Details

analyze278.0ms (0.6%)

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)

sample2.5s (5.3%)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 147 to 112 computations (23.8% saved)

simplify92.0ms (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)

localize83.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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 (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)

series1.9s (4.1%)

Counts

4 → 60

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)))
849.0ms	(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	(/.f32 (PI.f32) s)

rewrite342.0ms (0.7%)

Algorithm

4×	egg-rewrite

Rules

87×	`egg`
79×	`egg`
22×	`egg`
19×	`egg`

Counts

4 → 207

Calls

4 calls:

98.0ms	(/.f32 (neg.f32 (PI.f32)) s)
85.0ms	(*.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)))
84.0ms	(/.f32 (PI.f32) s)
72.0ms	(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))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	109	5
2	1169	5
3	4834	5
4	5071	5
0	4	5
1	84	5
2	1100	5
3	4818	5
4	5041	5
0	22	46
1	496	46
2	4969	46
3	5231	46
0	20	41
1	454	39
2	3990	39
3	5057	39

simplify179.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

748×	`associate-/r*_binary32`
678×	`associate-/l*_binary32`
527×	`fma-def_binary32`
221×	`+-commutative_binary32`
184×	`associate-+r+_binary32`

Counts

267 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	620	9680
1	2283	9572
2	5473	9572

prune287.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	196	5	201
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	196	6	202

Error

0.2b

Counts

202 → 6

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)))
	15.9b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.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)) 3)))
	31.4b	(pow.f32 (sqrt.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)))) 2)
▶	0.8b	(pow.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)))) 3)
	0.9b	(.f32 (pow.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)))) 2) (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)))))
	24.2b	(-.f32 (exp.f32 (log1p.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))))) 1)

Compiler

Compiled 15680 to 9139 computations (41.7% saved)

localize89.0ms (0.2%)

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 (PI.f32) s)))))) -1)))
	0.3b	(/.f32 (PI.f32) s)
	0.3b	(/.f32 (neg.f32 (PI.f32)) s)
✓	0.7b	(pow.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)))) 3)

series10.4s (22.3%)

Counts

1 → 24

Calls

1 calls:

10.4s

(pow.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)))) 3)

rewrite81.0ms (0.2%)

Algorithm

1×	egg-rewrite

Rules

24× egg

Counts

1 → 24

Calls

1 calls:

80.0ms

(pow.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)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	46
1	544	46
2	4839	46
3	4888	46

simplify491.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

886×	`fma-def_binary32`
372×	`*-commutative_binary32`
266×	`+-commutative_binary32`
240×	`associate-+r+_binary32`
179×	`distribute-rgt-in_binary32`

Counts

48 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	969	10964
1	3412	10605
2	4976	10263
3	4943	10177
4	4994	10177
5	4966	10177

prune456.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	209	7	216

Error

0.2b

Counts

216 → 7

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)))
	31.4b	(.f32 (pow.f32 (sqrt.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))))) 3) (pow.f32 (sqrt.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))))) 3))
	15.9b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.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)) 3)))
	31.4b	(pow.f32 (sqrt.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)))) 2)
✓	0.8b	(pow.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)))) 3)
▶	0.9b	(.f32 (pow.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)))) 2) (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)))))
	24.2b	(-.f32 (exp.f32 (log1p.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))))) 1)

Compiler

Compiled 23766 to 14130 computations (40.5% saved)

localize95.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (PI.f32) s)
	0.3b	(/.f32 (neg.f32 (PI.f32)) s)
✓	0.4b	(.f32 (pow.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)))) 2) (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)))))
✓	0.5b	(pow.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)))) 2)

series11.4s (24.6%)

Counts

2 → 48

Calls

2 calls:

10.4s

(pow.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)))) 2)

1.0s

(*.f32 (pow.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)))) 2) (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)))))

rewrite164.0ms (0.4%)

Algorithm

2×	egg-rewrite

Rules

25×	`egg`
19×	`egg`

Counts

2 → 44

Calls

2 calls:

85.0ms

(pow.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)))) 2)

77.0ms

(*.f32 (pow.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)))) 2) (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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	51
1	557	49
2	4827	49
3	5754	49
0	26	46
1	561	46
2	4843	46
3	4898	46

simplify391.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

618×	`*-commutative_binary32`
332×	`associate-+r+_binary32`
323×	`fma-def_binary32`
287×	`associate-r_binary32`
227×	`associate-/l*_binary32`

Counts

92 → 114

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1427	21295
1	5005	21295

prune850.0ms (1.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	300	4	304
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	300	11	311

Error

0.1b

Counts

311 → 11

Alt Table

Status	Error	Program
	10.7b	(.f32 (pow.f32 (pow.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))) 2) 1/3) (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)))))
✓	0.3b	(*.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)))
▶	0.8b	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.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))) 2)) (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)))))
	3.9b	(.f32 (.f32 (pow.f32 (cbrt.f32 -1) 2) (pow.f32 (exp.f32 (.f32 1/3 (+.f32 (log.f32 s) (log.f32 (log.f32 (+.f32 (/.f32 1 (-.f32 (+.f32 (/.f32 u (+.f32 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))) 1)) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))) 2)) (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)))))
	31.4b	(.f32 (pow.f32 (sqrt.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))))) 3) (pow.f32 (sqrt.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))))) 3))
	15.9b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.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)) 3)))
	31.4b	(pow.f32 (sqrt.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)))) 2)
✓	0.8b	(pow.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)))) 3)
✓	0.9b	(.f32 (pow.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)))) 2) (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)))))
	24.2b	(-.f32 (exp.f32 (log1p.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))))) 1)
	9.5b	(.f32 (cbrt.f32 (pow.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))) 2)) (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 42610 to 27339 computations (35.8% saved)

localize127.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.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))) 2)) (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 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.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))) 2))
✓	0.5b	(pow.f32 (cbrt.f32 (neg.f32 s)) 2)
✓	0.5b	(pow.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))) 2)

series13.2s (28.5%)

