0::fp32?
8+ ((1.0, 2.0, 3.0, 4.0, 5.0)) variance(col0::fp64, POPULATION::enum) = 2.0::fp64?
99
1010# uniform_values: Variance of uniform values
11- ((5.0, 5.0, 5.0, 5.0)) variance(col0::fp32, SAMPLE::enum) = 0.0::fp32
12- ((5.0, 5.0, 5.0, 5.0)) variance(col0::fp64, POPULATION::enum) = 0.0::fp64
11+ ((5.0, 5.0, 5.0, 5.0)) variance(col0::fp32, SAMPLE::enum) = 0.0::fp32?
12+ ((5.0, 5.0, 5.0, 5.0)) variance(col0::fp64, POPULATION::enum) = 0.0::fp64?
1313
1414# single_value: Variance with single value
15- ((42.0)) variance(col0::fp32, SAMPLE::enum) = Null::fp32
16- ((42.0)) variance(col0::fp64, POPULATION::enum) = 0.0::fp64
15+ ((42.0)) variance(col0::fp32, SAMPLE::enum) = Null::fp32?
16+ ((42.0)) variance(col0::fp64, POPULATION::enum) = 0.0::fp64?
1717
1818# negative_values: Variance with negative values
19- ((-5.0, -3.0, -1.0, 1.0, 3.0, 5.0)) variance(col0::fp32, SAMPLE::enum) = 15.166667::fp32
20- ((-5.0, -3.0, -1.0, 1.0, 3.0, 5.0)) variance(col0::fp64, SAMPLE::enum) = 15.166666666666666::fp64
21- ((-10.0, -5.0, 0.0, 5.0, 10.0)) variance(col0::fp32, POPULATION::enum) = 50.0::fp32
22- ((-10.0, -5.0, 0.0, 5.0, 10.0)) variance(col0::fp64, POPULATION::enum) = 50.0::fp64
19+ ((-5.0, -3.0, -1.0, 1.0, 3.0, 5.0)) variance(col0::fp32, SAMPLE::enum) = 15.166667::fp32?
20+ ((-5.0, -3.0, -1.0, 1.0, 3.0, 5.0)) variance(col0::fp64, SAMPLE::enum) = 15.166666666666666::fp64?
21+ ((-10.0, -5.0, 0.0, 5.0, 10.0)) variance(col0::fp32, POPULATION::enum) = 50.0::fp32?
22+ ((-10.0, -5.0, 0.0, 5.0, 10.0)) variance(col0::fp64, POPULATION::enum) = 50.0::fp64?
2323
2424# decimal_precision: Variance with decimal values
25- ((1.5, 2.5, 3.5, 4.5, 5.5)) variance(col0::fp32, SAMPLE::enum) = 2.5::fp32
26- ((1.5, 2.5, 3.5, 4.5, 5.5)) variance(col0::fp64, SAMPLE::enum) = 2.5::fp64
27- ((0.1, 0.2, 0.3, 0.4, 0.5)) variance(col0::fp64, POPULATION::enum) = 0.020000000000000004::fp64
25+ ((1.5, 2.5, 3.5, 4.5, 5.5)) variance(col0::fp32, SAMPLE::enum) = 2.5::fp32?
26+ ((1.5, 2.5, 3.5, 4.5, 5.5)) variance(col0::fp64, SAMPLE::enum) = 2.5::fp64?
27+ ((0.1, 0.2, 0.3, 0.4, 0.5)) variance(col0::fp64, POPULATION::enum) = 0.020000000000000004::fp64?
2828
2929# large_values: Variance with large values
30- ((1000.0, 2000.0, 3000.0, 4000.0, 5000.0)) variance(col0::fp32, SAMPLE::enum) = 2500000.0::fp32
31- ((1000.0, 2000.0, 3000.0, 4000.0, 5000.0)) variance(col0::fp64, SAMPLE::enum) = 2500000.0::fp64
30+ ((1000.0, 2000.0, 3000.0, 4000.0, 5000.0)) variance(col0::fp32, SAMPLE::enum) = 2500000.0::fp32?
31+ ((1000.0, 2000.0, 3000.0, 4000.0, 5000.0)) variance(col0::fp64, SAMPLE::enum) = 2500000.0::fp64?
3232
3333# small_values: Variance with small values
34- ((0.001, 0.002, 0.003, 0.004, 0.005)) variance(col0::fp64, SAMPLE::enum) = 0.0000025::fp64
35- ((0.001, 0.002, 0.003, 0.004, 0.005)) variance(col0::fp64, POPULATION::enum) = 0.000002::fp64
34+ ((0.001, 0.002, 0.003, 0.004, 0.005)) variance(col0::fp64, SAMPLE::enum) = 0.0000025::fp64?
