Details

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample2.2s (31.1%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify47.0ms (0.7%)

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 → 1

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

prune1.0ms (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

0.6b

Counts

2 → 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 69 to 30 computations (56.5% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 x (PI.f32))
✓	0.3b	(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))

series44.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

26.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
10.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
6.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
2.0ms	(*.f32 x (PI.f32))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

5.0ms	(/.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))
1.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

805×	`associate-/l*_binary32`
347×	`fma-def_binary32`
320×	`cancel-sign-sub-inv_binary32`
307×	`associate-/l/_binary32`
235×	`unswap-sqr_binary32`

Counts

149 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2890
1	484	2546
2	1854	2521
3	4970	2521

prune326.0ms (4.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	220	17	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	17	238

Error

0.1b

Counts

238 → 17

Alt Table

Status	Error	Program
	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))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))))
	0.8b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	4.8b	(.f32 (/.f32 (log.f32 (exp.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))))
	0.6b	(.f32 (/.f32 (expm1.f32 (log1p.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))))
	0.8b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.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 (sin.f32 (.f32 x (PI.f32))) x) (PI.f32)))
	0.9b	(.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))))
	0.8b	(.f32 (log.f32 (exp.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))))
	2.6b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.6b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6)))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (pow.f32 tau 2) (pow.f32 x 2)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) 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)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (.f32 1/5040 (pow.f32 (.f32 (PI.f32) x) 6)))))

Compiler

Compiled 7503 to 1686 computations (77.5% saved)

localize48.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 x (PI.f32))
✓	0.3b	(sin.f32 (.f32 (log1p.f32 (expm1.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 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))

series34.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(/.f32 (sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))
7.0ms	(sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary32`
11×	`add-exp-log_binary32`
4×	`*-un-lft-identity_binary32`
4×	`add-sqr-sqrt_binary32`
4×	`add-cube-cbrt_binary32`

Counts

2 → 34

Calls

2 calls:

5.0ms	(/.f32 (sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))
1.0ms	(sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

894×	`times-frac_binary32`
502×	`associate-/l*_binary32`
315×	`fma-def_binary32`
226×	`unswap-sqr_binary32`
211×	`cancel-sign-sub-inv_binary32`

Counts

82 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1967
1	349	1730
2	1313	1718
3	4752	1718
4	5023	1718

prune311.0ms (4.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	237	17	254

Error

0.1b

Counts

254 → 17

Alt Table

Status	Error	Program
	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))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))))
	0.8b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	4.8b	(.f32 (/.f32 (log.f32 (exp.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))))
	0.6b	(.f32 (/.f32 (expm1.f32 (log1p.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))))
	0.8b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.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 (sin.f32 (.f32 x (PI.f32))) x) (PI.f32)))
	0.9b	(.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))))
	0.8b	(.f32 (log.f32 (exp.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))))
	2.6b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.6b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
✓	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) 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)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (.f32 1/5040 (pow.f32 (.f32 (PI.f32) x) 6)))))

Compiler

Compiled 7924 to 1746 computations (78% saved)

localize47.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 x (PI.f32))
	0.3b	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series9.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(/.f32 (sin.f32 (*.f32 x (PI.f32))) (expm1.f32 (log1p.f32 (*.f32 x (PI.f32)))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary32`
9×	`times-frac_binary32`
9×	`add-sqr-sqrt_binary32`
9×	`add-cube-cbrt_binary32`
3×	`associate-/r*_binary32`

Counts

1 → 29

Calls

1 calls:

4.0ms

(/.f32 (sin.f32 (*.f32 x (PI.f32))) (expm1.f32 (log1p.f32 (*.f32 x (PI.f32)))))

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

542×	`fma-neg_binary32`
508×	`fma-def_binary32`
487×	`cancel-sign-sub-inv_binary32`
408×	`associate-/r/_binary32`
361×	`unswap-sqr_binary32`

