Details

analyze101.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 32 to 17 computations (46.9% saved)

sample62.0ms (0.6%)

Algorithm

1×

intervals

Results

38.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 57 to 29 computations (49.1% saved)

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/l/_binary32`
455×	`associate-/l*_binary32`
281×	`times-frac_binary32`
257×	`associate-/r/_binary32`
154×	`associate-*l/_binary32`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	24	36
2	80	36
3	299	36
4	822	36
5	1265	36
6	1211	36
7	1239	36
8	1247	36
9	1251	36
10	1253	36
11	1219	36
12	1217	36

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))

Compiler

Compiled 46 to 20 computations (56.5% saved)

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(*.f32 x PI.f32)
0.3b	(*.f32 x PI.f32)
0.4b	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
0.4b	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))

rewrite111.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

22×	`add-cbrt-cube_binary32`
22×	`add-exp-log_binary32`
16×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-cube-cbrt_binary32`

Counts

4 → 80

Calls

4 calls:

6.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
4.0ms	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
3.0ms	(*.f32 x PI.f32)
3.0ms	(*.f32 x PI.f32)

Compiler

Compiled 2096 to 327 computations (84.4% saved)

series98.0ms (1%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

43.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
20.0ms	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
9.0ms	(*.f32 x PI.f32)
7.0ms	(*.f32 x PI.f32)

Compiler

Compiled 1266 to 710 computations (43.9% saved)

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

722×	`associate-/l*_binary32`
434×	`cancel-sign-sub-inv_binary32`
371×	`*-commutative_binary32`
289×	`associate-/l/_binary32`
277×	`associate-*l/_binary32`

Counts

104 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	1993
1	388	1702
2	1413	1693
3	4323	1687
4	5114	1687

prune109.0ms (1.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	56	17	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	17	74

Error

0.1b

Counts

74 → 17

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.2b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	3.6b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 (.f32 tau tau) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 (.f32 tau x)) 6)))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 PI.f32 x))) x) (/.f32 (sqrt.f32 (sin.f32 (.f32 PI.f32 x))) PI.f32)))
	0.8b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 PI.f32 (sqrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.8b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 x x))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 x) 6)))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (.f32 PI.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x PI.f32))) (/.f32 PI.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 PI.f32 x))) x))))
	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 PI.f32 (.f32 tau x)) (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)))
	1.7b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))

Compiler

Compiled 2597 to 871 computations (66.5% saved)

localize59.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(*.f32 x PI.f32)
0.4b	(/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))
0.4b	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
13.7b	(log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))

rewrite143.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

26×	`add-exp-log_binary32`
20×	`add-cbrt-cube_binary32`
14×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-cube-cbrt_binary32`

Counts

4 → 81

Calls

4 calls:

6.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
4.0ms	(/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))
3.0ms	(log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))
3.0ms	(*.f32 x PI.f32)

Compiler

Compiled 2296 to 396 computations (82.8% saved)

series135.0ms (1.3%)

Error

0.1b

Counts

4 → 27

Calls

4 calls:

45.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
34.0ms	(log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))
17.0ms	(/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))
9.0ms	(*.f32 x PI.f32)

Compiler

Compiled 1677 to 995 computations (40.7% saved)

simplify121.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

771×	`associate-/l*_binary32`
292×	`associate-/l/_binary32`
286×	`cancel-sign-sub-inv_binary32`
271×	`associate-*l/_binary32`
206×	`associate-l_binary32`

Counts

108 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2463
1	501	2114
2	1780	2093
3	4678	2093
4	4994	2093
5	4960	2093

prune120.0ms (1.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	71	16	87

Error

0.1b

Counts

87 → 16

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.2b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (.f32 (/.f32 1 (.f32 PI.f32 x)) (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) tau)) (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.7b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 x x))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 x) 6)))))
	0.8b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))))) (log.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	3.6b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 (.f32 tau tau) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 (.f32 tau x)) 6)))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (.f32 PI.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x PI.f32))) (/.f32 PI.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 PI.f32 x))) x))))
▶	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 PI.f32 (.f32 tau x)) (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 PI.f32 (sqrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))

Compiler

Compiled 2560 to 945 computations (63.1% saved)

localize51.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
0.4b	(/.f32 1 (/.f32 (.f32 PI.f32 (.f32 tau x)) (sin.f32 (.f32 PI.f32 (.f32 tau x)))))
0.4b	(.f32 PI.f32 (.f32 tau x))
0.4b	(.f32 PI.f32 (.f32 tau x))

rewrite198.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

53×	`add-exp-log_binary32`
36×	`times-frac_binary32`
33×	`add-cbrt-cube_binary32`
24×	`*-un-lft-identity_binary32`
24×	`add-sqr-sqrt_binary32`

Counts

4 → 117

Calls

4 calls:

6.0ms	(/.f32 1 (/.f32 (.f32 PI.f32 (.f32 tau x)) (sin.f32 (.f32 PI.f32 (.f32 tau x)))))
5.0ms	(.f32 PI.f32 (.f32 tau x))
4.0ms	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
4.0ms	(.f32 PI.f32 (.f32 tau x))

Compiler

Compiled 3480 to 731 computations (79% saved)

series115.0ms (1.1%)

Error

0.1b

Counts

4 → 30

Calls

4 calls:

