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)

sample2.7s (27.4%)

Results

2.6s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 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)

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series56.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

35.0ms	(/.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)))
9.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
2.0ms	(*.f32 x (PI.f32))

rewrite18.0ms (0.2%)

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)))
4.0ms	(*.f32 x (PI.f32))
1.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))

simplify85.0ms (0.9%)

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

prune368.0ms (3.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	224	16	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	16	241

Error

0.1b

Counts

241 → 16

Alt Table

Status	Error	Program
	0.9b	(.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))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) tau) (/.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 (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))) (/.f32 (.f32 x (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 x (PI.f32))) (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (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))))
	0.7b	(.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 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (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)))))
	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 x) (cbrt.f32 x)) (*.f32 (cbrt.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 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.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))))
	0.9b	(.f32 (/.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 x 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 (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))))

Compiler

Compiled 7429 to 1621 computations (78.2% saved)

localize48.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series15.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32)))
5.0ms	(expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

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

simplify55.0ms (0.6%)

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

59 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	890
1	213	793
2	640	786
3	2625	778
4	5318	778

prune246.0ms (2.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	231	5	236
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	237	15	252

Error

0.0b

Counts

252 → 15

Alt Table

Status	Error	Program
	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 x) (cbrt.f32 x)) (*.f32 (cbrt.f32 x) (PI.f32)))))
	1.7b	(.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))))
	1.2b	(.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 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (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 (expm1.f32 (log1p.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))))
	0.7b	(.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 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sqrt.f32 (expm1.f32 (log1p.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 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.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))))
	0.9b	(.f32 (/.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 x 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 (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))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32))))

Compiler

Compiled 7612 to 1567 computations (79.4% saved)

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
	0.4b	(*.f32 x (PI.f32))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.5b	(/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))))

series37.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

37.0ms

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

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 62

Calls

1 calls:

6.0ms

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

simplify121.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

670×	`associate-/r*_binary32`
461×	`fma-def_binary32`
400×	`associate-*l/_binary32`
345×	`associate-/r/_binary32`
340×	`*-commutative_binary32`

Counts

86 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	2606
1	306	2289
2	1139	2239
3	4321	2235
4	4958	2235
5	4951	2235

prune318.0ms (3.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	285	16	301

Error

0.0b

Counts

301 → 16

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 (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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.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))))
	1.1b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (PI.f32) (cbrt.f32 x))) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
✓	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.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 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))))) (*.f32 x (PI.f32))))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (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 (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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.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))))
	0.9b	(.f32 (/.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 x 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 (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))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32))))

Compiler

Compiled 9424 to 2405 computations (74.5% saved)

localize49.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))
	0.4b	(*.f32 x (PI.f32))
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
✓	0.4b	(/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))))))

series11.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

11.0ms

(/.f32 1 (/.f32 (*.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32)))))))

rewrite9.0ms (0.1%)

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:

5.0ms

(/.f32 1 (/.f32 (*.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32)))))))

simplify75.0ms (0.8%)

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	109	1611
1	226	1406
2	752	1357
3	3379	1349
4	5342	1349

prune344.0ms (3.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	274	4	278
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	278	16	294

Error

0.0b

Counts

294 → 16

Alt Table

Status	Error	Program
	0.9b	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 tau (neg.f32 (.f32 (PI.f32) x)))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))))
	1.7b	(.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))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (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 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x))) tau)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	0.8b	(.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))))
	1.1b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (PI.f32) (cbrt.f32 x))) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
✓	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (expm1.f32 (log1p.f32 (*.f32 x (PI.f32))))))))
	0.7b	(.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (sqrt.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (/.f32 1 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.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))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (.f32 x (PI.f32))))

Compiler

Compiled 9133 to 2115 computations (76.8% saved)

regimes4.8s (48.1%)

Accuracy

Total 0.5b remaining (75.8%)

Threshold costs 0.5b (75.8%)

Counts

431 → 1

Compiler

Compiled 50700 to 27136 computations (46.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	16	44
2	16	44

end419.0ms (4.2%)

Compiler: Compiled 521 to 278 computations (46.6% saved)

Details

analyze3.0ms (0%)

sample2.7s (27.4%)

simplify48.0ms (0.5%)

prune2.0ms (0%)

localize41.0ms (0.4%)

series56.0ms (0.6%)

rewrite18.0ms (0.2%)

simplify85.0ms (0.9%)

prune368.0ms (3.7%)

localize48.0ms (0.5%)

series15.0ms (0.1%)

rewrite8.0ms (0.1%)

simplify55.0ms (0.6%)

prune246.0ms (2.5%)

localize40.0ms (0.4%)

series37.0ms (0.4%)

rewrite13.0ms (0.1%)

simplify121.0ms (1.2%)

prune318.0ms (3.2%)

localize49.0ms (0.5%)

series11.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify75.0ms (0.8%)

prune344.0ms (3.5%)

regimes4.8s (48.1%)

simplify4.0ms (0%)

end419.0ms (4.2%)

Profiling