Details

analyze493.0ms (9.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
37.5%	50%	12.6%	7
37.5%	50%	12.6%	8
43.7%	37.5%	18.8%	9
43.7%	37.5%	18.8%	10
46.8%	31.2%	22%	11
46.8%	31.2%	22%	12
48.4%	28.1%	23.5%	13
48.4%	28.1%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample3.7s (71.1%)

Results

1.0s	2006×	body	1024	valid
1.0s	2075×	body	1024	invalid
586.0ms	4753×	body	128	valid
317.0ms	1059×	body	512	invalid
313.0ms	1020×	body	512	valid
119.0ms	497×	body	256	invalid
97.0ms	470×	body	256	valid
89.0ms	699×	body	128	invalid
15.0ms	7×	body	2048	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-neg_binary64`
610×	`div-sub_binary64`
491×	`times-frac_binary64`
410×	`associate-/l*_binary64`
352×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	16	11
2	34	11
3	73	11
4	160	11
5	361	11
6	984	11
7	3177	11
8	4701	11
9	5010	11

prune2.0ms (0%)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 x)
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
✓	0.0b	(sinh.f64 y)

series45.0ms (0.9%)

Counts

3 → 40

Calls

3 calls:

35.0ms	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
8.0ms	(sinh.f64 y)
2.0ms	(cos.f64 x)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 53

Calls

3 calls:

5.0ms	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
1.0ms	(cos.f64 x)
1.0ms	(sinh.f64 y)

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

476×	`fma-def_binary64`
475×	`associate-l_binary64`
374×	`associate-/l*_binary64`
327×	`times-frac_binary64`
287×	`associate-*r/_binary64`

Counts

93 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	1580
1	494	1484
2	1603	1434
3	4670	1433
4	4987	1433
5	4999	1433
6	4944	1433

prune53.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Status	Error	Program
	30.8b	(.f64 (cos.f64 x) (/.f64 (.f64 (sqrt.f64 (sinh.f64 y)) (sqrt.f64 (sinh.f64 y))) y))
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
▶	1.5b	(.f64 (cos.f64 x) (fma.f64 1/6 (.f64 y y) 1))
	58.0b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y))) y))

Compiler

Compiled 1655 to 671 computations (59.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/6 (*.f64 y y) 1)
	0.0b	(cos.f64 x)
✓	0.0b	(.f64 (cos.f64 x) (fma.f64 1/6 (.f64 y y) 1))

series18.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

16.0ms	(.f64 (cos.f64 x) (fma.f64 1/6 (.f64 y y) 1))
2.0ms	(fma.f64 1/6 (*.f64 y y) 1)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(.f64 (cos.f64 x) (fma.f64 1/6 (.f64 y y) 1))
0.0ms	(fma.f64 1/6 (*.f64 y y) 1)

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
668×	`distribute-rgt-in_binary64`
292×	`associate-l_binary64`
260×	`sub-neg_binary64`
245×	`associate-r_binary64`

Counts

68 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1027
1	181	941
2	637	925
3	2298	925
4	5202	925

prune54.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	78	4	82

Error

Counts

82 → 4

Alt Table

Status	Error	Program
▶	30.8b	(.f64 (cos.f64 x) (/.f64 (.f64 (sqrt.f64 (sinh.f64 y)) (sqrt.f64 (sinh.f64 y))) y))
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
✓	1.5b	(.f64 (cos.f64 x) (fma.f64 1/6 (.f64 y y) 1))
	58.0b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y))) y))

Compiler

Compiled 1289 to 737 computations (42.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 x)
✓	0.0b	(sqrt.f64 (sinh.f64 y))
	0.0b	(sinh.f64 y)
✓	0.3b	(*.f64 (sqrt.f64 (sinh.f64 y)) (sqrt.f64 (sinh.f64 y)))

series21.0ms (0.4%)

Counts

2 → 20

Calls

2 calls:

14.0ms	(sqrt.f64 (sinh.f64 y))
7.0ms	(*.f64 (sqrt.f64 (sinh.f64 y)) (sqrt.f64 (sinh.f64 y)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 72

Calls

2 calls:

6.0ms	(*.f64 (sqrt.f64 (sinh.f64 y)) (sqrt.f64 (sinh.f64 y)))
1.0ms	(sqrt.f64 (sinh.f64 y))

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-/r*_binary64`
542×	`associate-/l/_binary64`
493×	`fma-def_binary64`
225×	`associate-*l/_binary64`
199×	`times-frac_binary64`

Counts

92 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	834
1	141	800
2	360	782
3	907	756
4	2462	756
5	4721	756
6	4947	756
7	4894	756

prune64.0ms (1.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	166	4	170

Error

Counts

170 → 4

Alt Table

Status	Error	Program
✓	30.8b	(.f64 (cos.f64 x) (/.f64 (.f64 (sqrt.f64 (sinh.f64 y)) (sqrt.f64 (sinh.f64 y))) y))
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
✓	1.5b	(.f64 (cos.f64 x) (fma.f64 1/6 (.f64 y y) 1))
▶	58.0b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y))) y))

Compiler

Compiled 2835 to 1021 computations (64% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 x)
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y))) y))
✓	0.0b	(/.f64 -1/2 (exp.f64 y))
✓	5.9b	(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))

series51.0ms (1%)

Counts

3 → 40

Calls

3 calls:

35.0ms	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y))) y))
11.0ms	(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))
6.0ms	(/.f64 -1/2 (exp.f64 y))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 73

Calls

3 calls:

5.0ms	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y))) y))
3.0ms	(/.f64 -1/2 (exp.f64 y))
1.0ms	(fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y)))

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

488×	`fma-def_binary64`
388×	`associate-/l*_binary64`
333×	`times-frac_binary64`
273×	`associate-*l/_binary64`
220×	`fma-neg_binary64`

Counts

113 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	2377
1	561	2154
2	1714	2134
3	4715	2127
4	4991	2127

prune73.0ms (1.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	147	4	151

Error

Counts

151 → 4

Alt Table

Status	Error	Program
✓	30.8b	(.f64 (cos.f64 x) (/.f64 (.f64 (sqrt.f64 (sinh.f64 y)) (sqrt.f64 (sinh.f64 y))) y))
✓	0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
✓	1.5b	(.f64 (cos.f64 x) (fma.f64 1/6 (.f64 y y) 1))
✓	58.0b	(*.f64 (cos.f64 x) (/.f64 (fma.f64 1/2 (exp.f64 y) (/.f64 -1/2 (exp.f64 y))) y))

Compiler

Compiled 3157 to 1665 computations (47.3% saved)

regimes85.0ms (1.6%)

Accuracy

Total 0.0b remaining (31.7%)

Threshold costs 0.0b (31.7%)

Counts

18 → 1

Compiler

Compiled 1055 to 729 computations (30.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end58.0ms (1.1%)

Compiler: Compiled 67 to 44 computations (34.3% saved)

Details

analyze493.0ms (9.6%)

sample3.7s (71.1%)

simplify52.0ms (1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series45.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify109.0ms (2.1%)

prune53.0ms (1%)

localize6.0ms (0.1%)

series18.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify54.0ms (1%)

prune54.0ms (1.1%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify94.0ms (1.8%)

prune64.0ms (1.3%)

localize8.0ms (0.2%)

series51.0ms (1%)

rewrite11.0ms (0.2%)

simplify91.0ms (1.8%)

prune73.0ms (1.4%)

regimes85.0ms (1.6%)

simplify3.0ms (0.1%)

end58.0ms (1.1%)

Profiling