Details

analyze1.3s (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.8s (38%)

Results

2.1s	2041×	body	1024	valid
934.0ms	4638×	body	128	valid
538.0ms	1020×	body	512	valid
208.0ms	546×	body	256	valid
20.0ms	11×	body	2048	valid

Compiler

Compiled 53 to 44 computations (17% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
9×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	20	22
2	31	22
3	41	22
4	49	22
5	51	22
6	50	22

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

14.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

Compiler

Compiled 61 to 48 computations (21.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 (*.f64 x 1/2))
✓	0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
✓	0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
✓	14.4b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

series21.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

13.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
2.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
1.0ms	(sin.f64 (*.f64 x 1/2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
5.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
1.0ms	(sin.f64 (*.f64 x 1/2))

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

672×	`times-frac_binary64`
637×	`associate-/l*_binary64`
499×	`fma-def_binary64`
421×	`associate-l_binary64`
300×	`cancel-sign-sub-inv_binary64`

Counts

122 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2170
1	382	1712
2	1149	1695
3	4046	1688
4	4931	1688

prune153.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	143	14	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	14	158

Error

0.1b

Counts

158 → 14

Alt Table

Status	Error	Program
	15.2b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (.f64 x 1/2))))) (cbrt.f64 (sin.f64 (.f64 x 1/2))))) (sin.f64 x))
	14.6b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (/.f64 1 (sin.f64 x)))
	14.7b	(/.f64 (.f64 (sqrt.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))) (sqrt.f64 (.f64 8/3 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2)))) (sin.f64 x))
	0.5b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))
	35.1b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 8/3))
	14.6b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
	14.7b	(/.f64 (expm1.f64 (log1p.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	14.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (expm1.f64 (log1p.f64 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	15.3b	(.f64 (.f64 (cbrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))) (cbrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x))))) (cbrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))))
▶	0.5b	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
	14.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	14.6b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))))
	1.3b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
	43.8b	(exp.f64 (-.f64 (+.f64 (log.f64 (sin.f64 (.f64 x 1/2))) (+.f64 (log.f64 8/3) (log.f64 (sin.f64 (.f64 x 1/2))))) (log.f64 (sin.f64 x))))

Compiler

Compiled 3596 to 2684 computations (25.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 (*.f64 x 1/2))
✓	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
✓	0.2b	(/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
	0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

series23.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
8.0ms	(/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2))))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

8.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
4.0ms	(/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2))))

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Rules

575×	`times-frac_binary64`
514×	`fma-def_binary64`
437×	`associate-/l*_binary64`
335×	`associate-/l/_binary64`
328×	`associate-/r*_binary64`

Counts

97 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2586
1	386	2201
2	1094	2197
3	4034	2153
4	4967	2153
5	4908	2153

prune203.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	200	8	208
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	212	10	222

Error

Counts

222 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 (*.f64 x 1/2))))
	14.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (expm1.f64 (log1p.f64 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	35.6b	(/.f64 (exp.f64 (log.f64 (sin.f64 (.f64 x 1/2)))) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
▶	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))))
	14.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	0.3b	(/.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) -3/8))
	0.4b	(/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) 3)))
	1.3b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) (/.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) 8/3)) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 (cbrt.f64 (sin.f64 x)) (sin.f64 (*.f64 x 1/2)))))
	0.5b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))

Compiler

Compiled 4778 to 3517 computations (26.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
✓	0.1b	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
✓	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))))
✓	0.2b	(/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))

series37.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))))
9.0ms	(/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))
8.0ms	(/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
7.0ms	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))

rewrite209.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

2211×	`times-frac_binary64`
977×	`*-un-lft-identity_binary64`
977×	`add-sqr-sqrt_binary64`
977×	`add-cube-cbrt_binary64`
197×	`associate-/r*_binary64`

Counts

4 → 885

Calls

4 calls:

23.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))))
9.0ms	(/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))
4.0ms	(/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))))
3.0ms	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))

simplify950.0ms (9.4%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-/r/_binary64`
565×	`associate-/l/_binary64`
510×	`associate-*l/_binary64`
449×	`associate-*r/_binary64`
322×	`associate-/l*_binary64`

Counts

933 → 1311

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	647	36760
1	1366	35124
2	4757	34279
3	4966	34279
4	4946	34279

prune1.5s (14.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1309	2	1311
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	1313	8	1321

Error

Counts

1321 → 8

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 (*.f64 x 1/2))))
	14.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (expm1.f64 (log1p.f64 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	1.1b	(.f64 (/.f64 1 (/.f64 1 (/.f64 (sqrt.f64 8/3) 1))) (/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 (sqrt.f64 8/3) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))
✓	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))))
	14.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	1.3b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))
	0.4b	(/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) 3)))
▶	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))

Compiler

Compiled 44828 to 34314 computations (23.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 (*.f64 x 1/2))
✓	0.1b	(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)
	0.1b	(/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))
✓	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))

series34.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

25.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))
8.0ms	(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-l_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

9.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))
6.0ms	(.f64 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) 3/8)

simplify114.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

603×	`times-frac_binary64`
506×	`fma-def_binary64`
407×	`associate-/l*_binary64`
302×	`associate-/r*_binary64`
287×	`cancel-sign-sub-inv_binary64`

Counts

84 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	1848
1	350	1489
2	943	1482
3	3488	1466
4	4792	1466
5	4962	1466
6	4901	1466

prune193.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Error

Counts

202 → 8

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 (*.f64 x 1/2))))
	14.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (expm1.f64 (log1p.f64 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	1.1b	(.f64 (/.f64 1 (/.f64 1 (/.f64 (sqrt.f64 8/3) 1))) (/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 (sqrt.f64 8/3) (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))))))
✓	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 8/3 (/.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))))))
	14.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	1.3b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))
	0.4b	(/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (pow.f64 (.f64 3/8 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2)))) 3)))
✓	0.3b	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 (sin.f64 x) (sin.f64 (*.f64 x 1/2))) 3/8))

Compiler

Compiled 4154 to 3029 computations (27.1% saved)

regimes1.1s (11.1%)

Accuracy

Total 0.3b remaining (85.7%)

Threshold costs 0.3b (85.7%)

Counts

334 → 1

Compiler

Compiled 13126 to 10714 computations (18.4% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	15	25
2	14	25

end144.0ms (1.4%)

Compiler: Compiled 181 to 151 computations (16.6% saved)

Details

analyze1.3s (12.5%)

sample3.8s (38%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series21.0ms (0.2%)

rewrite20.0ms (0.2%)

simplify79.0ms (0.8%)

prune153.0ms (1.5%)

localize8.0ms (0.1%)

series23.0ms (0.2%)

rewrite17.0ms (0.2%)

simplify104.0ms (1%)

prune203.0ms (2%)

localize9.0ms (0.1%)

series37.0ms (0.4%)

rewrite209.0ms (2.1%)

simplify950.0ms (9.4%)

prune1.5s (14.9%)

localize8.0ms (0.1%)

series34.0ms (0.3%)

rewrite18.0ms (0.2%)

simplify114.0ms (1.1%)

prune193.0ms (1.9%)

regimes1.1s (11.1%)

simplify17.0ms (0.2%)

end144.0ms (1.4%)

Profiling