Details

analyze1.2s (15.4%)

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)

sample4.0s (51.9%)

Results

2.2s	2087×	body	1024	valid
986.0ms	4637×	body	128	valid
531.0ms	1016×	body	512	valid
246.0ms	510×	body	256	valid
10.0ms	6×	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

13.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.2b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.3b	(.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)))
✓	12.9b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

series23.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

16.0ms	(/.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)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 65

Calls

3 calls:

6.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
5.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
4.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

672×	`times-frac_binary64`
637×	`associate-/l*_binary64`
493×	`fma-def_binary64`
403×	`associate-l_binary64`
346×	`associate-r_binary64`

Counts

101 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	1967
1	346	1521
2	1037	1506
3	4124	1499
4	4937	1499
5	4946	1499

prune134.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	103	14	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	14	118

Error

0.0b

Counts

118 → 14

Alt Table

Status	Error	Program
	13.1b	(/.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))
	21.2b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))))
	13.2b	(.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 2) (sin.f64 x)))
	13.2b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))))
	37.3b	(exp.f64 (-.f64 (log.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))) (log.f64 (sin.f64 x))))
	24.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (expm1.f64 (log1p.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	36.3b	(.f64 (sqrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (sqrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))))
	26.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (.f64 8/3 8/3) 8/3) (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	13.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))))
	13.8b	(/.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))
▶	0.5b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))
	29.4b	(.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))
	1.4b	(.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))))
	13.2b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (log1p.f64 (expm1.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))

Compiler

Compiled 2974 to 2224 computations (25.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))
✓	0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))
	0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

series24.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))
7.0ms	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

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

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
441×	`associate-/l*_binary64`
414×	`fma-def_binary64`
384×	`associate-*r/_binary64`
384×	`associate-*l/_binary64`

Counts

76 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	1666
1	296	1325
2	993	1323
3	3425	1316
4	3953	1316
5	4869	1316
6	4915	1316

prune153.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	129	13	142

Error

0.0b

Counts

142 → 13

Alt Table

Status	Error	Program
	0.6b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2))))))
	1.5b	(.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) (.f64 (.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))) (cbrt.f64 (sin.f64 (.f64 x 1/2)))))
	24.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (expm1.f64 (log1p.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	36.3b	(.f64 (sqrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (sqrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))))
	0.8b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))))
	0.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))))
	13.1b	(/.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))
	22.4b	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (/.f64 (.f64 (.f64 (.f64 8/3 8/3) 8/3) (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))) (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (sin.f64 x)))))
	13.2b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))))
▶	0.5b	(.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
	1.4b	(.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))))
	0.9b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))))
	26.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (.f64 8/3 8/3) 8/3) (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))

Compiler

Compiled 3294 to 2445 computations (25.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
✓	0.2b	(.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
	0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

series21.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

13.0ms	(.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
8.0ms	(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

6.0ms	(.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
3.0ms	(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-neg_binary64`
400×	`associate-/l*_binary64`
383×	`associate-*l/_binary64`
341×	`associate-*r/_binary64`
332×	`fma-def_binary64`

Counts

88 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	1790
1	327	1590
2	1104	1588
3	2981	1567
4	3547	1567
5	4742	1567
6	5220	1567

prune158.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	131	12	143

Error

Counts

143 → 12

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))
	0.9b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))))
	1.4b	(.f64 (.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)))) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
	24.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (expm1.f64 (log1p.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
	36.3b	(.f64 (sqrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (sqrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (sin.f64 x))))
	0.6b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2))))))
	13.1b	(/.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))
	22.4b	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (/.f64 (.f64 (.f64 (.f64 8/3 8/3) 8/3) (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))) (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (sin.f64 x)))))
	15.3b	(.f64 (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))) (sqrt.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))))
	1.4b	(.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))))
	0.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))))
	26.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (.f64 8/3 8/3) 8/3) (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))

Compiler

Compiled 3398 to 2500 computations (26.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

22.0ms

(*.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))

10.0ms

(*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)))

6.0ms

(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
20×	`associate-r_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`pow1_binary64`

Counts

3 → 87

Calls

3 calls:

9.0ms

(*.f64 (*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))

6.0ms

(*.f64 (sqrt.f64 8/3) (*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)))

4.0ms

(*.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3))

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
476×	`associate-/l*_binary64`
434×	`associate-*r/_binary64`
356×	`associate-*l/_binary64`
313×	`times-frac_binary64`

Counts

123 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2476
1	479	1968
2	1590	1954
3	4434	1938
4	4985	1938
5	4928	1938

prune238.0ms (3.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	191	4	195
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	195	12	207

Error

Counts

207 → 12

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 1 (.f64 8/3 (sin.f64 (.f64 1/2 x)))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))
	13.1b	(/.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))
✓	0.4b	(.f64 (.f64 (sqrt.f64 8/3) (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))
	0.9b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x)))))
	1.4b	(.f64 (.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)))) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
	21.1b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 8/3) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3)) (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))) (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)))
	0.6b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (/.f64 (sin.f64 x) (.f64 8/3 (sin.f64 (.f64 x 1/2))))))
	15.3b	(.f64 (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))) (sqrt.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))))
	0.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 8/3)) (.f64 (sqrt.f64 (sqrt.f64 8/3)) (.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3)))) (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)))
	0.9b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))))) (cbrt.f64 (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (sin.f64 x))))
	13.1b	(.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (/.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 2) (sin.f64 x))))
	26.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 (.f64 8/3 8/3) 8/3) (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))

Compiler

Compiled 5244 to 4102 computations (21.8% saved)

regimes965.0ms (12.4%)

Accuracy

Total 0.4b remaining (90.5%)

Threshold costs 0.4b (90.5%)

Counts

344 → 1

Compiler

Compiled 15402 to 12456 computations (19.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	16	29
2	16	29

end250.0ms (3.2%)

Compiler: Compiled 361 to 297 computations (17.7% saved)

Details

analyze1.2s (15.4%)

sample4.0s (51.9%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series23.0ms (0.3%)

rewrite18.0ms (0.2%)

simplify99.0ms (1.3%)

prune134.0ms (1.7%)

localize8.0ms (0.1%)

series24.0ms (0.3%)

rewrite15.0ms (0.2%)

simplify97.0ms (1.2%)

prune153.0ms (2%)

localize8.0ms (0.1%)

series21.0ms (0.3%)

rewrite13.0ms (0.2%)

simplify104.0ms (1.3%)

prune158.0ms (2%)

localize19.0ms (0.2%)

series37.0ms (0.5%)

rewrite27.0ms (0.3%)

simplify108.0ms (1.4%)

prune238.0ms (3.1%)

regimes965.0ms (12.4%)

simplify2.0ms (0%)

end250.0ms (3.2%)

Profiling