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)

sample2.3s (32.7%)

Results

2.2s

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

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 (0.5%)

Local error

Found 4 expressions with local error:

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

series62.0ms (0.9%)

Counts

4 → 84

Calls

4 calls:

32.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
12.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
11.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
7.0ms	(.f32 (.f32 x (PI.f32)) tau)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

6.0ms	(/.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 (.f32 x (PI.f32)) tau)
3.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

479×	`fma-def_binary32`
343×	`associate-/l/_binary32`
321×	`cancel-sign-sub-inv_binary32`
297×	`associate-*l/_binary32`
238×	`unswap-sqr_binary32`

Counts

161 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3095
1	483	2723
2	1876	2698
3	4615	2698
4	5047	2698

prune222.0ms (3.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	158	17	175
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	17	176

Error

0.1b

Counts

176 → 17

Alt Table

Status	Error	Program
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (exp.f32 (+.f32 (+.f32 (log.f32 x) (log.f32 (PI.f32))) (log.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 x (PI.f32)) tau)) (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))) (/.f32 x (/.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.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))))
	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 x (PI.f32)))) x) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32))))
	1.8b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x (PI.f32))) (/.f32 (sqrt.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 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.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 (cbrt.f32 (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.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)))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (PI.f32)) (.f32 (cbrt.f32 tau) (cbrt.f32 tau))) (cbrt.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 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	4.3b	(.f32 (/.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (expm1.f32 (log1p.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))))
	4.0b	(.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))))
	1.9b	(.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)))))
	0.8b	(.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) 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)) (expm1.f32 (log1p.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 6093 to 1499 computations (75.4% saved)

localize44.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series32.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

32.0ms

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

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:

3.0ms

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

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary32`
531×	`distribute-rgt-neg-in_binary32`
530×	`associate-r_binary32`
530×	`associate-l_binary32`
260×	`associate-/r*_binary32`

Counts

53 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1550
1	199	1460
2	635	1452
3	3711	1452
4	5224	1452

prune218.0ms (3.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	182	5	187
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	186	18	204

Error

0.1b

Counts

204 → 18

Alt Table

Status	Error	Program
	1.5b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (.f32 (.f32 x (PI.f32)) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (PI.f32) x) (.f32 (cbrt.f32 tau) (cbrt.f32 tau))) (cbrt.f32 tau))) (expm1.f32 (log1p.f32 (.f32 (.f32 x (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)) (exp.f32 (+.f32 (+.f32 (log.f32 x) (log.f32 (PI.f32))) (log.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 x (PI.f32)) tau)) (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))) (/.f32 x (/.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.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))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (.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 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)))))))
	1.7b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.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 x (PI.f32)))) x) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.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))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (PI.f32)) (.f32 (cbrt.f32 tau) (cbrt.f32 tau))) (cbrt.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 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	4.3b	(.f32 (/.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (expm1.f32 (log1p.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))))
	4.0b	(.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))))
	0.8b	(.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.3b	(.f32 (/.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (expm1.f32 (log1p.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 6958 to 1628 computations (76.6% saved)

localize41.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

36.0ms

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary32`
19×	`prod-exp_binary32`
15×	`add-cbrt-cube_binary32`
7×	`associate-r_binary32`
7×	`cbrt-unprod_binary32`

Counts

1 → 38

Calls

1 calls:

9.0ms

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

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

979×	`times-frac_binary32`
580×	`associate-/r*_binary32`
281×	`associate-*r/_binary32`
267×	`associate-*l/_binary32`
212×	`associate-/l*_binary32`

Counts

62 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	1618
1	286	1399
2	974	1391
3	4620	1391
4	4994	1391
5	4957	1391

prune222.0ms (3.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	184	5	189
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	190	17	207

