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)

sample2.1s (29.6%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 99 to 52 computations (47.5% saved)

simplify36.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

745×	`associate-/l/_binary32`
396×	`associate-/l*_binary32`
281×	`times-frac_binary32`
253×	`associate-/r/_binary32`
154×	`associate-*l/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	24	36
2	83	36
3	333	36
4	1180	36
5	2559	36
6	2687	36
7	2717	36
8	2727	36
9	2731	36
10	2733	36
11	2733	36

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.9b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.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 x (PI.f32))))

Status

Error

Program

0.9b

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

Compiler

Compiled 136 to 64 computations (52.9% saved)

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series43.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

27.0ms	(/.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)))
6.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
2.0ms	(*.f32 x (PI.f32))

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

720×	`prod-diff_binary32`
203×	`expm1-udef_binary32`
203×	`log1p-udef_binary32`
116×	`egg-rr`
111×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	49
1	213	49
2	3141	49

Stop Event

1×	node limit

Counts

4 → 116

Calls

4 calls:

54.0ms	(*.f32 x (PI.f32))
54.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
54.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
54.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-neg_binary32`
450×	`distribute-rgt-neg-in_binary32`
440×	`distribute-lft-neg-in_binary32`
299×	`*-commutative_binary32`
299×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1330
1	245	1314
2	922	1298
3	2791	1298
4	4774	1298

Stop Event

1×	node limit

Counts

188 → 140

prune205.0ms (2.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	173	15	188
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	174	16	190

Error

0.1b

Counts

190 → 16

Alt Table

Status	Error	Program
	0.9b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.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))))
	3.2b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32))) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 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)) (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (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 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (*.f32 x (PI.f32))))
	3.0b	(.f32 (pow.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 2) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) 1) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (cbrt.f32 (.f32 x (.f32 (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))) (log1p.f32 (expm1.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))) (pow.f32 (sqrt.f32 (*.f32 x (PI.f32))) 2)))
	5.2b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.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 x) (.f32 tau x))) -1/6 (fma.f32 (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (pow.f32 tau 4) 1)) (/.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 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) 2)))
	1.0b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sqrt.f32 (.f32 x (.f32 (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 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))

Compiler

Compiled 6001 to 1685 computations (71.9% saved)

localize41.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series12.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))))
3.0ms	(expm1.f32 (*.f32 x (PI.f32)))

rewrite38.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

703×	`expm1-log1p-u_binary32`
702×	`log1p-expm1-u_binary32`
278×	`prod-diff_binary32`
132×	`log1p-udef_binary32`
72×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	146	21
2	1879	21

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

37.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (log1p.f32 (expm1.f32 (.f32 x (PI.f32)))))
37.0ms	(expm1.f32 (*.f32 x (PI.f32)))

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

735×	`cancel-sign-sub-inv_binary32`
551×	`unswap-sqr_binary32`
349×	`distribute-rgt-neg-in_binary32`
348×	`associate-r_binary32`
344×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	366
1	138	366
2	432	359
3	2203	359

Stop Event

1×	node limit

Counts

83 → 76

prune152.0ms (2.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	153	16	169

Error

0.1b

Counts

169 → 16

Alt Table

Status	Error	Program
	0.9b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.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))))
	3.2b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32))) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 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)) (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (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 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (*.f32 x (PI.f32))))
	3.0b	(.f32 (pow.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))) 2) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) 1) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (cbrt.f32 (.f32 x (.f32 (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))) (log1p.f32 (expm1.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))) (pow.f32 (sqrt.f32 (*.f32 x (PI.f32))) 2)))
	5.2b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.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 x) (.f32 tau x))) -1/6 (fma.f32 (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (pow.f32 tau 4) 1)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) 1/120) (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 1)))
	1.0b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sqrt.f32 (.f32 x (.f32 (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 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))

Compiler

Compiled 5456 to 1591 computations (70.8% saved)

localize49.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (.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))
✓	1.0b	(pow.f32 (PI.f32) 3)

series18.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

17.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (.f32 x (PI.f32)))
0.0ms	(pow.f32 (PI.f32) 3)

rewrite44.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`log-prod_binary32`
357×	`prod-diff_binary32`
173×	`expm1-udef_binary32`
173×	`log1p-udef_binary32`
166×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	230	19
2	2719	19

Stop Event

1×	node limit

Counts

2 → 67

Calls

2 calls:

43.0ms	(/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3)))) (.f32 x (PI.f32)))
43.0ms	(pow.f32 (PI.f32) 3)

