Metrics for Numeric.Integration.TanhSinh:simpson from integration-0.2.1

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample1.0s (71.9%)

Results

840.0ms	7242×	body	256	valid
162.0ms	1014×	body	256	infinite

Bogosity

preprocess15.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

10×	`*-commutative`
8×	`count-2`
6×	`associate-r`
4×	`fma-def`
4×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	17	26
2	27	26
3	28	26
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

Inputs
(*.f64 x (+.f64 y y))
(*.f64 y (+.f64 x x))

Outputs
(*.f64 x (+.f64 y y))
(*.f64 y (+.f64 x x))
(*.f64 x (+.f64 y y))

Symmetry

(sort x y)

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify24.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative`
8×	`count-2`
6×	`associate-r`
4×	`fma-def`
2×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	13	13
2	24	13
3	28	13

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))

Outputs
(*.f64 x (+.f64 y y))

eval0.0ms (0%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Accurracy

99.3%

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 x (+.f64 y y))
▶	99.3%	(*.f64 x (+.f64 y y))

Compiler

Compiled 14 to 8 computations (42.9% saved)

localize42.0ms (3%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.3%	(*.f64 x (+.f64 y y))

Compiler

Compiled 13 to 5 computations (61.5% saved)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(*.f64 x (+.f64 y y))
1.0ms	x	@	inf	(*.f64 x (+.f64 y y))
1.0ms	x	@	0	(*.f64 x (+.f64 y y))
0.0ms	y	@	inf	(*.f64 x (+.f64 y y))
0.0ms	x	@	-inf	(*.f64 x (+.f64 y y))

rewrite96.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1276×	`pow1`
1186×	`add-exp-log`
1184×	`log1p-expm1-u`
1184×	`expm1-log1p-u`
1160×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	131	13
2	1886	13

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(*.f64 x (+.f64 y y))

Outputs
(+.f64 (.f64 x y) (.f64 x y))
(+.f64 (.f64 (.f64 x y) 1) (.f64 (.f64 x y) 1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 y y))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (*.f64 x y)))))
(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (.f64 x y))) (-.f64 (.f64 x y) (.f64 x y)))
(/.f64 (.f64 x (.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(/.f64 (*.f64 x 0) 0)
(/.f64 (.f64 (.f64 2 (pow.f64 y 3)) x) (fma.f64 y y 0))
(/.f64 (*.f64 0 x) 0)
(pow.f64 (*.f64 x (+.f64 y y)) 1)
(pow.f64 (*.f64 (+.f64 y y) (cbrt.f64 x)) 3)
(pow.f64 (*.f64 (+.f64 y y) (pow.f64 x 3)) 1/3)
(pow.f64 (*.f64 (+.f64 y y) (sqrt.f64 x)) 2)
(sqrt.f64 (.f64 (+.f64 y y) (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 y y)))
(cbrt.f64 (*.f64 (+.f64 y y) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 y y))))
(exp.f64 (log.f64 (*.f64 x (+.f64 y y))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 y y))))
(fma.f64 x y (*.f64 x y))
(fma.f64 y x (*.f64 x y))

simplify19.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

112×	`associate-r`
86×	`associate-l`
46×	`fma-def`
36×	`sqr-pow`
34×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	585
1	184	585
2	713	585