42.0ms	(/.f32 1 (/.f32 (.f32 PI.f32 (.f32 tau x)) (sin.f32 (.f32 PI.f32 (.f32 tau x)))))
20.0ms	(.f32 PI.f32 (.f32 tau x))
20.0ms	(.f32 PI.f32 (.f32 tau x))
17.0ms	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))

Compiler

Compiled 1597 to 899 computations (43.7% saved)

simplify146.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

490×	`associate-*l/_binary32`
377×	`associate-/l/_binary32`
360×	`associate-/r/_binary32`
353×	`associate-*r/_binary32`
274×	`cancel-sign-sub-inv_binary32`

Counts

147 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	3433
1	441	2947
2	1607	2896
3	4345	2896
4	4954	2896
5	5039	2896

prune103.0ms (1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	93	16	109

Error

0.1b

Counts

109 → 16

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.2b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 x x))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 x) 6)))))
	0.8b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))))) (log.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	3.6b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 (.f32 tau tau) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 (.f32 tau x)) 6)))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.1b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))))) PI.f32) (/.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (.f32 PI.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x PI.f32))) (/.f32 PI.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 PI.f32 x))) x))))
	2.7b	(.f32 (/.f32 1 (/.f32 (.f32 PI.f32 (.f32 tau x)) (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (+.f32 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4))) (-.f32 1 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 x x))))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 PI.f32 (sqrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.7b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))

Compiler

Compiled 2560 to 914 computations (64.3% saved)

localize57.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(*.f32 x PI.f32)
0.3b	(/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)
0.4b	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
0.4b	(.f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 PI.f32 x)) PI.f32))

rewrite214.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

49×	`add-sqr-sqrt_binary32`
39×	`add-exp-log_binary32`
37×	`times-frac_binary32`
32×	`*-un-lft-identity_binary32`
30×	`add-cube-cbrt_binary32`

Counts

4 → 124

Calls

4 calls:

9.0ms	(.f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 PI.f32 x)) PI.f32))
5.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
4.0ms	(/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)
3.0ms	(*.f32 x PI.f32)

Compiler

Compiled 3733 to 908 computations (75.7% saved)

series109.0ms (1.1%)

Error

0.1b

Counts

4 → 27

Calls

4 calls:

44.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
16.0ms	(.f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 PI.f32 x)) PI.f32))
14.0ms	(/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)
9.0ms	(*.f32 x PI.f32)

Compiler

Compiled 1558 to 935 computations (40% saved)

simplify148.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

446×	`associate-/l/_binary32`
433×	`cancel-sign-sub-inv_binary32`
227×	`associate-r_binary32`
227×	`associate-l_binary32`
207×	`neg-mul-1_binary32`

Counts

151 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	237	3280
1	604	2857
2	2097	2848
3	3890	2842
4	4778	2834
5	4954	2834

prune147.0ms (1.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	106	17	123

Error

0.1b

Counts

123 → 17

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.2b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.9b	(.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 PI.f32 x)) PI.f32)))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 PI.f32 (sqrt.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 PI.f32 x)) PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 1 x)) (cbrt.f32 (/.f32 1 x))) (.f32 (/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32) (cbrt.f32 (/.f32 1 x)))))
	2.7b	(.f32 (/.f32 1 (/.f32 (.f32 PI.f32 (.f32 tau x)) (sin.f32 (.f32 PI.f32 (.f32 tau x))))) (+.f32 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4))) (-.f32 1 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 x x))))))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4)))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 x x))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 x) 6)))))
	0.8b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 (.f32 x tau))))) (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 PI.f32 (cbrt.f32 x))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (+.f32 (.f32 2 (log.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))))) (log.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	3.6b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 (.f32 tau tau) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 PI.f32 (.f32 tau x)) 6)))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x PI.f32))) (/.f32 PI.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 PI.f32 x))) x))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (.f32 PI.f32 x))) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 PI.f32 x)) PI.f32)))
	0.9b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 x tau))) (.f32 PI.f32 x)) tau) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 PI.f32 x)) PI.f32)))
	1.7b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))

Compiler

Compiled 2768 to 880 computations (68.2% saved)

regimes4.7s (46.5%)

Accuracy

Total 0.5b remaining (77.7%)

Threshold costs 0.5b (77.7%)

Compiler

Compiled 60316 to 32396 computations (46.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	82
1	21	82
2	21	82

end1.0ms (0%)

Compiler: Compiled 50 to 15 computations (70% saved)

sample2.8s (28.3%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
186.0ms	8000×	pre	128	true

Compiler

Compiled 680 to 350 computations (48.5% saved)

Details

analyze101.0ms (1%)

sample62.0ms (0.6%)

simplify49.0ms (0.5%)

prune2.0ms (0%)

localize40.0ms (0.4%)

rewrite111.0ms (1.1%)

series98.0ms (1%)

simplify87.0ms (0.9%)

prune109.0ms (1.1%)

localize59.0ms (0.6%)

rewrite143.0ms (1.4%)

series135.0ms (1.3%)

simplify121.0ms (1.2%)

prune120.0ms (1.2%)

localize51.0ms (0.5%)

rewrite198.0ms (2%)

series115.0ms (1.1%)

simplify146.0ms (1.5%)

prune103.0ms (1%)

localize57.0ms (0.6%)

rewrite214.0ms (2.1%)

series109.0ms (1.1%)

simplify148.0ms (1.5%)

prune147.0ms (1.5%)

regimes4.7s (46.5%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.8s (28.3%)

Profiling