Counts

41 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	913
1	167	855
2	479	851
3	1839	840
4	4607	840
5	4999	840

prune334.0ms (4.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	253	16	269

Error

0.0b

Counts

269 → 16

Alt Table

Status	Error	Program
	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))))
	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))) (expm1.f32 (log1p.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))))
	0.8b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	4.8b	(.f32 (/.f32 (log.f32 (exp.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))))
▶	0.6b	(.f32 (/.f32 (expm1.f32 (log1p.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))))
	0.8b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.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 (sin.f32 (.f32 x (PI.f32))) x) (PI.f32)))
	2.7b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
	1.0b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.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))))
	0.8b	(.f32 (log.f32 (exp.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))))
	2.6b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
✓	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (.f32 1/5040 (pow.f32 (.f32 (PI.f32) x) 6)))))

Compiler

Compiled 8442 to 1762 computations (79.1% saved)

localize43.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 x (PI.f32))
	0.3b	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (.f32 x (PI.f32)) tau))

series29.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

29.0ms

(/.f32 (expm1.f32 (log1p.f32 (sin.f32 (*.f32 (*.f32 x (PI.f32)) tau)))) (*.f32 (*.f32 x (PI.f32)) tau))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary32`
10×	`add-exp-log_binary32`
3×	`associate-/l*_binary32`
3×	`*-un-lft-identity_binary32`
3×	`times-frac_binary32`

Counts

1 → 26

Calls

1 calls:

4.0ms

(/.f32 (expm1.f32 (log1p.f32 (sin.f32 (*.f32 (*.f32 x (PI.f32)) tau)))) (*.f32 (*.f32 x (PI.f32)) tau))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

793×	`times-frac_binary32`
678×	`associate-/r*_binary32`
448×	`associate-/l*_binary32`
394×	`fma-def_binary32`
274×	`*-commutative_binary32`

Counts

50 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	1382
1	267	1210
2	934	1202
3	4376	1198
4	4975	1198
5	4954	1198

prune293.0ms (4.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	2	12	14
Picked	0	1	1
Done	0	1	1
Total	239	16	255

Error

0.0b

Counts

255 → 16

Alt Table

Status	Error	Program
	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))))
	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))) (expm1.f32 (log1p.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))))
	0.8b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
✓	0.6b	(.f32 (/.f32 (expm1.f32 (log1p.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))))
	0.8b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.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 (sin.f32 (.f32 x (PI.f32))) x) (PI.f32)))
	2.7b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
	1.0b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.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))))
	0.8b	(.f32 (log.f32 (exp.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))))
	1.1b	(.f32 (/.f32 (expm1.f32 (log1p.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))))
	4.8b	(.f32 (/.f32 (log.f32 (exp.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))))
✓	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.6b	(.f32 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 (.f32 tau tau) (.f32 x x)) -1/6) (fma.f32 (.f32 (pow.f32 tau 6) (pow.f32 x 6)) (.f32 (pow.f32 (PI.f32) 6) -1/5040) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) (.f32 1/5040 (pow.f32 (.f32 (PI.f32) x) 6)))))

Compiler

Compiled 7503 to 1539 computations (79.5% saved)

regimes2.6s (37.6%)

Accuracy

Total 0.5b remaining (75.7%)

Threshold costs 0.5b (75.7%)

Counts

447 → 1

Compiler

Compiled 54816 to 28180 computations (48.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	18	40
2	18	40

end251.0ms (3.6%)

Compiler: Compiled 557 to 283 computations (49.2% saved)

Details

analyze3.0ms (0%)

sample2.2s (31.1%)

simplify47.0ms (0.7%)

prune1.0ms (0%)

localize33.0ms (0.5%)

series44.0ms (0.6%)

rewrite19.0ms (0.3%)

simplify75.0ms (1.1%)

prune326.0ms (4.7%)

localize48.0ms (0.7%)

series34.0ms (0.5%)

rewrite11.0ms (0.2%)

simplify77.0ms (1.1%)

prune311.0ms (4.5%)

localize47.0ms (0.7%)

series9.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify66.0ms (0.9%)

prune334.0ms (4.8%)

localize43.0ms (0.6%)

series29.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify74.0ms (1.1%)

prune293.0ms (4.2%)

regimes2.6s (37.6%)

simplify2.0ms (0%)

end251.0ms (3.6%)

Profiling