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)

sample1.9s (26.8%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 76 to 42 computations (44.7% saved)

preprocess90.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

967×	`associate-/l/_binary32`
808×	`associate-/l*_binary32`
710×	`times-frac_binary32`
520×	`associate-/r/_binary32`
385×	`associate-*r/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	72
1	49	72
2	173	72
3	733	72
4	2487	72
5	3267	72
6	3267	72
7	4554	72
8	4807	72
9	4927	72
10	4939	72
11	4939	72
12	4941	72
13	4941	72
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify37.0ms (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

0.5b

Counts

3 → 2

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))))
	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)))))

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))))

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)))))

Compiler

Compiled 136 to 64 computations (52.9% saved)

localize37.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(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))

series43.0ms (0.6%)

Counts

4 → 72

Calls

18 calls:

6.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	-inf
5.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	-inf
4.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	inf
4.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	inf
3.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	0

rewrite63.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

720×	`prod-diff_binary32`
203×	`expm1-udef_binary32`
203×	`log1p-udef_binary32`
111×	`*-un-lft-identity_binary32`
111×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	49
1	213	49
2	3114	49
0	10	49

Stop Event

1×	saturated
1×	node limit

Counts

4 → 116

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`
303×	`*-commutative_binary32`
293×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1330
1	245	1314
2	922	1298
3	2789	1298
4	4773	1298

Stop Event

1×	node limit

Counts

188 → 140

prune211.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	175	13	188
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	13	190

Error

0.1b

Counts

190 → 13

Alt Table

Status	Error	Program
	0.8b	(.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))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3)) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) x)))
	2.5b	(.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))))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2) 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 (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))))
	0.9b	(.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))))
	1.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (.f32 1/6 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))))
	1.1b	(.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 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 1 (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	1.2b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) 3) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 5837 to 1617 computations (72.3% saved)

localize45.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(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))

series32.0ms (0.4%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	-inf
5.0ms	(/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	-inf
4.0ms	(/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	inf
4.0ms	(/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	inf
3.0ms	(/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	0

rewrite50.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

663×	`prod-diff_binary32`
547×	`log-prod_binary32`
172×	`expm1-udef_binary32`
172×	`log1p-udef_binary32`
150×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	209	30
2	2538	30
0	11	38

Stop Event

1×	saturated
1×	node limit

Counts

2 → 68

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary32`
497×	`cancel-sign-sub-inv_binary32`
405×	`distribute-rgt-neg-in_binary32`
398×	`distribute-lft-neg-in_binary32`
372×	`fma-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1064
1	201	1048
2	767	1036
3	2321	1032
4	4905	1032

Stop Event

1×	node limit

Counts

116 → 84

prune207.0ms (2.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	187	8	195
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	193	15	208

Error

0.1b

Counts

208 → 15

Alt Table

Status	Error	Program
	0.8b	(.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))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.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))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 1 (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (*.f32 x (PI.f32))))))
	5.1b	(.f32 (/.f32 (-.f32 (.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))) (cos.f32 1)) (.f32 (cos.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 1))) (.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 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (.f32 1/6 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))))
	6.2b	(.f32 (/.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))) (log.f32 (cbrt.f32 (exp.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 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2))) 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 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))) -1))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) x)))
	1.1b	(.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 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	0.9b	(.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (log.f32 (sqrt.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))))
	1.4b	(.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))))) (log.f32 (cbrt.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))))
	2.5b	(.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 (expm1.f32 (log1p.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)))))))

Compiler

Compiled 6594 to 1790 computations (72.9% saved)

localize55.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau))
✓	1.0b	(pow.f32 (PI.f32) 3)

series37.0ms (0.5%)

Counts

2 → 24

Calls

6 calls:

16.0ms	(/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	-inf
5.0ms	(/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	-inf
4.0ms	(/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	0
4.0ms	(/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	inf
4.0ms	(/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	inf

rewrite49.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

471×	`prod-diff_binary32`
211×	`expm1-udef_binary32`
211×	`log1p-udef_binary32`
123×	`add-sqr-sqrt_binary32`
120×	`pow1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	306	25
2	3270	25
0	14	33

Stop Event

1×	saturated
1×	node limit

Counts

2 → 64

simplify36.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

753×	`cancel-sign-sub-inv_binary32`
705×	`fma-def_binary32`
509×	`fma-neg_binary32`
439×	`associate-r_binary32`
425×	`associate-l_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	616
1	127	608
2	440	600
3	2594	596