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

488×	`fma-def_binary32`
486×	`cancel-sign-sub-inv_binary32`
323×	`*-commutative_binary32`
274×	`fma-neg_binary32`
240×	`unswap-sqr_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	234
1	99	234
2	292	230
3	1300	228
4	4426	222

Stop Event

1×	node limit

Counts

79 → 77

prune185.0ms (2.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	3	11	14
Picked	1	0	1
Done	1	0	1
Total	155	15	170

Error

0.1b

Counts

170 → 15

Alt Table

Status	Error	Program
	0.9b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.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))))
	3.2b	(.f32 (.f32 (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (PI.f32))) (/.f32 (sqrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 x 4) 1/120) (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 1)))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32))))) (.f32 x (PI.f32))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) 1) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 x (.f32 (PI.f32) tau))) 2)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (cbrt.f32 (.f32 x (.f32 (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)) (pow.f32 (/.f32 (PI.f32) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)) -1))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))))
	5.2b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.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 x) (.f32 tau x))) -1/6 (fma.f32 (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (pow.f32 tau 4) 1)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sqrt.f32 (.f32 x (.f32 (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 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (exp.f32 (.f32 3 (log.f32 (PI.f32))))))) (.f32 x (PI.f32))))

Compiler

Compiled 5731 to 2293 computations (60% saved)

localize44.0ms (0.6%)

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	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	0.4b	(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) 1)
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series1.6s (22.4%)

Counts

1 → 12

Calls

1 calls:

1.6s	(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) 1)

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

601×	`prod-diff_binary32`
468×	`log-prod_binary32`
163×	`log1p-udef_binary32`
162×	`expm1-udef_binary32`
144×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	191	14
2	2552	14

Stop Event

1×	node limit

Counts

1 → 78

Calls

1 calls:

45.0ms

(-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1)

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

836×	`distribute-rgt-neg-in_binary32`
487×	`fma-def_binary32`
475×	`cancel-sign-sub-inv_binary32`
290×	`*-commutative_binary32`
274×	`fma-neg_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	206
1	82	206
2	243	202
3	1148	200
4	4116	194

Stop Event

1×	node limit

Counts

90 → 86

prune200.0ms (2.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	202	8	210
Fresh	7	7	14
Picked	0	1	1
Done	0	0	0
Total	209	16	225

Error

0.1b

Counts

225 → 16

Alt Table

Status	Error	Program
	0.9b	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) tau)) (.f32 x (*.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 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (sqrt.f32 (+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 1)) (sqrt.f32 (+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))) 1)) -1))
	4.9b	(.f32 (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau x) (.f32 tau x))) -1/6 (fma.f32 (.f32 (pow.f32 x 4) (.f32 1/120 (pow.f32 (PI.f32) 4))) (pow.f32 tau 4) 1)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 1/120 (pow.f32 (.f32 (PI.f32) x) 4) (fma.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 x x) -1/6) 1)))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (log.f32 (+.f32 1 (expm1.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))))) 1))
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (cbrt.f32 (+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) 1)) (pow.f32 (cbrt.f32 (+.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))) 1)) 2) -1))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	5.3b	(.f32 (/.f32 (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) 1) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	0.9b	(.f32 (.f32 (/.f32 1 x) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) tau))) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	5.2b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sqrt.f32 (.f32 x (.f32 (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 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))))))

Compiler

Compiled 7092 to 1998 computations (71.8% saved)

regimes1.8s (25.2%)

Accuracy

Total 0.5b remaining (79.6%)

Threshold costs 0.5b (79.6%)

Counts

352 → 1

Compiler

Compiled 43579 to 24348 computations (44.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	4294967295
1	19	4294967295

Stop Event

1×

saturated

end248.0ms (3.5%)

Compiler: Compiled 552 to 295 computations (46.6% saved)

Details

analyze3.0ms (0%)

sample2.1s (29.6%)

simplify36.0ms (0.5%)

prune3.0ms (0%)

localize32.0ms (0.5%)

series43.0ms (0.6%)

rewrite57.0ms (0.8%)

simplify58.0ms (0.8%)

prune205.0ms (2.9%)

localize41.0ms (0.6%)

series12.0ms (0.2%)

rewrite38.0ms (0.5%)

simplify26.0ms (0.4%)

prune152.0ms (2.2%)

localize49.0ms (0.7%)

series18.0ms (0.2%)

rewrite44.0ms (0.6%)

simplify30.0ms (0.4%)

prune185.0ms (2.6%)

localize44.0ms (0.6%)

series1.6s (22.4%)

rewrite46.0ms (0.7%)

simplify33.0ms (0.5%)

prune200.0ms (2.9%)

regimes1.8s (25.2%)

simplify2.0ms (0%)

end248.0ms (3.5%)

Profiling