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)

sample2.0s (27.3%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify45.0ms (0.6%)

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))
✓	0.4b	(*.f32 x (PI.f32))
✓	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series43.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

25.0ms	(/.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)))
7.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
3.0ms	(*.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:

7.0ms	(/.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))

simplify78.0ms (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

prune301.0ms (4%)

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
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	2.1b	(.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 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (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))))
	4.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.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 x) (.f32 (sqrt.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))))
	1.3b	(.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))))
	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)))) (cbrt.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 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.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 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.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 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.1b	(.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))))
	2.7b	(.f32 (exp.f32 (log.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))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 7463 to 1656 computations (77.8% saved)

localize46.0ms (0.6%)

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

series26.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

26.0ms

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

rewrite7.0ms (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 → 23

Calls

1 calls:

5.0ms

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

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

741×	`associate-l_binary32`
650×	`associate-r_binary32`
538×	`times-frac_binary32`
435×	`associate-/r*_binary32`
318×	`associate-/l*_binary32`

Counts

47 → 46

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	1261
1	215	1130
2	777	1122
3	4837	1122
4	5023	1122

prune565.0ms (7.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	234	17	251

Error

0.1b

Counts

251 → 17

Alt Table

Status	Error	Program
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	2.1b	(.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 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.1b	(.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))))
	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))))
	4.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.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 x) (.f32 (sqrt.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))))
	1.3b	(.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))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.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 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.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 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.7b	(.f32 (exp.f32 (log.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))))
✓	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.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 (PI.f32) (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 7874 to 1761 computations (77.6% saved)

localize64.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series18.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

18.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) (.f32 x (PI.f32)))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) (.f32 x (PI.f32)))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

716×	`times-frac_binary32`
491×	`unswap-sqr_binary32`
397×	`fma-def_binary32`
395×	`associate-/r*_binary32`
280×	`cancel-sign-sub-inv_binary32`

Counts

62 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	1398
1	239	931
2	807	793
3	2948	781
4	4624	754
5	4736	754
6	4993	754
7	4934	754

prune333.0ms (4.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	217	4	221
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	219	19	238

Error

0.1b

Counts

238 → 19

Alt Table

Status	Error	Program
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.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 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) x) (PI.f32)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	2.1b	(.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)))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))) tau)) (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.1b	(.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 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (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))))
	4.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.f32 (sin.f32 (.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 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 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.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))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.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 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))) (PI.f32))))
	2.7b	(.f32 (exp.f32 (log.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))))
	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 x) (.f32 (sqrt.f32 x) (PI.f32)))))
	1.2b	(.f32 (/.f32 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 9029 to 1806 computations (80% saved)

localize71.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))) x) (PI.f32))
	1.0b	(*.f32 (PI.f32) (PI.f32))

series17.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

17.0ms

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary32`
43×	`*-un-lft-identity_binary32`
43×	`add-sqr-sqrt_binary32`
43×	`add-cube-cbrt_binary32`
13×	`associate-/l*_binary32`

Counts

1 → 72

Calls

1 calls:

6.0ms

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

simplify111.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

528×	`cancel-sign-sub-inv_binary32`
519×	`fma-def_binary32`
391×	`unswap-sqr_binary32`
384×	`associate-/l/_binary32`
367×	`associate-/r*_binary32`

Counts

84 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	3960
1	415	3041
2	1015	3037
3	3233	2717
4	5342	2717

prune429.0ms (5.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	280	3	283
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	284	18	302

Error

0.1b

Counts

302 → 18

Alt Table

Status	Error	Program
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	2.1b	(.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)))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))) tau)) (.f32 (expm1.f32 (log1p.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 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (exp.f32 (log.f32 (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) x) (PI.f32)))
	5.1b	(.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))))
	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))))
	4.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1)) (/.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 x) (.f32 (sqrt.f32 x) (PI.f32)))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))) (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) (.f32 (cbrt.f32 x) (cbrt.f32 x))) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))) (cbrt.f32 x)) (cbrt.f32 (PI.f32)))))
✓	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (expm1.f32 (log1p.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 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) (*.f32 x (PI.f32))))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.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 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))) (PI.f32))))
	2.7b	(.f32 (exp.f32 (log.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))))
	1.2b	(.f32 (/.f32 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (expm1.f32 (log1p.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 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) (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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 11847 to 2437 computations (79.4% saved)

regimes2.8s (37.3%)

Accuracy

Total 0.5b remaining (79.2%)

Threshold costs 0.5b (79.2%)

Counts

496 → 1

Compiler

Compiled 64240 to 34484 computations (46.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	18	40
2	18	40

end247.0ms (3.3%)

Compiler: Compiled 676 to 343 computations (49.3% saved)

Details

analyze3.0ms (0%)

sample2.0s (27.3%)

simplify45.0ms (0.6%)

prune2.0ms (0%)

localize34.0ms (0.4%)

series43.0ms (0.6%)

rewrite18.0ms (0.2%)

simplify78.0ms (1%)

prune301.0ms (4%)

localize46.0ms (0.6%)

series26.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify66.0ms (0.9%)

prune565.0ms (7.5%)

localize64.0ms (0.9%)

series18.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify102.0ms (1.4%)

prune333.0ms (4.4%)

localize71.0ms (0.9%)

series17.0ms (0.2%)

rewrite14.0ms (0.2%)

simplify111.0ms (1.5%)

prune429.0ms (5.7%)

regimes2.8s (37.3%)

simplify2.0ms (0%)

end247.0ms (3.3%)

Profiling