Details

analyze242.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.6%	98.4%	0
0%	1.6%	98.4%	1
0%	1.6%	98.4%	2
0.4%	1.2%	98.4%	3
0.6%	1%	98.4%	4
0.9%	0.7%	98.4%	5
1%	0.5%	98.4%	6
1.2%	0.4%	98.4%	7
1.3%	0.3%	98.4%	8
1.4%	0.2%	98.4%	9
1.4%	0.1%	98.4%	10
1.5%	0.1%	98.4%	11
1.5%	0.1%	98.4%	12
1.5%	0%	98.4%	13
1.5%	0%	98.4%	14

Compiler

Compiled 54 to 41 computations (24.1% saved)

sample2.2s (18.9%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 108 to 82 computations (24.1% saved)

preprocess54.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1040×	`fma-def_binary32`
652×	`fma-neg_binary32`
201×	`associate-l_binary32`
197×	`associate-/l*_binary32`
173×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	118
1	72	118
2	132	118
3	240	102
4	396	96
5	761	92
6	1460	92
7	2661	92
8	4670	92
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 39 to 30 computations (23.1% saved)

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary32`
441×	`fma-neg_binary32`
420×	`times-frac_binary32`
347×	`associate-l_binary32`
269×	`associate-r_binary32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	42	59
2	73	59
3	133	51
4	213	48
5	367	46
6	652	46
7	1115	46
8	2001	46
9	4254	46

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))

Status

Error

Program

▶

0.3b

(*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (*.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))

Compiler

Compiled 145 to 105 computations (27.6% saved)

localize78.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (/.f32 (PI.f32) s))
✓	0.2b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
✓	0.4b	(/.f32 (PI.f32) s)
✓	0.4b	(/.f32 (neg.f32 (PI.f32)) s)

series620.0ms (5.2%)

Counts

4 → 44

Calls

15 calls:

366.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))	s	0
94.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))	u	0
68.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))	s	inf
61.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))	s	-inf
10.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))	u	-inf

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`add-sqr-sqrt_binary32`
238×	`log1p-expm1-u_binary32`
238×	`expm1-log1p-u_binary32`
236×	`add-cbrt-cube_binary32`
233×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	501	78

Stop Event

1×	node limit

Counts

4 → 76

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

668×	`times-frac_binary32`
443×	`associate-/r*_binary32`
423×	`associate-/l*_binary32`
279×	`fma-def_binary32`
221×	`associate-l_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	387	5134
1	1420	5028

Stop Event

1×	node limit

Counts

120 → 118

prune268.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	6	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	157	7	164

Error

0.2b

Counts

164 → 7

Alt Table

Status	Error	Program
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
	29.2b	(pow.f32 (pow.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) 3) 1/3)
▶	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))
	31.2b	(exp.f32 (log.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))
	31.2b	(pow.f32 (sqrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 2)
	0.9b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)
	4.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (+.f32 (/.f32 (PI.f32) s) 1))))) 1)))

Compiler

Compiled 11047 to 6479 computations (41.4% saved)

localize88.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(exp.f32 (/.f32 (PI.f32) s))
✓	0.2b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))
	0.4b	(/.f32 (PI.f32) s)
	0.4b	(/.f32 (neg.f32 (PI.f32)) s)

series595.0ms (5%)

Counts

1 → 24

Calls

6 calls:

357.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))	s	0
87.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))	u	0
69.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))	s	inf
61.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))	s	-inf
10.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))	u	inf

rewrite31.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`log1p-expm1-u_binary32`
251×	`expm1-log1p-u_binary32`
249×	`add-cbrt-cube_binary32`
247×	`add-log-exp_binary32`
242×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	613	59

Stop Event

1×	node limit

Counts

1 → 15

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

654×	`times-frac_binary32`
435×	`associate-/r*_binary32`
417×	`associate-/l*_binary32`
311×	`associate-r_binary32`
273×	`fma-def_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	375	4908
1	1383	4810

Stop Event

1×	node limit

Counts

39 → 49

prune210.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	4	1	5
Picked	0	1	1
Done	1	0	1
Total	143	4	147

Error

0.2b

Counts

147 → 4

Alt Table

Status	Error	Program
▶	0.3b	(neg.f32 (*.f32 s (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s))))))))))))
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))
	0.9b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)
	18.3b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.f32 (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))) 3)))

