Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample147.0ms (2.6%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 63 to 33 computations (47.6% saved)

simplify45.0ms (0.8%)

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

prune2.0ms (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)

localize36.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series100.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

81.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
9.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
8.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
2.0ms	(*.f32 x (PI.f32))

rewrite17.0ms (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))

simplify122.0ms (2.2%)

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 → 150

Iterations

Useful iterations: 2 (0.0ms)

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

prune321.0ms (5.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	221	19	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	19	241

Error

0.1b

Counts

241 → 19

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 x (PI.f32))) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 (cbrt.f32 x) (PI.f32)))))
	1.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 x) (log.f32 (PI.f32))))) (.f32 x (PI.f32))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.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 (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))))
	2.7b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (.f32 (PI.f32) x) (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) 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 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	1.0b	(.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))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) 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))))) (/.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 (.f32 x (PI.f32))) (sqrt.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))))
	0.9b	(.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32)))) 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 (.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))))
	0.8b	(.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))))))
	4.1b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) (pow.f32 tau 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 1/5040 (.f32 (pow.f32 (.f32 (PI.f32) x) 6) (pow.f32 tau 6))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))

Compiler

Compiled 7709 to 1727 computations (77.6% saved)

localize45.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

10.0ms

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

rewrite6.0ms (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:

5.0ms

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

simplify46.0ms (0.8%)

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

prune278.0ms (4.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	237	5	242
Fresh	8	10	18
Picked	1	0	1
Done	0	0	0
Total	246	15	261

Error

0.1b

Counts

261 → 15

Alt Table

Status	Error	Program
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.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))))
	1.0b	(.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))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) 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 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (expm1.f32 (log1p.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))))
	0.9b	(.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 x (PI.f32))))
	1.2b	(.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))))
	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 (cbrt.f32 x) (PI.f32)))))
	2.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (pow.f32 (.f32 (PI.f32) x) 6) -1/5040 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) -1/6) (fma.f32 1/120 (pow.f32 (*.f32 (PI.f32) x) 4) 1))))
▶	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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))
	4.1b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) (pow.f32 tau 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 1/5040 (.f32 (pow.f32 (.f32 (PI.f32) x) 6) (pow.f32 tau 6))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.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))))

Compiler

Compiled 8116 to 1737 computations (78.6% saved)

localize117.0ms (2.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))
✓	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series8.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

8.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary32`
14×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
10×	`add-cube-cbrt_binary32`
6×	`associate-r_binary32`

Counts

2 → 56

Calls

2 calls:

4.0ms	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary32`
457×	`unswap-sqr_binary32`
455×	`distribute-rgt-neg-in_binary32`
396×	`distribute-lft-neg-in_binary32`
382×	`sqr-pow_binary32`

Counts

68 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	832
1	197	728
2	559	713
3	1172	688
4	2835	619
5	4154	619
6	4985	619
7	4941	619

prune198.0ms (3.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	155	4	159
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	159	15	174

Error

0.1b

Counts

174 → 15

Alt Table

Status	Error	Program
	2.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (pow.f32 (.f32 (PI.f32) x) 6) -1/5040 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) -1/6) (fma.f32 1/120 (pow.f32 (*.f32 (PI.f32) x) 4) 1))))
	0.9b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32))))))
	1.2b	(.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))))
	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 (cbrt.f32 x) (PI.f32)))))
	1.0b	(.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))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) tau))) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (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 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
▶	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))
	4.1b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) (pow.f32 tau 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 1/5040 (.f32 (pow.f32 (.f32 (PI.f32) x) 6) (pow.f32 tau 6))))) (/.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))))
	0.9b	(.f32 (log.f32 (exp.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))))

Compiler

Compiled 9583 to 1781 computations (81.4% saved)

localize87.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))
	1.0b	(*.f32 (PI.f32) (PI.f32))

series38.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
10.0ms	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))

rewrite9.0ms (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 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
1.0ms	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

802×	`associate-/r*_binary32`
515×	`associate-/l*_binary32`
404×	`fma-def_binary32`
301×	`cancel-sign-sub-inv_binary32`
246×	`associate-/l/_binary32`

Counts

82 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	1964
1	336	1727
2	1339	1709
3	4812	1709
4	5026	1709

prune229.0ms (4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	157	15	172

Error

0.1b

Counts

172 → 15

Alt Table

Status	Error	Program
	2.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (pow.f32 (.f32 (PI.f32) x) 6) -1/5040 (fma.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) -1/6) (fma.f32 1/120 (pow.f32 (*.f32 (PI.f32) x) 4) 1))))
	0.9b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.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))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32))))))
	1.2b	(.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))))
	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 (cbrt.f32 x) (PI.f32)))))
	1.2b	(.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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) tau))) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (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 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
✓	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (cbrt.f32 (/.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) 4) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) x)) 2))) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))))
	4.1b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) (pow.f32 tau 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) (.f32 tau tau))) (.f32 1/5040 (.f32 (pow.f32 (.f32 (PI.f32) x) 6) (pow.f32 tau 6))))) (/.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))))
	0.9b	(.f32 (log.f32 (exp.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))))

Compiler

Compiled 8884 to 1514 computations (83% saved)

regimes1.7s (29.9%)

Accuracy

Total 0.5b remaining (80.3%)

Threshold costs 0.5b (80.3%)

Counts

340 → 1

Compiler

Compiled 45948 to 23436 computations (49% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	70
1	18	70
2	18	70

end0.0ms (0%)

Compiler: Compiled 42 to 13 computations (69% saved)

sample1.9s (34%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
218.0ms	8000×	pre	128	true

Compiler

Compiled 675 to 327 computations (51.6% saved)

Details

analyze4.0ms (0.1%)

sample147.0ms (2.6%)

simplify45.0ms (0.8%)

prune2.0ms (0%)

localize36.0ms (0.6%)

series100.0ms (1.8%)

rewrite17.0ms (0.3%)

simplify122.0ms (2.2%)

prune321.0ms (5.7%)

localize45.0ms (0.8%)

series10.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify46.0ms (0.8%)

prune278.0ms (4.9%)

localize117.0ms (2.1%)

series8.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify94.0ms (1.7%)

prune198.0ms (3.5%)

localize87.0ms (1.5%)

series38.0ms (0.7%)

rewrite9.0ms (0.2%)

simplify72.0ms (1.3%)

prune229.0ms (4%)

regimes1.7s (29.9%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (34%)

Profiling