Details

analyze245.0ms (1.4%)

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)

sample150.0ms (0.8%)

Algorithm

1×

intervals

Results

41.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 95 to 73 computations (23.2% saved)

simplify75.0ms (0.4%)

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

prune5.0ms (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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(*.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)

localize79.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (/.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)))
✓	0.4b	(/.f32 (PI.f32) s)
✓	0.4b	(/.f32 (neg.f32 (PI.f32)) s)

series1.0s (5.9%)

Counts

4 → 44

Calls

4 calls:

1.0s	(*.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 (PI.f32) s))
3.0ms	(/.f32 (neg.f32 (PI.f32)) s)
2.0ms	(/.f32 (PI.f32) s)

rewrite63.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary32`
56×	`*-un-lft-identity_binary32`
52×	`times-frac_binary32`
48×	`add-cube-cbrt_binary32`
16×	`log-prod_binary32`

Counts

4 → 156

Calls

4 calls:

43.0ms	(*.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)))
3.0ms	(/.f32 (neg.f32 (PI.f32)) s)
2.0ms	(exp.f32 (/.f32 (PI.f32) s))
2.0ms	(/.f32 (PI.f32) s)

simplify154.0ms (0.9%)

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

200 → 237

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	593	9374
1	1771	8936
2	5237	8936

prune386.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	9	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

0.1b

Counts

238 → 9

Alt Table

Status	Error	Program
▶	0.4b	(*.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 1 (/.f32 s (PI.f32)))))))) -1)))
	1.7b	(.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))))
	0.6b	(+.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) (*.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 (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 (pow.f32 (exp.f32 (/.f32 1 (.f32 (cbrt.f32 s) (cbrt.f32 s)))) (/.f32 (PI.f32) (cbrt.f32 s))))))) -1)))
	0.4b	(+.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)))
	0.6b	(.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))))
	0.4b	(+.f32 (.f32 (log.f32 (+.f32 (/.f32 1 (sqrt.f32 (+.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 (-.f32 (/.f32 1 (sqrt.f32 (+.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 (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)))))

Compiler

Compiled 13985 to 7836 computations (44% saved)

localize84.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	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 1 (/.f32 s (PI.f32)))))))) -1)))
✓	0.3b	(/.f32 1 (/.f32 s (PI.f32)))
✓	0.3b	(/.f32 s (PI.f32))
	0.4b	(/.f32 (neg.f32 (PI.f32)) s)

series1.0s (5.8%)

Counts

3 → 36

Calls

3 calls:

1.0s

(*.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 1 (/.f32 s (PI.f32)))))))) -1)))

6.0ms

(/.f32 s (PI.f32))

2.0ms

(/.f32 1 (/.f32 s (PI.f32)))

rewrite67.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`times-frac_binary32`
69×	`add-sqr-sqrt_binary32`
67×	`*-un-lft-identity_binary32`
59×	`add-cube-cbrt_binary32`
18×	`add-exp-log_binary32`

Counts

3 → 152

Calls

3 calls:

49.0ms

(*.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 1 (/.f32 s (PI.f32)))))))) -1)))

4.0ms

(/.f32 1 (/.f32 s (PI.f32)))

2.0ms

(/.f32 s (PI.f32))

simplify159.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

683×	`times-frac_binary32`
464×	`associate-/r*_binary32`
450×	`associate-/l*_binary32`
280×	`fma-def_binary32`
140×	`*-commutative_binary32`

Counts

188 → 228

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	547	9598
1	1692	8782
2	5036	8782

prune624.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	299	3	302
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	303	8	311

Error

0.1b

Counts

311 → 8

Alt Table

Status	Error	Program
▶	0.4b	(*.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 (exp.f32 (neg.f32 (log.f32 (/.f32 s (PI.f32)))))))))) -1)))
	0.6b	(.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 (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) (*.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))))
	1.7b	(.f32 (.f32 (neg.f32 s) (sqrt.f32 (log.f32 (+.f32 -1 (/.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)))))))))) (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 1 (/.f32 s (PI.f32)))))))) -1))))
	0.4b	(+.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 1 (/.f32 s (PI.f32)))))))) -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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s)))
	0.4b	(+.f32 (.f32 (log.f32 (+.f32 (/.f32 1 (sqrt.f32 (+.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 (-.f32 (/.f32 1 (sqrt.f32 (+.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 (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)))))

Compiler

Compiled 16800 to 9793 computations (41.7% saved)

localize86.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	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 (exp.f32 (neg.f32 (log.f32 (/.f32 s (PI.f32)))))))))) -1)))
	0.3b	(/.f32 s (PI.f32))
	0.4b	(/.f32 (neg.f32 (PI.f32)) s)
✓	3.2b	(exp.f32 (neg.f32 (log.f32 (/.f32 s (PI.f32)))))

series1.7s (9.6%)

Counts

2 → 36

Calls

2 calls:

1.5s

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

252.0ms

(exp.f32 (neg.f32 (log.f32 (/.f32 s (PI.f32)))))

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`log-prod_binary32`
28×	`add-sqr-sqrt_binary32`
26×	`*-un-lft-identity_binary32`
18×	`add-cube-cbrt_binary32`
13×	`times-frac_binary32`

Counts

2 → 83

Calls

2 calls:

48.0ms

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

4.0ms

(exp.f32 (neg.f32 (log.f32 (/.f32 s (PI.f32)))))

simplify172.0ms (1%)