Stop Event

1×

unsound

Counts

45 → 23

Calls

Call 1

Inputs
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(.f64 2 (.f64 y x))
(+.f64 (.f64 x y) (.f64 x y))
(+.f64 (.f64 (.f64 x y) 1) (.f64 (.f64 x y) 1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 y y))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (*.f64 x y)))))
(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (.f64 x y))) (-.f64 (.f64 x y) (.f64 x y)))
(/.f64 (.f64 x (.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(/.f64 (*.f64 x 0) 0)
(/.f64 (.f64 (.f64 2 (pow.f64 y 3)) x) (fma.f64 y y 0))
(/.f64 (*.f64 0 x) 0)
(pow.f64 (*.f64 x (+.f64 y y)) 1)
(pow.f64 (*.f64 (+.f64 y y) (cbrt.f64 x)) 3)
(pow.f64 (*.f64 (+.f64 y y) (pow.f64 x 3)) 1/3)
(pow.f64 (*.f64 (+.f64 y y) (sqrt.f64 x)) 2)
(sqrt.f64 (.f64 (+.f64 y y) (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 y y)))
(cbrt.f64 (*.f64 (+.f64 y y) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 y y))))
(exp.f64 (log.f64 (*.f64 x (+.f64 y y))))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 y y))))
(fma.f64 x y (*.f64 x y))
(fma.f64 y x (*.f64 x y))

Outputs
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))
(+.f64 (.f64 x y) (.f64 x y))
(*.f64 x (+.f64 y y))
(+.f64 (.f64 (.f64 x y) 1) (.f64 (.f64 x y) 1))
(*.f64 x (+.f64 y y))
(-.f64 (+.f64 1 (*.f64 x (+.f64 y y))) 1)
(*.f64 x (+.f64 y y))
(/.f64 (+.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (*.f64 x y)))))
(*.f64 x (+.f64 y y))
(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 x y) (.f64 x y))) (-.f64 (.f64 x y) (.f64 x y)))
(*.f64 x (+.f64 y y))
(/.f64 (.f64 x (.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(*.f64 x (+.f64 y y))
(/.f64 (*.f64 x 0) 0)
(*.f64 x (+.f64 y y))
(/.f64 (.f64 (.f64 2 (pow.f64 y 3)) x) (fma.f64 y y 0))
(*.f64 x (+.f64 y y))
(/.f64 (*.f64 0 x) 0)
(*.f64 x (+.f64 y y))
(pow.f64 (*.f64 x (+.f64 y y)) 1)
(*.f64 x (+.f64 y y))
(pow.f64 (*.f64 (+.f64 y y) (cbrt.f64 x)) 3)
(*.f64 x (+.f64 y y))
(pow.f64 (*.f64 (+.f64 y y) (pow.f64 x 3)) 1/3)
(*.f64 x (+.f64 y y))
(pow.f64 (*.f64 (+.f64 y y) (sqrt.f64 x)) 2)
(*.f64 x (+.f64 y y))
(sqrt.f64 (.f64 (+.f64 y y) (.f64 x x)))
(*.f64 x (+.f64 y y))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 y y)))
(*.f64 x (+.f64 y y))
(cbrt.f64 (*.f64 (+.f64 y y) (pow.f64 x 3)))
(*.f64 x (+.f64 y y))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 y y))))
(*.f64 x (+.f64 y y))
(exp.f64 (log.f64 (*.f64 x (+.f64 y y))))
(*.f64 x (+.f64 y y))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 y y))))
(*.f64 x (+.f64 y y))
(fma.f64 x y (*.f64 x y))
(*.f64 x (+.f64 y y))
(fma.f64 y x (*.f64 x y))
(*.f64 x (+.f64 y y))

eval4.0ms (0.3%)

Compiler: Compiled 219 to 86 computations (60.7% saved)

prune5.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	2	24

Accurracy

100.0%

Counts

24 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 x (+.f64 y y))
▶	100.0%	(.f64 2 (.f64 y x))
✓	99.3%	(*.f64 x (+.f64 y y))
▶	100.0%	(.f64 2 (.f64 y x))

Compiler

Compiled 28 to 18 computations (35.7% saved)

localize21.0ms (1.5%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(.f64 2 (.f64 y x))

Compiler

Compiled 14 to 7 computations (50% saved)

series0.0ms (0%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(.f64 2 (.f64 y x))
0.0ms	y	@	inf	(.f64 2 (.f64 y x))
0.0ms	y	@	-inf	(.f64 2 (.f64 y x))
0.0ms	x	@	-inf	(.f64 2 (.f64 y x))
0.0ms	x	@	inf	(.f64 2 (.f64 y x))

rewrite63.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1302×	`pow1`
1192×	`add-exp-log`
1192×	`log1p-expm1-u`
1192×	`expm1-log1p-u`
1166×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	141	13
2	1631	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 2 (.f64 y x))

