Details

analyze247.0ms (0.5%)

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 (4.9%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 147 to 112 computations (23.8% saved)

simplify73.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1145×	`fma-def_binary32`
518×	`unswap-sqr_binary32`
445×	`fma-neg_binary32`
420×	`times-frac_binary32`
354×	`associate-l_binary32`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	42	59
2	72	59
3	120	51
4	179	48
5	319	46
6	505	46
7	788	46
8	1249	46
9	2584	46
10	4419	46
11	4832	46
12	4827	46

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	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 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))

Compiler

Compiled 127 to 93 computations (26.8% saved)

localize78.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (/.f32 (neg.f32 (PI.f32)) s))
✓	0.3b	(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
✓	0.3b	(/.f32 (PI.f32) s)
✓	0.3b	(/.f32 (neg.f32 (PI.f32)) s)

series954.0ms (2.1%)

Counts

4 → 48

Calls

4 calls:

944.0ms	(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
4.0ms	(exp.f32 (/.f32 (neg.f32 (PI.f32)) s))
3.0ms	(/.f32 (PI.f32) s)
3.0ms	(/.f32 (neg.f32 (PI.f32)) s)

rewrite67.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`times-frac_binary32`
71×	`add-sqr-sqrt_binary32`
69×	`*-un-lft-identity_binary32`
61×	`add-cube-cbrt_binary32`
34×	`exp-prod_binary32`

Counts

4 → 179

Calls

4 calls:

45.0ms	(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
5.0ms	(exp.f32 (/.f32 (neg.f32 (PI.f32)) s))
3.0ms	(/.f32 (neg.f32 (PI.f32)) s)
2.0ms	(/.f32 (PI.f32) s)

simplify149.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

717×	`times-frac_binary32`
490×	`associate-/l*_binary32`
475×	`associate-/r*_binary32`
286×	`fma-def_binary32`
146×	`*-commutative_binary32`

Counts

227 → 273

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	609	9743
1	1790	9284
2	5297	9284

prune367.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	266	7	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	267	7	274

Error

0.0b

Counts

274 → 7

Alt Table

Status	Error	Program
	0.4b	(+.f32 (.f32 (log.f32 (.f32 (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)) (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (neg.f32 s)) (*.f32 (log.f32 (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)))
	0.9b	(.f32 (.f32 (neg.f32 s) (sqrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (sqrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))
	0.9b	(.f32 (.f32 (neg.f32 s) (*.f32 (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
	0.4b	(+.f32 (.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))) (.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1))))
	0.5b	(.f32 (sqrt.f32 s) (.f32 (neg.f32 (sqrt.f32 s)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
▶	0.3b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)))

Compiler

Compiled 15117 to 8360 computations (44.7% saved)

localize80.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))
✓	0.3b	(*.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s))
	0.3b	(/.f32 (PI.f32) s)
	0.3b	(/.f32 (neg.f32 (PI.f32)) s)

series1.4s (3.1%)

Counts

2 → 48

Calls

2 calls:

1.2s

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

223.0ms

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

rewrite53.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary32`
12×	`*-un-lft-identity_binary32`
10×	`associate-r_binary32`
8×	`sqrt-prod_binary32`
7×	`add-cube-cbrt_binary32`

Counts

2 → 56

Calls

2 calls:

43.0ms

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

6.0ms

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

simplify188.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary32`
556×	`associate-/l*_binary32`
313×	`*-commutative_binary32`
206×	`+-commutative_binary32`
166×	`associate-+r+_binary32`

Counts

104 → 148

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	815	12754
1	2831	12121
2	5310	12121

prune1.5s (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	506	2	508
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	507	8	515

Error

0.0b

Counts

515 → 8

Alt Table

Status	Error	Program
	0.4b	(+.f32 (.f32 (log.f32 (.f32 (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)) (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (neg.f32 s)) (*.f32 (log.f32 (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)))
	0.9b	(.f32 (.f32 (neg.f32 s) (sqrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (sqrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))
	0.4b	(+.f32 (.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))) (.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1))))
	0.5b	(.f32 (sqrt.f32 s) (.f32 (neg.f32 (sqrt.f32 s)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
✓	0.3b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)))
▶	0.3b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (log.f32 (expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (neg.f32 s)))
	0.5b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (*.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (sqrt.f32 s)) (neg.f32 (sqrt.f32 s))))

Compiler

Compiled 52895 to 30061 computations (43.2% saved)

localize97.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s))
	0.3b	(/.f32 (PI.f32) s)
	0.3b	(/.f32 (neg.f32 (PI.f32)) s)
✓	1.2b	(expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))

series217.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

217.0ms

(expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))

simplify95.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

449×	`fma-def_binary32`
402×	`associate-+r+_binary32`
288×	`associate-r_binary32`
252×	`associate-/r*_binary32`
241×	`associate-l_binary32`

