Details

analyze4.0ms (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 (27.4%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify51.0ms (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

0.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.6b	(.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))

series50.0ms (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)))
8.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
2.0ms	(*.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))

simplify77.0ms (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

prune259.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	224	13	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	13	238

Error

0.1b

Counts

238 → 13

Alt Table

Status	Error	Program
	0.7b	(.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)))))
	0.8b	(.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.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)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	2.0b	(.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 (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 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))
▶	0.6b	(.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.0b	(.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))))
	0.7b	(.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 x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) 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))))
	0.8b	(.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 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))

Compiler

Compiled 7287 to 1566 computations (78.5% saved)

localize48.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series39.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

5.0ms	(/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))
1.0ms	(sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

894×	`times-frac_binary32`
502×	`associate-/l*_binary32`
315×	`fma-def_binary32`
226×	`unswap-sqr_binary32`
211×	`cancel-sign-sub-inv_binary32`

Counts

82 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1967
1	349	1730
2	1313	1718
3	4752	1718
4	5023	1718

prune235.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	238	12	250

Error

0.0b

Counts

250 → 12

Alt Table

Status	Error	Program
	2.0b	(.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 (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 (.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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 (PI.f32) (cbrt.f32 x)))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))
▶	0.7b	(.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 x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.0b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))) (/.f32 tau (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.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 (.f32 (cbrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))) (cbrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.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))))
	0.7b	(.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)))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.0b	(.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))))

Compiler

Compiled 7721 to 1657 computations (78.5% saved)

localize86.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.5b	(/.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 x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))
✓	0.5b	(.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series163.0ms (2.1%)

Counts

3 → 48

Calls

3 calls:

141.0ms

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

21.0ms

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

0.0ms

(*.f32 (PI.f32) (PI.f32))

rewrite233.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

709×	`add-cbrt-cube_binary32`
709×	`add-exp-log_binary32`
518×	`cbrt-unprod_binary32`
518×	`prod-exp_binary32`
93×	`cbrt-undiv_binary32`

Counts

3 → 258

Calls

3 calls:

60.0ms

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

6.0ms

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

3.0ms

(*.f32 (PI.f32) (PI.f32))

simplify275.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

720×	`unswap-sqr_binary32`
414×	`associate-l_binary32`
413×	`associate-r_binary32`
352×	`fma-def_binary32`
339×	`times-frac_binary32`

Counts

306 → 240

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	23011
1	531	8919
2	2983	8875
3	5345	8875

prune268.0ms (3.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	284	13	297

Error

0.0b

Counts

297 → 13

Alt Table

Status	Error	Program
	2.0b	(.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 (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 (.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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 (PI.f32) (cbrt.f32 x)))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))
✓	0.7b	(.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 x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.0b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))) (/.f32 tau (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.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 (.f32 (cbrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))) (cbrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.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))))
▶	0.7b	(.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)))))
	2.5b	(.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 (+.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (log.f32 (.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.0b	(.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))))

Compiler

Compiled 17977 to 2554 computations (85.8% saved)

localize50.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.2%)

Counts

2 → 4

Calls

2 calls:

8.0ms	(/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))
5.0ms	(*.f32 (PI.f32) x)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-cube-cbrt_binary32`
9×	`times-frac_binary32`
6×	`add-cbrt-cube_binary32`

Counts

2 → 49

Calls

2 calls:

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

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary32`
619×	`cancel-sign-sub-inv_binary32`
526×	`fma-neg_binary32`
282×	`distribute-rgt-neg-in_binary32`
269×	`associate-l_binary32`

Counts

53 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	843
1	216	777
2	565	773
3	1648	771
4	4274	771
5	5027	771

prune490.0ms (6.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	196	13	209

Error

0.0b

Counts

209 → 13

Alt Table

Status	Error	Program
	2.0b	(.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 (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 (.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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (*.f32 (PI.f32) (cbrt.f32 x)))))
	0.8b	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))
✓	0.7b	(.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 x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.0b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))) (/.f32 tau (/.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.8b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.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 (.f32 (cbrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))) (cbrt.f32 (sin.f32 (.f32 (expm1.f32 (log1p.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))))
✓	0.7b	(.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)))))
	2.5b	(.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 (+.f32 (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (log.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (log.f32 (.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 tau tau) tau)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (.f32 x (PI.f32))) (sqrt.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.0b	(.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))))

Compiler

Compiled 6243 to 1682 computations (73.1% saved)

regimes2.9s (37.3%)

Accuracy

Total 0.5b remaining (76.5%)

Threshold costs 0.5b (76.5%)

Counts

482 → 1

Compiler

Compiled 63107 to 33805 computations (46.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	18	40
2	18	40

end233.0ms (2.9%)

Compiler: Compiled 508 to 259 computations (49% saved)

Details

analyze4.0ms (0%)

sample2.2s (27.4%)

simplify51.0ms (0.7%)

prune2.0ms (0%)

localize34.0ms (0.4%)

series50.0ms (0.6%)

rewrite18.0ms (0.2%)

simplify77.0ms (1%)

prune259.0ms (3.3%)

localize48.0ms (0.6%)

series39.0ms (0.5%)

rewrite10.0ms (0.1%)

simplify74.0ms (0.9%)

prune235.0ms (3%)

localize86.0ms (1.1%)

series163.0ms (2.1%)

rewrite233.0ms (2.9%)

simplify275.0ms (3.5%)

prune268.0ms (3.4%)

localize50.0ms (0.6%)

series13.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify64.0ms (0.8%)

prune490.0ms (6.2%)

regimes2.9s (37.3%)

simplify3.0ms (0%)

end233.0ms (2.9%)

Profiling