Counts

4 → 84

Calls

4 calls:

8.0s	(*.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.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))) 2))
4.2s	(pow.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))) 2)
1.0s	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.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))) 2)) (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)))))
53.0ms	(pow.f32 (cbrt.f32 (neg.f32 s)) 2)

rewrite210.0ms (0.5%)

Algorithm

4×	egg-rewrite

Rules

65×	`egg`
22×	`egg`
21×	`egg`
18×	`egg`

Counts

4 → 126

Calls

4 calls:

77.0ms	(pow.f32 (cbrt.f32 (neg.f32 s)) 2)
45.0ms	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.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))) 2)) (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)))))
43.0ms	(*.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.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))) 2))
41.0ms	(pow.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))) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	514	44
2	4911	44
0	6	8
1	122	4
2	1016	4
3	4555	4
4	5500	4
0	27	53
1	593	52
2	5040	52
0	30	46
1	653	46
2	5348	46

simplify462.0ms (1%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-def_binary32`
350×	`associate-/l*_binary32`
242×	`associate-/r*_binary32`
228×	`associate-*l/_binary32`
183×	`times-frac_binary32`

Counts

210 → 235

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2471	39179
1	5092	39179

prune1.4s (2.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	225	10	235
Fresh	2	5	7
Picked	1	0	1
Done	1	2	3
Total	229	17	246

Error

0.1b

Counts

246 → 17

Alt Table

Status	Error	Program
	10.7b	(.f32 (pow.f32 (pow.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))) 2) 1/3) (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)))))
✓	0.3b	(*.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)))
	1.7b	(.f32 (.f32 (.f32 (pow.f32 (sqrt.f32 (pow.f32 s 2/9)) 3) (pow.f32 (sqrt.f32 (pow.f32 s 2/9)) 3)) (pow.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))) 2)) (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)))))
	1.5b	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (-.f32 (exp.f32 (log1p.f32 (pow.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)) 2/3))) 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)))))
	1.5b	(.f32 (.f32 (.f32 (pow.f32 (pow.f32 s 2/3) 5/6) (pow.f32 s 1/9)) (pow.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))) 2)) (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 (pow.f32 (.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 (neg.f32 s))) 2) (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)))))
	1.7b	(.f32 (.f32 (.f32 (sqrt.f32 s) (pow.f32 s 1/6)) (pow.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))) 2)) (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)))))
	31.4b	(.f32 (pow.f32 (sqrt.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))))) 3) (pow.f32 (sqrt.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))))) 3))
	0.7b	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (cbrt.f32 (pow.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)) 2))) (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 (pow.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)))) 2) (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)))))
	1.5b	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.f32 (sqrt.f32 (pow.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)) 2/3)) 2)) (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)))))
	2.7b	(.f32 (.f32 (pow.f32 (exp.f32 1) (.f32 2/3 (log.f32 s))) (pow.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))) 2)) (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)))))
	15.9b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.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)) 3)))
	31.4b	(pow.f32 (sqrt.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)))) 2)
	24.2b	(-.f32 (exp.f32 (log1p.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))))) 1)
	1.6b	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.f32 (cbrt.f32 (pow.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)) 2/3)) 3)) (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)))))
	0.8b	(.f32 (.f32 (pow.f32 (cbrt.f32 (neg.f32 s)) 2) (pow.f32 (pow.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)) 2) 1/3)) (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 59070 to 38154 computations (35.4% saved)

regimes521.0ms (1.1%)

Accuracy

Total 0.2b remaining (68.1%)

Threshold costs 0.2b (68.1%)

Counts

53 → 1

Compiler

Compiled 9999 to 7286 computations (27.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-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	46
1	38	46
2	52	46
3	63	46
4	68	46
5	69	46
6	68	46

end515.0ms (1.1%)

Compiler: Compiled 1067 to 785 computations (26.4% saved)

Details

analyze278.0ms (0.6%)

sample2.5s (5.3%)

simplify92.0ms (0.2%)

prune4.0ms (0%)

localize83.0ms (0.2%)

series1.9s (4.1%)

rewrite342.0ms (0.7%)

simplify179.0ms (0.4%)

prune287.0ms (0.6%)

localize89.0ms (0.2%)

series10.4s (22.3%)

rewrite81.0ms (0.2%)

simplify491.0ms (1.1%)

prune456.0ms (1%)

localize95.0ms (0.2%)

series11.4s (24.6%)

rewrite164.0ms (0.4%)

simplify391.0ms (0.8%)

prune850.0ms (1.8%)

localize127.0ms (0.3%)

series13.2s (28.5%)

rewrite210.0ms (0.5%)

simplify462.0ms (1%)

prune1.4s (2.9%)

regimes521.0ms (1.1%)

simplify5.0ms (0%)

end515.0ms (1.1%)

Profiling