Metrics for Statistics.Distribution.CauchyLorentz:$cdensity from math-functions-0.1.5.2

analyze67.0ms (1.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
25%	25%	74.9%	0.1%	0%	0%	0%	4
37.5%	37.4%	62.4%	0.1%	0%	0%	0%	5
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	6
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	7
65.6%	65.5%	34.3%	0.1%	0%	0%	0%	8
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	9
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	10
82%	81.9%	17.9%	0.1%	0%	0%	0%	11
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

Operation ival-div, time spent: 14.0ms, 43.0% of total-time

Operation ival-mult, time spent: 12.0ms, 37.0% of total-time

Operation ival-add, time spent: 6.0ms, 18.0% of total-time

Operation const, time spent: 1.0ms, 3.0% of total-time

sample1.5s (24.1%)

Results

1.2s	7669×	valid
114.0ms	586×	infinite
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 474.0ms

Operation ival-mult, time spent: 153.0ms, 32.0% of total-time

Operation ival-add, time spent: 149.0ms, 31.0% of total-time

Operation ival-div, time spent: 147.0ms, 31.0% of total-time

Operation const, time spent: 25.0ms, 5.0% of total-time

Bogosity

preprocess1.1s (17.7%)

Algorithm

1×	egg-herbie

Rules

1572×	`fma-def`
1556×	`div-sub`
984×	`unsub-neg`
978×	`sub-neg`
776×	`associate-/l*`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))`
-	-	`(*.f64 z z)`
-	-	`y`
-	-	`z`
-	-	`(/.f64 1 x)`
-	-	`(+.f64 1 (*.f64 z z))`
-	-	`(.f64 y (+.f64 1 (.f64 z z)))`
-	-	`1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	485
1	137	429
2	364	429
3	1104	429
4	2843	429
5	5552	429
6	7966	429

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 (/.f64 1 (neg.f64 x)) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 (/.f64 1 x) (.f64 (neg.f64 y) (+.f64 1 (.f64 z z))))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 (neg.f64 z) (neg.f64 z)))))
(neg.f64 (/.f64 (/.f64 1 (neg.f64 x)) (.f64 y (+.f64 1 (.f64 z z)))))
(neg.f64 (/.f64 (/.f64 1 x) (.f64 (neg.f64 y) (+.f64 1 (.f64 z z)))))
(neg.f64 (/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 (neg.f64 z) (neg.f64 z))))))
(/.f64 (/.f64 1 y) (.f64 x (+.f64 1 (.f64 z z))))
(/.f64 (/.f64 1 z) (.f64 y (+.f64 1 (.f64 x x))))
(/.f64 (/.f64 1 x) (.f64 z (+.f64 1 (.f64 y y))))

Outputs
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))
(/.f64 (/.f64 1 (neg.f64 x)) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 (/.f64 (/.f64 1 (neg.f64 x)) y) (+.f64 1 (*.f64 z z)))
(/.f64 -1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 (/.f64 -1 x) (*.f64 y (fma.f64 z z 1)))
(/.f64 (/.f64 1 x) (.f64 (neg.f64 y) (+.f64 1 (.f64 z z))))
(/.f64 (/.f64 (/.f64 1 (neg.f64 x)) y) (+.f64 1 (*.f64 z z)))
(/.f64 -1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 (/.f64 -1 x) (*.f64 y (fma.f64 z z 1)))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 (neg.f64 z) (neg.f64 z)))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))
(neg.f64 (/.f64 (/.f64 1 (neg.f64 x)) (.f64 y (+.f64 1 (.f64 z z)))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))
(neg.f64 (/.f64 (/.f64 1 x) (.f64 (neg.f64 y) (+.f64 1 (.f64 z z)))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))
(neg.f64 (/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 (neg.f64 z) (neg.f64 z))))))
(/.f64 (/.f64 (/.f64 1 (neg.f64 x)) y) (+.f64 1 (*.f64 z z)))
(/.f64 -1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 (/.f64 -1 x) (*.f64 y (fma.f64 z z 1)))
(/.f64 (/.f64 1 y) (.f64 x (+.f64 1 (.f64 z z))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))
(/.f64 (/.f64 1 z) (.f64 y (+.f64 1 (.f64 x x))))
(/.f64 1 (.f64 y (.f64 (fma.f64 x x 1) z)))
(/.f64 1 (.f64 z (.f64 y (fma.f64 x x 1))))
(/.f64 1 (.f64 y (.f64 z (fma.f64 x x 1))))
(/.f64 (/.f64 1 x) (.f64 z (+.f64 1 (.f64 y y))))
(/.f64 1 (.f64 (fma.f64 y y 1) (.f64 z x)))
(/.f64 (/.f64 1 x) (*.f64 z (fma.f64 y y 1)))

