Details

analyze107.0ms (1.3%)

Algorithm

1×

Search

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

Compiler

Compiled 32 to 17 computations (46.9% saved)

sample53.0ms (0.6%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 57 to 29 computations (49.1% saved)

simplify50.0ms (0.6%)

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

prune3.0ms (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

0.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.7b	(.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)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite115.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

20×	`add-exp-log_binary32` `add-cbrt-cube_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`add-cube-cbrt_binary32` `*-un-lft-identity_binary32`
6×	`pow1_binary32` `times-frac_binary32` `associate-/l*_binary32`
5×	`prod-exp_binary32` `div-exp_binary32` `cbrt-undiv_binary32` `cbrt-unprod_binary32`

Counts

4 → 69

Calls

4 calls:

7.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
5.0ms	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
4.0ms	(*.f32 x PI.f32)
2.0ms	(sin.f32 (.f32 (.f32 x PI.f32) tau))

Compiler

Compiled 1878 to 277 computations (85.3% saved)

series170.0ms (2.1%)

Error

0.3b

Counts

4 → 33

Calls

4 calls:

53.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
38.0ms	(sin.f32 (.f32 (.f32 x PI.f32) tau))
21.0ms	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
9.0ms	(*.f32 x PI.f32)

Compiler

Compiled 2119 to 1158 computations (45.4% saved)

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

494×	`cancel-sign-sub-inv_binary32`
395×	`associate-/l/_binary32`
363×	`associate-*l/_binary32`
297×	`distribute-rgt-neg-in_binary32`
288×	`distribute-lft-neg-in_binary32`

Counts

102 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	2309
1	500	1981
2	1956	1972
3	4423	1966
4	4991	1966

prune133.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	13	83

Error

0.2b

Counts

83 → 13

Alt Table

Status	Error	Program
	4.3b	(.f32 (/.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 tau 5) (.f32 (pow.f32 PI.f32 5) (pow.f32 x 5)))) (-.f32 (.f32 tau (.f32 PI.f32 x)) (.f32 1/6 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 3)))) (.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 tau (.f32 PI.f32 x)))) (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	3.0b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 PI.f32 2) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 6)))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.0b	(.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)))
	1.8b	(.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)))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (/.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)) (log.f32 (exp.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 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (*.f32 PI.f32 x)))))
▶	0.7b	(.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)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 PI.f32 (cbrt.f32 x)))))
	5.1b	(.f32 (/.f32 (log.f32 (exp.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))))) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))

Compiler

Compiled 2561 to 813 computations (68.3% saved)

localize46.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.4b	(sin.f32 (.f32 (.f32 x PI.f32) tau))
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))
14.9b	(log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))

rewrite135.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

24×	`add-exp-log_binary32`
18×	`add-cbrt-cube_binary32`
10×	`add-cube-cbrt_binary32` `add-sqr-sqrt_binary32` `*-un-lft-identity_binary32`
9×	`times-frac_binary32`
7×	`log-prod_binary32` `div-exp_binary32`

Counts

4 → 70

Calls

4 calls:

7.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
5.0ms	(/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))
4.0ms	(sin.f32 (.f32 (.f32 x PI.f32) tau))
4.0ms	(log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))

Compiler

Compiled 2060 to 322 computations (84.4% saved)

series229.0ms (2.8%)

Error

0.1b

Counts

4 → 36

Calls

4 calls:

55.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
42.0ms	(sin.f32 (.f32 (.f32 x PI.f32) tau))
40.0ms	(log.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))
22.0ms	(/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))

Compiler

Compiled 2597 to 1483 computations (42.9% saved)

simplify112.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

578×	`cancel-sign-sub-inv_binary32`
422×	`associate-/l/_binary32`
351×	`distribute-rgt-neg-in_binary32`
341×	`distribute-lft-neg-in_binary32`
295×	`neg-mul-1_binary32`

Counts

106 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	2779
1	596	2393
2	2258	2372
3	4516	2372
4	5093	2372

prune133.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	76	13	89

Error

0.2b

Counts

89 → 13

Alt Table

Status	Error	Program
	4.3b	(.f32 (/.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 tau 5) (.f32 (pow.f32 PI.f32 5) (pow.f32 x 5)))) (-.f32 (.f32 tau (.f32 PI.f32 x)) (.f32 1/6 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 3)))) (.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 tau (.f32 PI.f32 x)))) (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	3.0b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 PI.f32 2) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 6)))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (/.f32 1 (/.f32 (.f32 x PI.f32) (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) tau))) (exp.f32 (log.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)) (exp.f32 (log.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (log.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 PI.f32 x))) (/.f32 x (/.f32 (sqrt.f32 (sin.f32 (*.f32 x PI.f32))) PI.f32))))))
	1.8b	(.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)))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (/.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)) (log.f32 (exp.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 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (*.f32 PI.f32 x)))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (.f32 (.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) (cbrt.f32 (log.f32 (/.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 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 PI.f32 (cbrt.f32 x)))))

