Details

analyze101.0ms (1.4%)

Algorithm

1×

Search

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

Compiler

Compiled 32 to 17 computations (46.9% saved)

sample55.0ms (0.8%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 57 to 29 computations (49.1% saved)

simplify52.0ms (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)

localize36.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite16.0ms (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:

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)
1.0ms	(sin.f32 (.f32 (.f32 x PI.f32) tau))

series84.0ms (1.2%)

Counts

4 → 72

Calls

4 calls:

53.0ms	(/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))
16.0ms	(/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32))
8.0ms	(sin.f32 (.f32 (.f32 x PI.f32) tau))
7.0ms	(*.f32 x PI.f32)

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

805×	`associate-/l*_binary32`
334×	`fma-def_binary32`
320×	`cancel-sign-sub-inv_binary32`
307×	`associate-/l/_binary32`
235×	`unswap-sqr_binary32`

Counts

149 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2894
1	483	2546
2	1851	2521
3	4959	2521

prune192.0ms (2.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	214	15	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	215	15	230

Error

0.1b

Counts

230 → 15

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)))))
	3.8b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 PI.f32 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (+.f32 (.f32 1/5040 (.f32 (pow.f32 PI.f32 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6)))) (.f32 1/6 (.f32 (pow.f32 PI.f32 2) (.f32 (pow.f32 tau 2) (pow.f32 x 2)))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 PI.f32)) (.f32 (sqrt.f32 x) (sqrt.f32 PI.f32))) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	1.0b	(.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)))
	3.2b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.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)))
	4.1b	(.f32 (/.f32 (fma.f32 PI.f32 (.f32 tau x) (fma.f32 1/120 (.f32 (pow.f32 PI.f32 5) (.f32 (pow.f32 tau 5) (pow.f32 x 5))) (fma.f32 (pow.f32 (.f32 PI.f32 (.f32 tau x)) 3) -1/6 (.f32 (.f32 (pow.f32 tau 7) (pow.f32 x 7)) (.f32 (pow.f32 PI.f32 7) -1/5040))))) (.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)))
	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 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)))
	0.8b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)))) (cbrt.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)))
	0.8b	(.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)))))
▶	0.7b	(.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)))
	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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 PI.f32)) (sqrt.f32 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 (.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)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 1 x) (/.f32 (sin.f32 (*.f32 x PI.f32)) PI.f32)))

Compiler

Compiled 5290 to 1442 computations (72.7% saved)

localize51.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 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))

0.0ms

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

series605.0ms (8.6%)

Counts

3 → 60

Calls

3 calls:

465.0ms

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

96.0ms

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

43.0ms

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

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

549×	`times-frac_binary32`
360×	`associate-l_binary32`
360×	`associate-/l*_binary32`
348×	`associate-/r*_binary32`
336×	`fma-def_binary32`

Counts

105 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	417	4974
1	1385	4294
2	5163	4294

prune256.0ms (3.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	251	5	256
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	255	16	271

Error

0.1b

Counts

271 → 16

Alt Table

Status	Error	Program
	0.8b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) 3) (.f32 (pow.f32 tau 3) (pow.f32 (.f32 PI.f32 x) 3)))) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	3.8b	(.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 PI.f32 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6)))))) (/.f32 (sin.f32 (.f32 x PI.f32)) (.f32 x PI.f32)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 PI.f32)) (.f32 (sqrt.f32 x) (sqrt.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 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x PI.f32))) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.0b	(.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)))
	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 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)))
	8.1b	(.f32 (/.f32 (sin.f32 (.f32 (-.f32 (+.f32 (exp.f32 (-.f32 (log.f32 PI.f32) (log.f32 (/.f32 1 x)))) (/.f32 (exp.f32 (-.f32 (log.f32 PI.f32) (log.f32 (/.f32 1 x)))) (.f32 PI.f32 x))) 1) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))
	3.0b	(.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 PI.f32 (.f32 tau x)))) (sqrt.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 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)))) (cbrt.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)))
	0.8b	(.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)))))
▶	0.7b	(.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 PI.f32)) (sqrt.f32 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 (.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)))
	0.8b	(.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)))))
	3.2b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.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)))

Compiler

Compiled 10169 to 4037 computations (60.3% saved)

localize41.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

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)))

series17.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

17.0ms

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

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary32`
596×	`unswap-sqr_binary32`
420×	`associate-l_binary32`
399×	`times-frac_binary32`
366×	`fma-neg_binary32`

Counts

46 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	861
1	212	735
2	664	728
3	2885	720
4	4865	720
5	4970	720
6	4958	720

prune211.0ms (3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	244	5	249
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	249	16	265