Stop Event

1×	node limit

Counts

88 → 74

prune227.0ms (3.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	170	14	184

Error

0.1b

Counts

184 → 14

Alt Table

Status	Error	Program
	0.8b	(.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))))
	0.9b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 (.f32 tau x) (PI.f32)))) (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sqrt.f32 (.f32 (.f32 tau x) (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	5.1b	(.f32 (/.f32 (-.f32 (.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))) (cos.f32 1)) (.f32 (cos.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 1))) (.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 (+.f32 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4))) 1) (+.f32 (.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6))) (.f32 1/6 (*.f32 (pow.f32 (PI.f32) 2) (pow.f32 x 2))))))
	6.2b	(.f32 (/.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))) (log.f32 (cbrt.f32 (exp.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 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))))) (log.f32 (cbrt.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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (sqrt.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)) (pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))) -1))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (PI.f32)) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) x)))
	1.1b	(.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 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	0.9b	(.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (log.f32 (sqrt.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))))
	2.5b	(.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 (expm1.f32 (log1p.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)))))))

Compiler

Compiled 6073 to 2485 computations (59.1% saved)

localize50.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) -1)
	0.4b	(sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau))
	0.4b	(*.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))

series25.0ms (0.3%)

Counts

1 → 12

Calls

3 calls:

13.0ms

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

-inf

8.0ms

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

inf

3.0ms

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

rewrite44.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

815×	`log1p-expm1-u_binary32`
815×	`expm1-log1p-u_binary32`
84×	`add-sqr-sqrt_binary32`
82×	`pow1_binary32`
81×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	167	14
2	2198	14
0	8	17

Stop Event

1×	saturated
1×	node limit

Counts

1 → 51

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

63 → 59

prune212.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	208	13	221

Error

0.0b

Counts

221 → 13

Alt Table

Status	Error	Program
	6.2b	(.f32 (/.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))) (log.f32 (cbrt.f32 (exp.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 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))))) (log.f32 (cbrt.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))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 x 3) (pow.f32 (PI.f32) 3))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) 2) (sqrt.f32 (.f32 x (PI.f32)))) (/.f32 (cbrt.f32 (sin.f32 (.f32 x (PI.f32)))) (sqrt.f32 (.f32 x (PI.f32))))))
	0.9b	(.f32 (.f32 (/.f32 1 (sqrt.f32 (.f32 (.f32 tau x) (PI.f32)))) (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sqrt.f32 (.f32 (.f32 tau x) (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.8b	(.f32 (/.f32 (sin.f32 (.f32 (expm1.f32 (log1p.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 x 6) -1/5040) (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 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))))) (pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))) -1))
	5.1b	(.f32 (/.f32 (-.f32 (.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))) (cos.f32 1)) (.f32 (cos.f32 (exp.f32 (log1p.f32 (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 1))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.7b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) 3) (pow.f32 (.f32 x (.f32 (PI.f32) tau)) 3))) (pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))) -1))
	1.1b	(.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 (cbrt.f32 (*.f32 x (PI.f32))) 3)))
	0.9b	(.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))))) (log.f32 (sqrt.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))))
	2.5b	(.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 (expm1.f32 (log1p.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)))))))

Compiler

Compiled 6673 to 1849 computations (72.3% saved)

regimes3.3s (46.6%)

Accuracy

Total 0.5b remaining (80.6%)

Threshold costs 0.5b (80.6%)

Counts

548 → 1

Compiler

Compiled 70907 to 39875 computations (43.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	22	52

Stop Event

1×

saturated

end203.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 541 to 279 computations (48.4% saved)

Details

analyze3.0ms (0%)

sample1.9s (26.8%)

preprocess90.0ms (1.3%)

simplify37.0ms (0.5%)

prune3.0ms (0%)

localize37.0ms (0.5%)

series43.0ms (0.6%)

rewrite63.0ms (0.9%)

simplify58.0ms (0.8%)

prune211.0ms (3%)

localize45.0ms (0.6%)

series32.0ms (0.4%)

rewrite50.0ms (0.7%)

simplify52.0ms (0.7%)

prune207.0ms (2.9%)

localize55.0ms (0.8%)

series37.0ms (0.5%)

rewrite49.0ms (0.7%)

simplify36.0ms (0.5%)

prune227.0ms (3.2%)

localize50.0ms (0.7%)

series25.0ms (0.3%)

rewrite44.0ms (0.6%)

simplify33.0ms (0.5%)

prune212.0ms (3%)

regimes3.3s (46.6%)

simplify2.0ms (0%)

end203.0ms (2.8%)

Profiling