Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample145.0ms (2.1%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 63 to 33 computations (47.6% saved)

simplify46.0ms (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)

localize33.0ms (0.5%)

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

series51.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

31.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
9.0ms	(/.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:

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))

simplify73.0ms (1.1%)

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 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2890
1	484	2546
2	1854	2521
3	4970	2521

prune283.0ms (4.2%)

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
	1.3b	(.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))))
	4.8b	(.f32 (/.f32 (log.f32 (exp.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))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) (cbrt.f32 (/.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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) 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 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.0b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.8b	(.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)))))
	1.3b	(.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))))
	1.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 x) (log.f32 (PI.f32))))) (.f32 x (PI.f32))))
▶	0.7b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.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 (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)) (log.f32 (exp.f32 (/.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 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x 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 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) x) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (PI.f32)))) (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))))

Compiler

Compiled 7547 to 1631 computations (78.4% saved)

localize51.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series87.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

47.0ms	(expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))
31.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
8.0ms	(.f32 (PI.f32) (.f32 x tau))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary32`
17×	`add-exp-log_binary32`
8×	`pow1_binary32`
6×	`cbrt-unprod_binary32`
6×	`prod-exp_binary32`

Counts

3 → 56

Calls

3 calls:

5.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
4.0ms	(.f32 (PI.f32) (.f32 x tau))
0.0ms	(expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

882×	`associate-/l*_binary32`
332×	`fma-def_binary32`
307×	`associate-/l/_binary32`
275×	`cancel-sign-sub-inv_binary32`
260×	`associate-*l/_binary32`

Counts

128 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	3592
1	408	3231
2	1638	3211
3	4987	3211

prune239.0ms (3.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	181	4	185
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	184	17	201

Error

0.1b

Counts

201 → 17

Alt Table

Status	Error	Program
	4.8b	(.f32 (/.f32 (log.f32 (exp.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))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	1.2b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) (cbrt.f32 (sin.f32 (.f32 (PI.f32) x)))) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) x))) (PI.f32))))
▶	0.8b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.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 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	14.6b	(.f32 (log1p.f32 (fma.f32 1/24 (/.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 4) (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4)))) (fma.f32 1/6 (pow.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) 3) (fma.f32 1/2 (/.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 2) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x)))) (/.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 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x 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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) 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 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.0b	(.f32 (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.8b	(.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)))))
	1.3b	(.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))))
	0.8b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 x tau))))) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (sin.f32 (.f32 x (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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 x) (log.f32 (PI.f32))))) (.f32 x (PI.f32))))

Compiler

Compiled 6995 to 1890 computations (73% saved)

localize55.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

prune243.0ms (3.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	179	6	185
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	185	17	202

Error

0.1b

Counts

202 → 17

Alt Table

Status	Error	Program
	1.1b	(.f32 (log1p.f32 (log.f32 (exp.f32 (.f32 (.f32 (cbrt.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))))) (cbrt.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))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	4.8b	(.f32 (/.f32 (log.f32 (exp.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))))
	1.8b	(.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)))))
	1.3b	(.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 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 (PI.f32) x) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 x tau))))) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (sin.f32 (.f32 x (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))))
	1.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 x) (log.f32 (PI.f32))))) (.f32 x (PI.f32))))
▶	0.8b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))))) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
	0.9b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))))) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x 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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))))) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) (sqrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))))
	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))))

Compiler

Compiled 7335 to 2151 computations (70.7% saved)

localize60.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series343.0ms (5.1%)

Counts

2 → 48

Calls

2 calls:

312.0ms	(expm1.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
31.0ms	(/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 73

Calls

2 calls:

7.0ms	(/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
0.0ms	(expm1.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

570×	`associate-*l/_binary32`
449×	`associate-/l/_binary32`
411×	`associate-/r/_binary32`
370×	`fma-def_binary32`
276×	`cancel-sign-sub-inv_binary32`

Counts

121 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	4447
1	437	3953
2	1925	3891
3	5037	3891

prune315.0ms (4.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	233	15	248

Error

0.1b

Counts

248 → 15

Alt Table

Status	Error	Program
	4.8b	(.f32 (/.f32 (log.f32 (exp.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 (log1p.f32 (log.f32 (exp.f32 (.f32 (.f32 (cbrt.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))))) (cbrt.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))))
	1.8b	(.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)))))
	1.3b	(.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))))
	0.8b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))))) (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))
	0.9b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 (PI.f32) x) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 x tau))))) (.f32 (PI.f32) (.f32 x tau))))) (/.f32 (sin.f32 (.f32 x (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))))
	0.9b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))))) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x 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) x) (/.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (exp.f32 (+.f32 (log.f32 x) (log.f32 (PI.f32))))) (.f32 x (PI.f32))))

Compiler

Compiled 8734 to 2873 computations (67.1% saved)

regimes2.6s (37.8%)

Accuracy

Total 0.5b remaining (78.7%)

Threshold costs 0.5b (78.7%)

Counts

428 → 1

Compiler

Compiled 56086 to 30771 computations (45.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	16	36
2	16	36

end0.0ms (0%)

Compiler: Compiled 23 to 11 computations (52.2% saved)

sample2.0s (28.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
206.0ms	8000×	pre	128	true

Compiler

Compiled 574 to 279 computations (51.4% saved)

Details

analyze4.0ms (0.1%)

sample145.0ms (2.1%)

simplify46.0ms (0.7%)

prune2.0ms (0%)

localize33.0ms (0.5%)

series51.0ms (0.8%)

rewrite18.0ms (0.3%)

simplify73.0ms (1.1%)

prune283.0ms (4.2%)

localize51.0ms (0.7%)

series87.0ms (1.3%)

rewrite12.0ms (0.2%)

simplify80.0ms (1.2%)

prune239.0ms (3.5%)

localize55.0ms (0.8%)

prune243.0ms (3.6%)

localize60.0ms (0.9%)

series343.0ms (5.1%)

rewrite14.0ms (0.2%)

simplify96.0ms (1.4%)

prune315.0ms (4.7%)

regimes2.6s (37.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (28.9%)

Profiling