Details

analyze91.0ms (1.6%)

Algorithm

1×

Search

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample56.0ms (1%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 63 to 33 computations (47.6% saved)

simplify48.0ms (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)

localize34.0ms (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 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series53.0ms (0.9%)

Counts

4 → 72

Calls

4 calls:

30.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
11.0ms	(/.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 (0.3%)

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

simplify74.0ms (1.3%)

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

prune284.0ms (4.9%)

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
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (log1p.f32 (expm1.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))))
	1.5b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) x)))) (*.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 (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 tau 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 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.1b	(.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))))
	6.3b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) -1/6 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 (.f32 x (PI.f32)) tau)) (/.f32 (sin.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)) (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 x (PI.f32)))) (+.f32 (log.f32 x) (log.f32 (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)))))
	3.0b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (+.f32 (log.f32 (.f32 x (PI.f32))) (log.f32 tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.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 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (cbrt.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)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	1.0b	(.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))))

Compiler

Compiled 7481 to 1640 computations (78.1% saved)

localize42.0ms (0.7%)

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 (expm1.f32 (log1p.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))

series11.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

11.0ms

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

rewrite5.0ms (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:

4.0ms

(/.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

prune273.0ms (4.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	236	4	240
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	240	16	256

Error

0.1b

Counts

256 → 16

Alt Table

Status	Error	Program
	4.6b	(.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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.2b	(.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 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.5b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) x)))) (*.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 (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 tau 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 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.1b	(.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))))
✓	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))))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 x (PI.f32)))) (+.f32 (log.f32 x) (log.f32 (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)))))
	3.0b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (+.f32 (log.f32 (.f32 x (PI.f32))) (log.f32 tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	0.7b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (cbrt.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)) (log.f32 (exp.f32 (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))))
	1.0b	(.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))))

Compiler

Compiled 8045 to 1742 computations (78.3% saved)

localize56.0ms (1%)

Local error

Found 4 expressions with local error:

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

series79.0ms (1.4%)

Counts

3 → 32

Calls

3 calls:

42.0ms	(expm1.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)))
7.0ms	(.f32 (PI.f32) (.f32 tau x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 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))
0.0ms	(expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))

simplify97.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

791×	`associate-/l*_binary32`
591×	`fma-def_binary32`
276×	`cancel-sign-sub-inv_binary32`
248×	`associate-*l/_binary32`
248×	`associate-/l/_binary32`

Counts

88 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	3080
1	391	2719
2	1563	2699
3	4701	2683
4	5030	2683

prune205.0ms (3.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	4	10	14
Picked	1	0	1
Done	1	0	1
Total	152	14	166

Error

0.1b

Counts

166 → 14

Alt Table

Status	Error	Program
▶	0.7b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	4.6b	(.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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.5b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) x)))) (*.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 (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 tau tau) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.1b	(.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))))
	1.9b	(.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)))))
	3.0b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (+.f32 (log.f32 (.f32 x (PI.f32))) (log.f32 tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (log1p.f32 (-.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))) 1)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (cbrt.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)) (log.f32 (exp.f32 (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))))
	0.8b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (/.f32 1 (.f32 (PI.f32) x))))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 x (PI.f32)))) (+.f32 (log.f32 x) (log.f32 (PI.f32))))))

Compiler

Compiled 6045 to 1647 computations (72.8% saved)

localize65.0ms (1.1%)

Local error

Found 4 expressions with local error:

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

prune203.0ms (3.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	150	14	164

Error

0.1b

Counts

164 → 14

Alt Table

Status	Error	Program
	4.6b	(.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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (PI.f32) (.f32 tau x))))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))) (/.f32 1 (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	1.5b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) x)))) (*.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 (cbrt.f32 (/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 tau tau) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.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))))
	1.9b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))) (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))))
	3.0b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (+.f32 (log.f32 (.f32 x (PI.f32))) (log.f32 tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))))) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log1p.f32 (-.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))) 1)) (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (cbrt.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)) (log.f32 (exp.f32 (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))))
	0.8b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32))))) (/.f32 1 (.f32 (PI.f32) x))))

Compiler

Compiled 5874 to 1609 computations (72.6% saved)

regimes2.2s (37%)

Accuracy

Total 0.5b remaining (78.2%)

Threshold costs 0.5b (78.2%)

Counts

403 → 1

Compiler

Compiled 52886 to 27996 computations (47.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary32`
11×	`neg-sub0_binary32`
11×	`neg-mul-1_binary32`
10×	`+-commutative_binary32`
10×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	30	40
2	52	40
3	68	40
4	81	40
5	88	40
6	91	40
7	92	40
8	92	40

end1.0ms (0%)

Compiler: Compiled 25 to 13 computations (48% saved)

sample1.9s (32.7%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
201.0ms	8000×	pre	128	true

Compiler

Compiled 550 to 288 computations (47.6% saved)

Details

analyze91.0ms (1.6%)

sample56.0ms (1%)

simplify48.0ms (0.8%)

prune2.0ms (0%)

localize34.0ms (0.6%)

series53.0ms (0.9%)

rewrite18.0ms (0.3%)

simplify74.0ms (1.3%)

prune284.0ms (4.9%)

localize42.0ms (0.7%)

series11.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify46.0ms (0.8%)

prune273.0ms (4.7%)

localize56.0ms (1%)

series79.0ms (1.4%)

rewrite12.0ms (0.2%)

simplify97.0ms (1.7%)

prune205.0ms (3.5%)

localize65.0ms (1.1%)

prune203.0ms (3.5%)

regimes2.2s (37%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.9s (32.7%)

Profiling