Outputs
(-.f64 (+.f64 1 (.f64 2 (.f64 y x))) 1)
(pow.f64 (.f64 2 (.f64 y x)) 1)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 y x))) 3)
(pow.f64 (pow.f64 (.f64 2 (.f64 y x)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 y x))) 2)
(sqrt.f64 (.f64 (pow.f64 (.f64 y x) 2) 4))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) y) 2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 y x)) 3))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 y x))))
(exp.f64 (log.f64 (.f64 2 (.f64 y x))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 y x))))

simplify55.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2116×	`log-prod`
850×	`*-commutative`
788×	`distribute-lft-in`
778×	`distribute-rgt-in`
758×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	275
1	90	209
2	336	143
3	2200	143
4	6248	143

Stop Event

1×	node limit

Counts

11 → 14

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (.f64 2 (.f64 y x))) 1)
(pow.f64 (.f64 2 (.f64 y x)) 1)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 y x))) 3)
(pow.f64 (pow.f64 (.f64 2 (.f64 y x)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 y x))) 2)
(sqrt.f64 (.f64 (pow.f64 (.f64 y x) 2) 4))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) y) 2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 y x)) 3))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 y x))))
(exp.f64 (log.f64 (.f64 2 (.f64 y x))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 y x))))

Outputs
(-.f64 (+.f64 1 (.f64 2 (.f64 y x))) 1)
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(pow.f64 (.f64 2 (.f64 y x)) 1)
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 y x))) 3)
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(pow.f64 (pow.f64 (.f64 2 (.f64 y x)) 3) 1/3)
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 y x))) 2)
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(sqrt.f64 (.f64 (pow.f64 (.f64 y x) 2) 4))
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) y) 2))
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 y x)) 3))
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 y x))))
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(exp.f64 (log.f64 (.f64 2 (.f64 y x))))
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 y x))))
(+.f64 (+.f64 1 (.f64 2 (.f64 y x))) -1)
(+.f64 (.f64 x (.f64 2 y)) 0)
(.f64 2 (.f64 y x))

eval3.0ms (0.2%)

Compiler: Compiled 108 to 69 computations (36.1% saved)

prune3.0ms (0.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	14	2	16

Accurracy

100.0%

Counts

16 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 x (+.f64 y y))
✓	100.0%	(.f64 2 (.f64 y x))

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes13.0ms (0.9%)

Accuracy

Total -0.5b remaining (-12228%)

Threshold costs -0.5b (-12228%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 2 (.f64 y x))
(*.f64 x (+.f64 y y))

Outputs
(.f64 2 (.f64 y x))

Calls

4 calls:

4.0ms	(*.f64 x (+.f64 y y))
3.0ms	(+.f64 y y)
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(*.f64 x (+.f64 y y))`
100.0%	1	`(+.f64 y y)`

Compiler

Compiled 30 to 18 computations (40% saved)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	9	13

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 2 (.f64 y x))

Outputs
(.f64 2 (.f64 y x))

Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness0.0ms (0%)

end24.0ms (1.7%)

Remove: (sort x y)
Compiler: Compiled 42 to 28 computations (33.3% saved)

analyze0.0ms (0%)

sample1.0s (71.9%)

preprocess15.0ms (1.1%)

simplify24.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize42.0ms (3%)

series3.0ms (0.2%)

rewrite96.0ms (6.8%)

simplify19.0ms (1.4%)

eval4.0ms (0.3%)

prune5.0ms (0.3%)

localize21.0ms (1.5%)

series0.0ms (0%)

rewrite63.0ms (4.5%)

simplify55.0ms (3.9%)

eval3.0ms (0.2%)

prune3.0ms (0.2%)

regimes13.0ms (0.9%)

simplify4.0ms (0.3%)

soundness0.0ms (0%)

end24.0ms (1.7%)

Profiling