Symmetry

(abs z)

(negabs x)

(negabs y)

(sort x y)

Compiler

Compiled 88 to 48 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 661.0ms

Operation ival-add, time spent: 475.0ms, 72.0% of total-time

Operation ival-mult, time spent: 95.0ms, 14.0% of total-time

Operation ival-div, time spent: 73.0ms, 11.0% of total-time

Operation const, time spent: 17.0ms, 3.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 34 to 22 computations (35.3% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	86.9%	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
▶	86.6%	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
▶	91.1%	(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))

Compiler

Compiled 41 to 29 computations (29.3% saved)

localize3.0s (48%)

Compiler: Compiled 108 to 51 computations (52.8% saved)
Precisions: Click to see histograms. Total time spent on operations: 2.8s
Operation ival-mult, time spent: 2.4s, 86.0% of total-time
Operation ival-add, time spent: 187.0ms, 7.0% of total-time
Operation ival-div, time spent: 99.0ms, 4.0% of total-time
Operation ival-fma, time spent: 74.0ms, 3.0% of total-time
Operation const, time spent: 20.0ms, 1.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	0	0
Total	3	3

Accuracy

91.4%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	86.9%	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
✓	86.6%	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
✓	91.1%	(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))

Compiler

Compiled 76 to 51 computations (32.9% saved)

regimes30.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

Inputs
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))

Outputs
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))

Calls

8 calls:

5.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
4.0ms	(*.f64 z z)
4.0ms	x
4.0ms	(/.f64 1 x)
3.0ms	z

Results

Accuracy	Segments	Branch
91.1%	1	`x`
91.1%	1	`y`
91.1%	1	`z`
91.1%	1	`(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))`
91.1%	1	`(/.f64 1 x)`
91.1%	1	`(.f64 y (+.f64 1 (.f64 z z)))`
91.1%	1	`(+.f64 1 (*.f64 z z))`
91.1%	1	`(*.f64 z z)`

Compiler

Compiled 56 to 41 computations (26.8% saved)

regimes24.0ms (0.4%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

Outputs
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

Calls

8 calls:

4.0ms	x
4.0ms	y
3.0ms	(/.f64 1 x)
3.0ms	z
3.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Results

Accuracy	Segments	Branch
86.9%	1	`y`
86.9%	1	`z`
86.9%	1	`(+.f64 1 (*.f64 z z))`
86.9%	1	`(*.f64 z z)`
86.9%	1	`x`
86.9%	1	`(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))`
86.9%	1	`(/.f64 1 x)`
86.9%	1	`(.f64 y (+.f64 1 (.f64 z z)))`

Compiler

Compiled 56 to 41 computations (26.8% saved)

regimes16.0ms (0.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))

Outputs
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))

Calls

6 calls:

3.0ms	z
3.0ms	y
3.0ms	(.f64 y (+.f64 1 (.f64 z z)))
3.0ms	x
2.0ms	(*.f64 z z)

Results

Accuracy	Segments	Branch
86.6%	1	`x`
86.6%	1	`y`
86.6%	1	`z`
86.6%	1	`(.f64 y (+.f64 1 (.f64 z z)))`
86.6%	1	`(+.f64 1 (*.f64 z z))`
86.6%	1	`(*.f64 z z)`

Compiler

Compiled 36 to 26 computations (27.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative`
3×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	125
1	33	125

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))

Outputs
(/.f64 1 (.f64 y (.f64 x (fma.f64 z z 1))))
(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
(/.f64 1 (.f64 x (.f64 y (+.f64 1 (*.f64 z z)))))

Compiler

Compiled 41 to 29 computations (29.3% saved)

soundness400.0ms (6.4%)

Rules

1572×	`fma-def`
1572×	`fma-def`
1556×	`div-sub`
1556×	`div-sub`
984×	`unsub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	485
1	137	429
2	364	429
3	1104	429
4	2843	429
5	5552	429
6	7966	429
0	42	485
1	137	429
2	364	429
3	1104	429
4	2843	429
5	5552	429
6	7966	429

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 208 to 124 computations (40.4% saved)

end0.0ms (0%)

preprocess96.0ms (1.5%)

Remove

(negabs y)

(abs z)

Compiler

Compiled 834 to 564 computations (32.4% saved)

analyze67.0ms (1.1%)

sample1.5s (24.1%)

preprocess1.1s (17.7%)

eval1.0ms (0%)

prune2.0ms (0%)

localize3.0s (48%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes30.0ms (0.5%)

regimes24.0ms (0.4%)

regimes16.0ms (0.3%)

simplify3.0ms (0.1%)

soundness400.0ms (6.4%)

end0.0ms (0%)

preprocess96.0ms (1.5%)

Profiling