Error

0.1b

Counts

265 → 16

Alt Table

Status	Error	Program
	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)))))
	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 1 (.f32 x PI.f32))))
	0.8b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) 3) (.f32 (pow.f32 tau 3) (pow.f32 (.f32 PI.f32 x) 3)))) (/.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 (/.f32 (sin.f32 (*.f32 PI.f32 x)) x) (/.f32 1 PI.f32)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 PI.f32)) (sqrt.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 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 x PI.f32)) (/.f32 1 (.f32 x PI.f32)))) (sqrt.f32 (.f32 (sin.f32 (.f32 x PI.f32)) (/.f32 1 (.f32 x PI.f32))))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 PI.f32)) (.f32 (sqrt.f32 x) (sqrt.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 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x PI.f32))) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.0b	(.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)))
	0.8b	(.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 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)))
	8.1b	(.f32 (/.f32 (sin.f32 (.f32 (-.f32 (+.f32 (exp.f32 (-.f32 (log.f32 PI.f32) (log.f32 (/.f32 1 x)))) (/.f32 (exp.f32 (-.f32 (log.f32 PI.f32) (log.f32 (/.f32 1 x)))) (.f32 PI.f32 x))) 1) 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 (.f32 (cbrt.f32 (sin.f32 (.f32 x PI.f32))) (cbrt.f32 (sin.f32 (.f32 x PI.f32)))) (/.f32 (cbrt.f32 (sin.f32 (.f32 PI.f32 x))) (*.f32 PI.f32 x))))
	0.8b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)))) (cbrt.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)))
	0.8b	(.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)))))
	0.9b	(.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 1 (.f32 x PI.f32))))
	3.2b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.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)))

Compiler

Compiled 5956 to 1914 computations (67.9% saved)

localize55.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 x PI.f32)
	0.3b	(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))
✓	0.5b	(.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) x) (/.f32 1 PI.f32))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary32`
25×	`times-frac_binary32`
23×	`add-exp-log_binary32`
17×	`*-un-lft-identity_binary32`
15×	`add-cube-cbrt_binary32`

Counts

1 → 59

Calls

1 calls:

9.0ms

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

series17.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

17.0ms

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

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

511×	`fma-def_binary32`
369×	`cancel-sign-sub-inv_binary32`
366×	`fma-neg_binary32`
352×	`associate-l_binary32`
350×	`times-frac_binary32`

Counts

71 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1467
1	309	1267
2	836	1263
3	2876	1261
4	4877	1261
5	5011	1261

prune242.0ms (3.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	461	5	466
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	467	15	482

Error

0.1b

Counts

482 → 15

Alt Table

Status	Error	Program
	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)))))
	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 PI.f32 x))) (sqrt.f32 x)) (.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 PI.f32 x))) (sqrt.f32 x)) (/.f32 1 PI.f32))))
	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 1 (.f32 x PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 PI.f32)) (.f32 (sqrt.f32 x) (sqrt.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 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x PI.f32))) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (.f32 PI.f32 x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) (*.f32 PI.f32 x)))))
	1.0b	(.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)))
	3.2b	(.f32 (/.f32 (sqrt.f32 (sin.f32 (.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)))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) x)) (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) x))) (/.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 PI.f32 x)) x)) PI.f32)))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (.f32 (.f32 x x) x) (.f32 (.f32 PI.f32 PI.f32) PI.f32))) tau)) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 (sin.f32 (*.f32 PI.f32 x)) x) (/.f32 1 PI.f32)))
	0.8b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)))) (cbrt.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)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 PI.f32 (.f32 tau x))) (.f32 (.f32 x PI.f32) tau)) (.f32 (/.f32 (sin.f32 (*.f32 PI.f32 x)) x) (/.f32 1 PI.f32)))
	0.8b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (.f32 x PI.f32) tau)) (.f32 (.f32 x PI.f32) tau)))) (.f32 (/.f32 (sin.f32 (*.f32 PI.f32 x)) x) (/.f32 1 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)))))
	0.9b	(.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 1 (.f32 x PI.f32))))
	8.1b	(.f32 (/.f32 (sin.f32 (.f32 (-.f32 (+.f32 (exp.f32 (-.f32 (log.f32 PI.f32) (log.f32 (/.f32 1 x)))) (/.f32 (exp.f32 (-.f32 (log.f32 PI.f32) (log.f32 (/.f32 1 x)))) (.f32 PI.f32 x))) 1) tau)) (.f32 (.f32 x PI.f32) tau)) (/.f32 (sin.f32 (.f32 x PI.f32)) (*.f32 x PI.f32)))

Compiler

Compiled 6673 to 1899 computations (71.5% saved)

regimes2.7s (38%)

Accuracy

Total 0.5b remaining (76.5%)

Threshold costs 0.5b (76.5%)

Compiler

Compiled 57366 to 30457 computations (46.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	19	41
2	19	41

end1.0ms (0%)

Compiler: Compiled 26 to 14 computations (46.2% saved)

sample1.9s (27.5%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
179.0ms	8000×	pre	128	true

Compiler

Compiled 575 to 278 computations (51.7% saved)

Details

analyze101.0ms (1.4%)

sample55.0ms (0.8%)

simplify52.0ms (0.7%)

prune2.0ms (0%)

localize36.0ms (0.5%)

rewrite16.0ms (0.2%)

series84.0ms (1.2%)

simplify84.0ms (1.2%)

prune192.0ms (2.7%)

localize51.0ms (0.7%)

rewrite8.0ms (0.1%)

series605.0ms (8.6%)

simplify96.0ms (1.4%)

prune256.0ms (3.6%)

localize41.0ms (0.6%)

rewrite9.0ms (0.1%)

series17.0ms (0.2%)

simplify91.0ms (1.3%)

prune211.0ms (3%)

localize55.0ms (0.8%)

rewrite12.0ms (0.2%)

series17.0ms (0.2%)

simplify95.0ms (1.3%)

prune242.0ms (3.4%)

regimes2.7s (38%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.9s (27.5%)

Profiling