Compiler

Compiled 9864 to 5551 computations (43.7% saved)

localize75.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f32 (PI.f32) s)
	0.4b	(/.f32 (neg.f32 (PI.f32)) s)
✓	1.6b	(expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))
✓	4.9b	(log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))

series672.0ms (5.7%)

Counts

2 → 36

Calls

9 calls:

406.0ms	(expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))	s	0
75.0ms	(expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))	s	inf
73.0ms	(log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))	s	0
73.0ms	(expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))	s	-inf
15.0ms	(expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))	u	0

rewrite33.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary32`
192×	`expm1-log1p-u_binary32`
191×	`log1p-expm1-u_binary32`
188×	`add-log-exp_binary32`
187×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	61
1	416	47

Stop Event

1×	node limit

Counts

2 → 47

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

775×	`times-frac_binary32`
454×	`associate-/l*_binary32`
413×	`associate-/r*_binary32`
277×	`fma-def_binary32`
174×	`associate-*r/_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	368	8974
1	1525	5493

Stop Event

1×	node limit

Counts

83 → 94

prune381.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	199	4	203

Error

0.2b

Counts

203 → 4

Alt Table

Status	Error	Program
✓	0.3b	(neg.f32 (*.f32 s (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s))))))))))))
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))
▶	0.9b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)
	18.3b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.f32 (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))) 3)))

Compiler

Compiled 15135 to 9621 computations (36.4% saved)

localize80.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
	0.4b	(/.f32 (PI.f32) s)
	0.4b	(/.f32 (neg.f32 (PI.f32)) s)
✓	0.8b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)

series5.0s (42.4%)

Counts

2 → 44

Calls

12 calls:

3.2s	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)	u	0
801.0ms	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)	s	inf
354.0ms	(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))	s	0
186.0ms	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)	s	-inf
113.0ms	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)	u	-inf

rewrite38.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`add-sqr-sqrt_binary32`
247×	`log1p-expm1-u_binary32`
247×	`expm1-log1p-u_binary32`
245×	`add-cbrt-cube_binary32`
241×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	118
1	548	118

Stop Event

1×	node limit

Counts

2 → 35

simplify128.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

680×	`times-frac_binary32`
508×	`fma-def_binary32`
469×	`associate-/r*_binary32`
434×	`associate-/l*_binary32`
189×	`+-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	511	10550
1	1908	10313

Stop Event

1×	node limit

Counts

79 → 76

prune274.0ms (2.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	141	7	148

Error

0.1b

Counts

148 → 7

Alt Table

Status	Error	Program
	1.4b	(.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) 2) 3) (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))
✓	0.3b	(neg.f32 (*.f32 s (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s))))))))))))
	31.2b	(pow.f32 (cbrt.f32 (pow.f32 (sqrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 2)) 3)
	18.3b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.f32 (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))) (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (PI.f32) s)))))))))) 3)))
	0.9b	(.f32 (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 2))
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (PI.f32) s)))))) 1)))
✓	0.9b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) 3)

Compiler

Compiled 15072 to 8808 computations (41.6% saved)

regimes151.0ms (1.3%)

Accuracy

Total 0.2b remaining (56.1%)

Threshold costs 0.2b (56.1%)

Counts

34 → 1

Compiler

Compiled 4227 to 3191 computations (24.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary32`
8×	`*-commutative_binary32`
7×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	37	59
2	54	59
3	65	59
4	70	59
5	71	59

Stop Event

1×

saturated

end214.0ms (1.8%)

Stop Event

1×

fuel

Compiler

Compiled 437 to 319 computations (27% saved)

Details

analyze242.0ms (2%)

sample2.2s (18.9%)

preprocess54.0ms (0.5%)

simplify33.0ms (0.3%)

prune4.0ms (0%)

localize78.0ms (0.7%)

series620.0ms (5.2%)

rewrite53.0ms (0.5%)

simplify81.0ms (0.7%)

prune268.0ms (2.3%)

localize88.0ms (0.7%)

series595.0ms (5%)

rewrite31.0ms (0.3%)

simplify70.0ms (0.6%)

prune210.0ms (1.8%)

localize75.0ms (0.6%)

series672.0ms (5.7%)

rewrite33.0ms (0.3%)

simplify97.0ms (0.8%)

prune381.0ms (3.2%)

localize80.0ms (0.7%)

series5.0s (42.4%)

rewrite38.0ms (0.3%)

simplify128.0ms (1.1%)

prune274.0ms (2.3%)

regimes151.0ms (1.3%)

simplify3.0ms (0%)

end214.0ms (1.8%)

Profiling