Details

analyze120.0ms (0.9%)

Algorithm

1×

Search

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample111.0ms (0.9%)

Algorithm

1×

intervals

Results

67.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 63 to 33 computations (47.6% saved)

simplify55.0ms (0.4%)

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

prune3.0ms (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

0.7b

Counts

2 → 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 69 to 30 computations (56.5% saved)

localize77.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series113.0ms (0.9%)

Counts

4 → 72

Calls

4 calls:

68.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
21.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
18.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
5.0ms	(*.f32 x (PI.f32))

rewrite36.0ms (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:

11.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
8.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
6.0ms	(*.f32 x (PI.f32))
4.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))

simplify146.0ms (1.2%)

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

prune541.0ms (4.3%)

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
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (log1p.f32 (expm1.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))))
	3.9b	(.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 tau 6) (pow.f32 (.f32 (PI.f32) x) 6))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.1b	(.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 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (*.f32 x (PI.f32))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (cbrt.f32 (sin.f32 (.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 (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)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	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))))
	0.9b	(.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))))
	2.8b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 (PI.f32) x)) (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))) tau) (/.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 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) 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)) (log.f32 (exp.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)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))

Compiler

Compiled 7531 to 1658 computations (78% saved)

localize87.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
	0.3b	(*.f32 x (PI.f32))
	0.4b	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series22.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

22.0ms

(/.f32 1 (/.f32 (*.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`times-frac_binary32`
22×	`add-exp-log_binary32`
17×	`*-un-lft-identity_binary32`
17×	`add-sqr-sqrt_binary32`
17×	`add-cube-cbrt_binary32`

Counts

1 → 58

Calls

1 calls:

10.0ms

(/.f32 1 (/.f32 (*.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))))

simplify120.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary32`
604×	`unswap-sqr_binary32`
443×	`associate-/l*_binary32`
398×	`associate-l_binary32`
360×	`associate-r_binary32`

Counts

70 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1611
1	224	1406
2	750	1357
3	3377	1349
4	5340	1349

prune673.0ms (5.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	276	6	282
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	281	18	299

Error

0.1b

Counts

299 → 18

Alt Table

Status	Error	Program
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	2.8b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 (PI.f32) x)) (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) tau)) (/.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 (/.f32 1 (/.f32 x (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))))) (/.f32 (PI.f32) (cbrt.f32 (sin.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 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (log1p.f32 (expm1.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))))
	0.7b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))) tau) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.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 1 (.f32 (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))) (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))))) (/.f32 1 (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (cbrt.f32 (sin.f32 (.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 (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)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	3.9b	(.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 tau 6) (pow.f32 (.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 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x))) tau)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.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 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) 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)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	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)) (expm1.f32 (log1p.f32 (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))))

Compiler

Compiled 9500 to 2460 computations (74.1% saved)

localize87.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series21.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

21.0ms

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 24

Calls

1 calls:

8.0ms

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

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

632×	`fma-def_binary32`
589×	`unswap-sqr_binary32`
559×	`cancel-sign-sub-inv_binary32`
346×	`times-frac_binary32`
313×	`fma-neg_binary32`

Counts

36 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	738
1	208	651
2	631	644
3	2606	636
4	5267	636

prune591.0ms (4.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	235	5	240
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	239	19	258

Error

0.1b

Counts

258 → 19

Alt Table

Status	Error	Program
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	2.8b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 (PI.f32) x)) (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) tau)) (/.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 (/.f32 1 (/.f32 x (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))))) (/.f32 (PI.f32) (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (expm1.f32 (log1p.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 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (log1p.f32 (expm1.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))))
	0.7b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))) tau) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.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 1 (.f32 (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))) (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))))) (/.f32 1 (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))))))
	1.1b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (cbrt.f32 (sin.f32 (.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 (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)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x))) tau)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))
	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) 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)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	1.0b	(.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 (expm1.f32 (log1p.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)) (expm1.f32 (log1p.f32 (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))))

Compiler

Compiled 8190 to 1790 computations (78.1% saved)

localize130.0ms (1%)

Local error

Found 4 expressions with local error:

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

series70.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

65.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau))
5.0ms	(*.f32 (PI.f32) x)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary32`
9×	`add-exp-log_binary32`
8×	`add-sqr-sqrt_binary32`
6×	`*-un-lft-identity_binary32`
6×	`add-cube-cbrt_binary32`

Counts

2 → 43

Calls

2 calls:

8.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau))
5.0ms	(*.f32 (PI.f32) x)

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary32`
620×	`associate-/r*_binary32`
413×	`associate-/l*_binary32`
409×	`fma-def_binary32`
262×	`*-commutative_binary32`

Counts

67 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1428
1	262	1277
2	938	1269
3	4177	1259
4	4848	1259
5	4985	1259
6	4940	1259

prune471.0ms (3.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	183	18	201

Error

0.1b

Counts

201 → 18

Alt Table

Status	Error	Program
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	2.8b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 (PI.f32) x)) (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) tau)) (/.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 (/.f32 1 (/.f32 x (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))))) (/.f32 (PI.f32) (cbrt.f32 (sin.f32 (*.f32 x (PI.f32)))))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (log1p.f32 (expm1.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) x)) (sqrt.f32 (.f32 (PI.f32) x)))))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x))) tau)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))
	0.7b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))) tau) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.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 1 (.f32 (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))) (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))))) (/.f32 1 (cbrt.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))))))
	1.1b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (cbrt.f32 (sin.f32 (.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 (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)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) 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)) (log.f32 (exp.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)) (expm1.f32 (log1p.f32 (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))))

Compiler

Compiled 6190 to 1282 computations (79.3% saved)

regimes5.0s (39.5%)

Accuracy

Total 0.6b remaining (81%)

Threshold costs 0.6b (81%)

Counts

467 → 1

Compiler

Compiled 60086 to 31874 computations (47% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	20	39
2	19	39

end1.0ms (0%)

Compiler: Compiled 25 to 13 computations (48% saved)

sample3.9s (30.7%)

Algorithm

1×

intervals

Results

2.0s	8000×	body	128	valid
415.0ms	8000×	pre	128	true

Compiler

Compiled 627 to 306 computations (51.2% saved)

Details

analyze120.0ms (0.9%)

sample111.0ms (0.9%)

simplify55.0ms (0.4%)

prune3.0ms (0%)

localize77.0ms (0.6%)

series113.0ms (0.9%)

rewrite36.0ms (0.3%)

simplify146.0ms (1.2%)

prune541.0ms (4.3%)

localize87.0ms (0.7%)

series22.0ms (0.2%)

rewrite20.0ms (0.2%)

simplify120.0ms (0.9%)

prune673.0ms (5.3%)

localize87.0ms (0.7%)

series21.0ms (0.2%)

rewrite10.0ms (0.1%)

simplify83.0ms (0.7%)

prune591.0ms (4.7%)

localize130.0ms (1%)

series70.0ms (0.6%)

rewrite18.0ms (0.1%)

simplify164.0ms (1.3%)

prune471.0ms (3.7%)

regimes5.0s (39.5%)

simplify5.0ms (0%)

end1.0ms (0%)

sample3.9s (30.7%)

Profiling