Compiler

Compiled 2581 to 915 computations (64.5% saved)

localize63.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.5b	(.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))))
14.9b	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
14.9b	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
14.9b	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))

rewrite219.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

26×	`add-sqr-sqrt_binary32`
24×	`add-exp-log_binary32` `cbrt-prod_binary32`
21×	`log-prod_binary32`
20×	`pow1_binary32` `*-un-lft-identity_binary32`
18×	`add-cube-cbrt_binary32`

Counts

4 → 102

Calls

4 calls:

9.0ms	(.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))))
4.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
4.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
4.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))

Compiler

Compiled 4673 to 493 computations (89.5% saved)

series273.0ms (3.3%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

72.0ms	(.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))))
44.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
43.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
43.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))

Compiler

Compiled 3312 to 1599 computations (51.7% saved)

simplify133.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

585×	`associate-l_binary32`
523×	`associate-r_binary32`
458×	`distribute-rgt-neg-in_binary32`
451×	`distribute-lft-neg-in_binary32`
179×	`*-commutative_binary32`

Counts

126 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	3944
1	314	3600
2	845	3190
3	3222	3148
4	4999	3148

prune208.0ms (2.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	87	14	101

Error

0.1b

Counts

101 → 14

Alt Table

Status	Error	Program
	2.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (.f32 (+.f32 (cbrt.f32 (.f32 (pow.f32 x 4) (.f32 (pow.f32 PI.f32 4) 1/36))) (.f32 (cbrt.f32 (.f32 (pow.f32 x 4) (.f32 (pow.f32 PI.f32 4) 1/36))) (+.f32 (.f32 (.f32 (.f32 x x) (pow.f32 PI.f32 2)) 1/45) (.f32 (.f32 (pow.f32 x 4) (pow.f32 PI.f32 4)) 73/56700)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))))))
	4.3b	(.f32 (/.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 tau 5) (.f32 (pow.f32 PI.f32 5) (pow.f32 x 5)))) (-.f32 (.f32 tau (.f32 PI.f32 x)) (.f32 1/6 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 3)))) (.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 tau (.f32 PI.f32 x)))) (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	3.0b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 PI.f32 2) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 6)))) (/.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 (log.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (log.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 PI.f32 x))) (/.f32 x (/.f32 (sqrt.f32 (sin.f32 (*.f32 x PI.f32))) PI.f32))))))
	1.8b	(.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)))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 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)) (exp.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) 5) (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))))) (cbrt.f32 (log.f32 (/.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)) (log.f32 (exp.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 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (*.f32 PI.f32 x)))))
✓	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (.f32 (.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) (cbrt.f32 (log.f32 (/.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 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 PI.f32 (cbrt.f32 x)))))

Compiler

Compiled 4600 to 1309 computations (71.5% saved)

localize71.0ms (0.9%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) 5)
14.9b	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
14.9b	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
14.9b	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))

rewrite224.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

23×	`add-exp-log_binary32`
21×	`log-prod_binary32`
14×	`add-cube-cbrt_binary32` `add-sqr-sqrt_binary32` `*-un-lft-identity_binary32`
11×	`cbrt-prod_binary32`
10×	`unpow-prod-down_binary32`

Counts

4 → 82

Calls

4 calls:

5.0ms	(pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) 5)
4.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
4.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
4.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))

Compiler

Compiled 4265 to 676 computations (84.2% saved)

series260.0ms (3.1%)

Error

0.1b

Counts

4 → 21

Calls

4 calls:

59.0ms	(pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) 5)
45.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
45.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
44.0ms	(log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))

Compiler

Compiled 3122 to 1450 computations (53.6% saved)

simplify175.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

457×	`distribute-rgt-neg-in_binary32`
451×	`unswap-sqr_binary32`
450×	`distribute-lft-neg-in_binary32`
309×	`associate-l_binary32`
300×	`associate-r_binary32`