Counts

35 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	371	5043
1	1250	4838
2	5461	4838

prune969.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	344	8	352

Error

0.0b

Counts

352 → 8

Alt Table

Status	Error	Program
	0.4b	(+.f32 (.f32 (log.f32 (.f32 (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)) (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (neg.f32 s)) (*.f32 (log.f32 (cbrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)))
	0.9b	(.f32 (.f32 (neg.f32 s) (sqrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (sqrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))) (cbrt.f32 (.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))
▶	0.4b	(+.f32 (.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))) (.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1))))
	0.5b	(.f32 (sqrt.f32 s) (.f32 (neg.f32 (sqrt.f32 s)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
✓	0.3b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)))
✓	0.3b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (log.f32 (expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (neg.f32 s)))
	0.5b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (*.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (sqrt.f32 s)) (neg.f32 (sqrt.f32 s))))

Compiler

Compiled 32947 to 18915 computations (42.6% saved)

localize84.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1)))
✓	0.3b	(*.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))
✓	0.3b	(+.f32 (.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))) (.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1))))
	0.3b	(/.f32 (PI.f32) s)

series30.8s (68.2%)

Counts

3 → 52

Calls

3 calls:

19.4s

(+.f32 (*.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))) (*.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1))))

5.8s

(*.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))

5.5s

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

rewrite104.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary32`
32×	`log-prod_binary32`
27×	`*-un-lft-identity_binary32`
20×	`associate-l_binary32`
16×	`distribute-lft-in_binary32`

Counts

3 → 106

Calls

3 calls:

43.0ms

(+.f32 (*.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))) (*.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1))))

43.0ms

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

4.0ms

(*.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))

simplify816.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1161×	`fma-def_binary32`
416×	`times-frac_binary32`
13×	`cube-mult_binary32`
13×	`unpow3_binary32`
12×	`unpow2_binary32`

Counts

158 → 173

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3152	88652
1	5043	88652

prune2.7s (6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	4	1	5
Picked	1	0	1
Done	1	1	2
Total	304	5	309

Error

0.0b

Counts

309 → 5

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 s) (.f32 (neg.f32 (sqrt.f32 s)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
	0.6b	(+.f32 (.f32 (.f32 (neg.f32 s) (.f32 (cbrt.f32 (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))) (cbrt.f32 (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))))) (cbrt.f32 (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))) (.f32 (neg.f32 s) (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1))))
	0.4b	(+.f32 (fma.f32 (neg.f32 s) (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))) (.f32 (log.f32 (+.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))) 1)) (neg.f32 s))) (.f32 (log.f32 (-.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))) 1)) (neg.f32 s)))
	0.3b	(neg.f32 (fma.f32 s (log1p.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))) (*.f32 s (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1)))))
✓	0.3b	(+.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (neg.f32 s)) (.f32 (log.f32 (expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (neg.f32 s)))

Compiler

Compiled 110985 to 65535 computations (41% saved)

regimes1.6s (3.6%)

Accuracy

Total 0.3b remaining (76.3%)

Threshold costs 0.3b (76.3%)

Counts

278 → 1

Compiler

Compiled 48927 to 33503 computations (31.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary32`
5×	`*-commutative_binary32`
5×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	91
1	39	91
2	48	91
3	54	91
4	56	91
5	55	91

end223.0ms (0.5%)

Compiler: Compiled 470 to 311 computations (33.8% saved)

Details

analyze247.0ms (0.5%)

sample2.2s (4.9%)

simplify73.0ms (0.2%)

prune4.0ms (0%)

localize78.0ms (0.2%)

series954.0ms (2.1%)

rewrite67.0ms (0.1%)

simplify149.0ms (0.3%)

prune367.0ms (0.8%)

localize80.0ms (0.2%)

series1.4s (3.1%)

rewrite53.0ms (0.1%)

simplify188.0ms (0.4%)

prune1.5s (3.4%)

localize97.0ms (0.2%)

series217.0ms (0.5%)

rewrite1.0ms (0%)

simplify95.0ms (0.2%)

prune969.0ms (2.1%)

localize84.0ms (0.2%)

series30.8s (68.2%)

rewrite104.0ms (0.2%)

simplify816.0ms (1.8%)

prune2.7s (6%)

regimes1.6s (3.6%)

simplify4.0ms (0%)

end223.0ms (0.5%)

Profiling