35+ ((0.001, 0.002, 0.003, 0.004, 0.005)) variance(col0::fp64, POPULATION::enum) = 0.000002::fp64?
3636
3737# null_handling: Examples with null as input or output
38- ((Null, Null, Null)) variance(col0::fp32, SAMPLE::enum) = Null::fp32
39- (()) variance(col0::fp32, SAMPLE::enum) = Null::fp32
40- ((1.0, Null, 3.0, Null, 5.0)) variance(col0::fp32, SAMPLE::enum) = 4.0::fp32
41- ((1.0, Null, 3.0, Null, 5.0)) variance(col0::fp64, POPULATION::enum) = 2.666666666666667::fp64
38+ ((Null, Null, Null)) variance(col0::fp32? , SAMPLE::enum) = Null::fp32?
39+ (()) variance(col0::fp32, SAMPLE::enum) = Null::fp32?
40+ ((1.0, Null, 3.0, Null, 5.0)) variance(col0::fp32? , SAMPLE::enum) = 4.0::fp32?
41+ ((1.0, Null, 3.0, Null, 5.0)) variance(col0::fp64? , POPULATION::enum) = 2.666666666666667::fp64?
4242
4343# rounding: Examples with different rounding modes
44- ((1.1, 2.2, 3.3, 4.4, 5.5)) variance(col0::fp32, SAMPLE::enum) [rounding:TIE_TO_EVEN] = 3.03::fp32
45- ((1.1, 2.2, 3.3, 4.4, 5.5)) variance(col0::fp64, SAMPLE::enum) [rounding:TRUNCATE] = 3.0299999999999994::fp64
44+ ((1.1, 2.2, 3.3, 4.4, 5.5)) variance(col0::fp32, SAMPLE::enum) [rounding:TIE_TO_EVEN] = 3.03::fp32?
45+ ((1.1, 2.2, 3.3, 4.4, 5.5)) variance(col0::fp64, SAMPLE::enum) [rounding:TRUNCATE] = 3.0299999999999994::fp64?
4646
4747# two_values: Variance with two values
48- ((10.0, 20.0)) variance(col0::fp32, SAMPLE::enum) = 50.0::fp32
49- ((10.0, 20.0)) variance(col0::fp64, POPULATION::enum) = 25.0::fp64
48+ ((10.0, 20.0)) variance(col0::fp32, SAMPLE::enum) = 50.0::fp32?
49+ ((10.0, 20.0)) variance(col0::fp64, POPULATION::enum) = 25.0::fp64?
5050
5151# mixed_range: Variance with mixed range values
52- ((0.0, 100.0, 50.0, 25.0, 75.0)) variance(col0::fp32, SAMPLE::enum) = 1681.25::fp32
53- ((0.0, 100.0, 50.0, 25.0, 75.0)) variance(col0::fp64, POPULATION::enum) = 1345.0::fp64
52+ ((0.0, 100.0, 50.0, 25.0, 75.0)) variance(col0::fp32, SAMPLE::enum) = 1681.25::fp32?
53+ ((0.0, 100.0, 50.0, 25.0, 75.0)) variance(col0::fp64, POPULATION::enum) = 1345.0::fp64?
5454
5555# zero_mean: Variance with values around zero
56- ((-2.0, -1.0, 0.0, 1.0, 2.0)) variance(col0::fp32, SAMPLE::enum) = 2.5::fp32
57- ((-2.0, -1.0, 0.0, 1.0, 2.0)) variance(col0::fp64, POPULATION::enum) = 2.0::fp64
56+ ((-2.0, -1.0, 0.0, 1.0, 2.0)) variance(col0::fp32, SAMPLE::enum) = 2.5::fp32?
57+ ((-2.0, -1.0, 0.0, 1.0, 2.0)) variance(col0::fp64, POPULATION::enum) = 2.0::fp64?
5858
5959# three_values: Variance with three values
60- ((10.0, 20.0, 30.0)) variance(col0::fp32, SAMPLE::enum) = 100.0::fp32
61- ((10.0, 20.0, 30.0)) variance(col0::fp64, POPULATION::enum) = 66.66666666666667::fp64
60+ ((10.0, 20.0, 30.0)) variance(col0::fp32, SAMPLE::enum) = 100.0::fp32?
61+ ((10.0, 20.0, 30.0)) variance(col0::fp64, POPULATION::enum) = 66.66666666666667::fp64?
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