Counts

103 → 59

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	141	2832
1	295	2609
2	692	2557
3	2309	2557
4	4644	2557
5	4909	2521
6	4917	2521

prune167.0ms (2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	57	16	73

Error

0.1b

Counts

73 → 16

Alt Table

Status	Error	Program
	1.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) 5) (cbrt.f32 (cbrt.f32 (-.f32 (.f32 (pow.f32 x 6) (.f32 (pow.f32 PI.f32 6) -1/2835)) (+.f32 (.f32 (.f32 (.f32 x x) (pow.f32 PI.f32 2)) 1/6) (.f32 (pow.f32 (.f32 x PI.f32) 4) (+.f32 1/180 (.f32 1/37800 (pow.f32 (.f32 x PI.f32) 4))))))))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))))))
	2.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (.f32 (+.f32 (cbrt.f32 (.f32 (pow.f32 x 4) (.f32 (pow.f32 PI.f32 4) 1/36))) (.f32 (cbrt.f32 (.f32 (pow.f32 x 4) (.f32 (pow.f32 PI.f32 4) 1/36))) (+.f32 (.f32 (.f32 (.f32 x x) (pow.f32 PI.f32 2)) 1/45) (.f32 (.f32 (pow.f32 x 4) (pow.f32 PI.f32 4)) 73/56700)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))))))
	4.3b	(.f32 (/.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 tau 5) (.f32 (pow.f32 PI.f32 5) (pow.f32 x 5)))) (-.f32 (.f32 tau (.f32 PI.f32 x)) (.f32 1/6 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 3)))) (.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 tau (.f32 PI.f32 x)))) (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))))) (.f32 PI.f32 x)) (/.f32 (cbrt.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x)))) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	3.0b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 tau 4) (.f32 (pow.f32 PI.f32 4) (pow.f32 x 4))))) (+.f32 (.f32 1/6 (.f32 (.f32 tau tau) (.f32 (pow.f32 PI.f32 2) (.f32 x x)))) (.f32 1/5040 (pow.f32 (.f32 tau (.f32 PI.f32 x)) 6)))) (/.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 (log.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (log.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 PI.f32 x))) (/.f32 x (/.f32 (sqrt.f32 (sin.f32 (*.f32 x PI.f32))) PI.f32))))))
	1.8b	(.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)))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 x))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 tau (.f32 PI.f32 x))) (.f32 tau (.f32 PI.f32 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)) (exp.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) 5) (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))))) (cbrt.f32 (log.f32 (/.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)) (exp.f32 (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) 2)) 5) (pow.f32 (cbrt.f32 (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))))) 5)) (cbrt.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))))) (cbrt.f32 (log.f32 (/.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)) (log.f32 (exp.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 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 (.f32 PI.f32 x)) (cbrt.f32 (.f32 PI.f32 x))) (cbrt.f32 (*.f32 PI.f32 x)))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (exp.f32 (.f32 (.f32 (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))) (cbrt.f32 (log.f32 (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))))) (cbrt.f32 (log.f32 (/.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 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 PI.f32 (cbrt.f32 x)))))

Compiler

Compiled 3366 to 971 computations (71.2% saved)

regimes2.7s (32.3%)

Accuracy

Total 0.5b remaining (75.6%)

Threshold costs 0.5b (75.6%)

Compiler

Compiled 36914 to 17788 computations (51.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	16	36
2	16	36

end1.0ms (0%)

Compiler: Compiled 23 to 11 computations (52.2% saved)

sample2.4s (28.7%)

Algorithm

1×

intervals

Results

818.0ms	8000×	body	128	valid
193.0ms	8000×	pre	128	true

Compiler

Compiled 797 to 386 computations (51.6% saved)

Details

analyze107.0ms (1.3%)

sample53.0ms (0.6%)

simplify50.0ms (0.6%)

prune3.0ms (0%)

localize35.0ms (0.4%)

rewrite115.0ms (1.4%)

series170.0ms (2.1%)

simplify97.0ms (1.2%)

prune133.0ms (1.6%)

localize46.0ms (0.6%)

rewrite135.0ms (1.6%)

series229.0ms (2.8%)

simplify112.0ms (1.4%)

prune133.0ms (1.6%)

localize63.0ms (0.8%)

rewrite219.0ms (2.7%)

series273.0ms (3.3%)

simplify133.0ms (1.6%)

prune208.0ms (2.5%)

localize71.0ms (0.9%)

rewrite224.0ms (2.7%)

series260.0ms (3.1%)

simplify175.0ms (2.1%)

prune167.0ms (2%)

regimes2.7s (32.3%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.4s (28.7%)

Profiling