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 (26.2%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify44.0ms (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)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series51.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

29.0ms	(/.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))

rewrite29.0ms (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:

14.0ms	(*.f32 x (PI.f32))
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)))
2.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))

simplify83.0ms (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

prune271.0ms (3.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	221	16	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	16	238

Error

0.1b

Counts

238 → 16

Alt Table

Status	Error	Program
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 x (PI.f32)) (sqrt.f32 (sin.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.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))))
	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 (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)))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (.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))))))
	3.7b	(.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 (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))))

Compiler

Compiled 7421 to 1630 computations (78% saved)

localize39.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

10.0ms

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

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary32`
10×	`add-cbrt-cube_binary32`
10×	`prod-exp_binary32`
7×	`associate-r_binary32`
6×	`add-sqr-sqrt_binary32`

Counts

1 → 34

Calls

1 calls:

7.0ms

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

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary32`
596×	`unswap-sqr_binary32`
420×	`associate-l_binary32`
399×	`times-frac_binary32`
363×	`associate-r_binary32`

Counts

46 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	857
1	213	735
2	667	728
3	2897	720
4	4896	720
5	4984	720
6	4965	720

prune353.0ms (4.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	245	5	250
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	250	16	266

Error

0.1b

Counts

266 → 16

Alt Table

Status	Error	Program
	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 1 (.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 x (PI.f32)) (sqrt.f32 (sin.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (*.f32 x (PI.f32)))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.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 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 (expm1.f32 (log1p.f32 (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (.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 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 1 (*.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))))))
	0.8b	(.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)))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
	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 1 (.f32 (.f32 (cbrt.f32 (.f32 (PI.f32) x)) (cbrt.f32 (.f32 (PI.f32) x))) (cbrt.f32 (.f32 (PI.f32) x))))))
	3.7b	(.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))))

Compiler

Compiled 8269 to 2345 computations (71.6% saved)

localize39.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite10.0ms (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 (*.f32 x (PI.f32)))))

simplify70.0ms (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	107	1611
1	224	1406
2	750	1357
3	3377	1349
4	5340	1349

prune331.0ms (4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	276	6	282
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	282	16	298

Error

0.1b

Counts

298 → 16

Alt Table

Status	Error	Program
▶	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 1 (.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 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	0.9b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.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 1 (.f32 (cbrt.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))) (cbrt.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))) (cbrt.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))))
	3.1b	(.f32 (/.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (sqrt.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))))))
	0.8b	(.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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 x (PI.f32)) (sqrt.f32 (sin.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (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 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (.f32 x (PI.f32)))))
	1.4b	(.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 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))))
	0.8b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (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 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 1 (*.f32 x (PI.f32)))))
	3.7b	(.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))))

Compiler

Compiled 9356 to 2414 computations (74.2% saved)

localize43.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

29.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
7.0ms	(.f32 (PI.f32) (.f32 tau x))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
7×	`pow1_binary32`
6×	`cbrt-unprod_binary32`
6×	`prod-exp_binary32`

Counts

2 → 45

Calls

2 calls:

5.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
4.0ms	(.f32 (PI.f32) (.f32 tau x))

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

997×	`times-frac_binary32`
670×	`associate-/r*_binary32`
418×	`associate-/l*_binary32`
213×	`fma-def_binary32`
176×	`associate-/l/_binary32`

Counts

53 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1266
1	262	1046
2	939	1032
3	4621	1032
4	4990	1032
5	4985	1032

prune277.0ms (3.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	194	15	209

Error

0.1b

Counts

209 → 15

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 1 (.f32 x (PI.f32))))))
	0.9b	(.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (.f32 (PI.f32) (.f32 tau x)))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.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 1 (.f32 (cbrt.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))) (cbrt.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))) (cbrt.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 x (PI.f32)) (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))))))
	1.2b	(.f32 (/.f32 (sin.f32 (.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 (PI.f32) (.f32 tau x))) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (.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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (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 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (.f32 x (PI.f32)))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (.f32 (sin.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (/.f32 1 (.f32 x (PI.f32)))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (log.f32 (exp.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 1 (.f32 x (PI.f32)))))))
	3.7b	(.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))))
	3.1b	(.f32 (/.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (sqrt.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))))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (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 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 1 (*.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 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))

Compiler

Compiled 6128 to 1632 computations (73.4% saved)

regimes4.0s (48.2%)

Accuracy

Total 0.6b remaining (79.5%)

Threshold costs 0.6b (79.5%)

Counts

589 → 1

Compiler

Compiled 69740 to 36744 computations (47.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	82
1	21	82
2	21	82

end222.0ms (2.7%)

Compiler: Compiled 611 to 277 computations (54.7% saved)

Details

analyze3.0ms (0%)

sample2.2s (26.2%)

simplify44.0ms (0.5%)

prune2.0ms (0%)

localize34.0ms (0.4%)

series51.0ms (0.6%)

rewrite29.0ms (0.3%)

simplify83.0ms (1%)

prune271.0ms (3.3%)

localize39.0ms (0.5%)

series10.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify80.0ms (1%)

prune353.0ms (4.2%)

localize39.0ms (0.5%)

series9.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify70.0ms (0.8%)

prune331.0ms (4%)

localize43.0ms (0.5%)

series36.0ms (0.4%)

rewrite12.0ms (0.1%)

simplify70.0ms (0.8%)

prune277.0ms (3.3%)

regimes4.0s (48.2%)

simplify3.0ms (0%)

end222.0ms (2.7%)

Profiling