Error

0.1b

Counts

207 → 17

Alt Table

Status	Error	Program
	1.5b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (.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 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) x) (PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (PI.f32) x) (.f32 (cbrt.f32 tau) (cbrt.f32 tau))) (cbrt.f32 tau))) (expm1.f32 (log1p.f32 (.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 x (PI.f32)) tau)) (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))) (/.f32 x (/.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.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))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.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))))
▶	0.8b	(.f32 (expm1.f32 (log1p.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 1 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (*.f32 (PI.f32) x))))
	4.3b	(.f32 (/.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (expm1.f32 (log1p.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.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))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (.f32 (.f32 x (PI.f32)) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (PI.f32)) (.f32 (cbrt.f32 tau) (cbrt.f32 tau))) (cbrt.f32 tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.3b	(.f32 (.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	4.0b	(.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))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) x)) (/.f32 1 tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 6792 to 2001 computations (70.5% saved)

localize50.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series79.0ms (1.1%)

Counts

4 → 40

Calls

4 calls:

31.0ms	(expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))))
30.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
9.0ms	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
8.0ms	(.f32 (PI.f32) (.f32 tau x))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary32`
18×	`add-exp-log_binary32`
9×	`pow1_binary32`
7×	`*-un-lft-identity_binary32`
7×	`add-sqr-sqrt_binary32`

Counts

4 → 65

Calls

4 calls:

6.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
4.0ms	(.f32 (PI.f32) (.f32 tau x))
2.0ms	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
0.0ms	(expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))))

simplify347.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

734×	`associate-/r*_binary32`
452×	`associate-/l*_binary32`
401×	`fma-def_binary32`
290×	`cancel-sign-sub-inv_binary32`
196×	`unswap-sqr_binary32`

Counts

105 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2602
1	346	2268
2	1303	2236
3	4689	2236
4	4985	2236
5	4975	2236

prune124.0ms (1.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	103	17	120

Error

0.1b

Counts

120 → 17

Alt Table

Status	Error	Program
	1.5b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (.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 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) x) (PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (PI.f32) x) (.f32 (cbrt.f32 tau) (cbrt.f32 tau))) (cbrt.f32 tau))) (expm1.f32 (log1p.f32 (.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 x (PI.f32)) tau)) (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))) (/.f32 x (/.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.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 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.0b	(.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))))
	0.9b	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) x)) (/.f32 1 tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.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 1 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (*.f32 (PI.f32) x))))
	4.3b	(.f32 (/.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (expm1.f32 (log1p.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (cbrt.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))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (.f32 (.f32 x (PI.f32)) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (PI.f32)) (.f32 (cbrt.f32 tau) (cbrt.f32 tau))) (cbrt.f32 tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.3b	(.f32 (.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.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))))

Compiler

Compiled 3734 to 1029 computations (72.4% saved)

regimes2.6s (37.3%)

Accuracy

Total 0.5b remaining (79.5%)

Threshold costs 0.5b (79.5%)

Counts

427 → 1

Compiler

Compiled 56214 to 28788 computations (48.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	19	41
2	19	41

end237.0ms (3.4%)

Compiler: Compiled 588 to 306 computations (48% saved)

Details

analyze3.0ms (0%)

sample2.3s (32.7%)

simplify47.0ms (0.7%)

prune2.0ms (0%)

localize36.0ms (0.5%)

series62.0ms (0.9%)

rewrite22.0ms (0.3%)

simplify99.0ms (1.4%)

prune222.0ms (3.1%)

localize44.0ms (0.6%)

series32.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify74.0ms (1%)

prune218.0ms (3.1%)

localize41.0ms (0.6%)

series37.0ms (0.5%)

rewrite14.0ms (0.2%)

simplify86.0ms (1.2%)

prune222.0ms (3.1%)

localize50.0ms (0.7%)

series79.0ms (1.1%)

rewrite15.0ms (0.2%)

simplify347.0ms (4.9%)

prune124.0ms (1.7%)

regimes2.6s (37.3%)

simplify3.0ms (0%)

end237.0ms (3.4%)

Profiling