Algorithm

1×	egg-herbie

Rules

808×	`times-frac_binary32`
465×	`associate-/l*_binary32`
296×	`fma-def_binary32`
155×	`*-commutative_binary32`
111×	`+-commutative_binary32`

Counts

119 → 167

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	621	12018
1	1933	10028
2	5023	10028

prune661.0ms (3.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	273	8	281

Error

0.1b

Counts

281 → 8

Alt Table

Status	Error	Program
✓	0.4b	(*.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 (exp.f32 (neg.f32 (log.f32 (/.f32 s (PI.f32)))))))))) -1)))
	0.6b	(.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 (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) (*.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))))
	1.7b	(.f32 (.f32 (neg.f32 s) (sqrt.f32 (log.f32 (+.f32 -1 (/.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)))))))))) (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 1 (/.f32 s (PI.f32)))))))) -1))))
▶	0.4b	(+.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 1 (/.f32 s (PI.f32)))))))) -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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s)))
	0.4b	(+.f32 (.f32 (log.f32 (+.f32 (/.f32 1 (sqrt.f32 (+.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 (-.f32 (/.f32 1 (sqrt.f32 (+.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 (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)))))

Compiler

Compiled 19594 to 11944 computations (39% saved)

localize87.0ms (0.5%)

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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s))
	0.3b	(/.f32 1 (/.f32 s (PI.f32)))
	0.3b	(/.f32 s (PI.f32))
	0.4b	(/.f32 (neg.f32 (PI.f32)) s)

series1.2s (6.8%)

Counts

1 → 24

Calls

1 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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`associate-r_binary32`
7×	`add-sqr-sqrt_binary32`
6×	`associate-l_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-cube-cbrt_binary32`

Counts

1 → 31

Calls

1 calls:

5.0ms

(*.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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s))

simplify116.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

737×	`times-frac_binary32`
537×	`associate-/r*_binary32`
447×	`associate-/l*_binary32`
405×	`fma-def_binary32`
179×	`*-commutative_binary32`

Counts

55 → 85

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	489	7126
1	1710	6776
2	5229	6776

prune1.7s (9.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	574	4	578
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	575	11	586

Error

0.1b

Counts

586 → 11

Alt Table

Status	Error	Program
	0.6b	(+.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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s)) (.f32 (.f32 (cbrt.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 1 (/.f32 s (PI.f32)))))))) -1)))) (cbrt.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 1 (/.f32 s (PI.f32)))))))) -1))))) (.f32 (cbrt.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 1 (/.f32 s (PI.f32)))))))) -1)))) (neg.f32 s))))
✓	0.4b	(*.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 (exp.f32 (neg.f32 (log.f32 (/.f32 s (PI.f32)))))))))) -1)))
	0.6b	(.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))))
	19.7b	(+.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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s)) (log.f32 (exp.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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s)))))
	0.4b	(+.f32 (.f32 (log.f32 (+.f32 (/.f32 1 (sqrt.f32 (+.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 (-.f32 (/.f32 1 (sqrt.f32 (+.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)))
	31.0b	(+.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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s)) (exp.f32 (log.f32 (.f32 (log.f32 (sqrt.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))) 1)) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 1 (/.f32 s (PI.f32))))))))))) (neg.f32 s)))))
	0.9b	(.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)))))
	0.6b	(+.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) (*.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))))
	1.7b	(.f32 (.f32 (neg.f32 s) (sqrt.f32 (log.f32 (+.f32 -1 (/.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)))))))))) (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 1 (/.f32 s (PI.f32)))))))) -1))))
	0.4b	(+.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 1 (/.f32 s (PI.f32)))))))) -1))) (neg.f32 s)) (.f32 1/2 (*.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 1 (/.f32 s (PI.f32)))))))) -1)) (neg.f32 s))))

Compiler

Compiled 50521 to 30274 computations (40.1% saved)

regimes5.1s (28.8%)

Accuracy

Total 0.3b remaining (86.3%)

Threshold costs 0.3b (86.3%)

Counts

643 → 1

Compiler

Compiled 119658 to 87182 computations (27.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary32`
9×	`*-commutative_binary32`
8×	`sub-neg_binary32`
7×	`neg-sub0_binary32`
7×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	69
1	46	69
2	62	69
3	74	69
4	79	69
5	80	69
6	79	69

end3.0ms (0%)

Compiler: Compiled 42 to 29 computations (31% saved)

sample2.7s (15%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
209.0ms	8000×	pre	128	true

Compiler

Compiled 875 to 624 computations (28.7% saved)

Details

analyze245.0ms (1.4%)

sample150.0ms (0.8%)

simplify75.0ms (0.4%)

prune5.0ms (0%)

localize79.0ms (0.4%)

series1.0s (5.9%)

rewrite63.0ms (0.4%)

simplify154.0ms (0.9%)

prune386.0ms (2.2%)

localize84.0ms (0.5%)

series1.0s (5.8%)

rewrite67.0ms (0.4%)

simplify159.0ms (0.9%)

prune624.0ms (3.5%)

localize86.0ms (0.5%)

series1.7s (9.6%)

rewrite61.0ms (0.3%)

simplify172.0ms (1%)

prune661.0ms (3.7%)

localize87.0ms (0.5%)

series1.2s (6.8%)

rewrite8.0ms (0%)

simplify116.0ms (0.7%)

prune1.7s (9.7%)

regimes5.1s (28.8%)

simplify4.0ms (0%)

end3.0ms (0%)

sample2.7s (15%)

Profiling