Details

analyze244.0ms (0.3%)

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 (3%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 147 to 112 computations (23.8% saved)

simplify72.0ms (0.1%)

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)

localize74.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series740.0ms (1%)

Counts

4 → 60

Calls

4 calls:

633.0ms	(*.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)))
100.0ms	(+.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 (PI.f32) s)
3.0ms	(/.f32 (neg.f32 (PI.f32)) s)

rewrite76.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

250×	`add-sqr-sqrt_binary32`
237×	`log1p-expm1-u_binary32`
237×	`expm1-log1p-u_binary32`
234×	`add-log-exp_binary32`
231×	`add-exp-log_binary32`

Counts

4 → 86

Calls

4 calls:

74.0ms	(+.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)
74.0ms	(*.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)))
74.0ms	(/.f32 (PI.f32) s)
74.0ms	(/.f32 (neg.f32 (PI.f32)) s)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	97
1	496	97
2	4969	97
3	5231	97

simplify181.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary32`
636×	`associate-/l*_binary32`
627×	`associate-/r*_binary32`
186×	`+-commutative_binary32`
159×	`*-commutative_binary32`

Counts

146 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	561	8298
1	2057	8190
2	4986	8095
3	5335	8095

prune283.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	8	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	8	150

Error

0.1b

Counts

150 → 8

Alt Table

Status	Error	Program
	0.9b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (exp.f32 (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 (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 (pow.f32 (/.f32 s (PI.f32)) -1)))))) -1)))
	17.6b	(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)))
	24.2b	(log.f32 (pow.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)))
	0.8b	(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)
	0.5b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.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) 1/3)))
	0.3b	(*.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (-.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 (pow.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))))) -3) -1) (+.f32 (pow.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))))) -2) (-.f32 1 (.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 12558 to 7119 computations (43.3% saved)

localize82.0ms (0.1%)

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

series816.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

799.0ms

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

11.0ms

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

6.0ms

(/.f32 s (PI.f32))

rewrite38.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`add-sqr-sqrt_binary32`
251×	`log1p-expm1-u_binary32`
251×	`expm1-log1p-u_binary32`
247×	`add-log-exp_binary32`
244×	`add-exp-log_binary32`

Counts

3 → 56

Calls

3 calls:

37.0ms

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

37.0ms

(/.f32 s (PI.f32))

37.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	62
1	524	62
2	5171	62

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

92 → 90

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	380	4992
1	1385	4894
2	5321	4894

prune234.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	114	8	122

Error

0.1b

Counts

122 → 8

Alt Table

Status	Error	Program
	0.9b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (exp.f32 (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 (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 (pow.f32 (/.f32 s (PI.f32)) -1)))))) -1)))
	17.6b	(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)))
	24.2b	(log.f32 (pow.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)))
	0.8b	(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)
	0.5b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.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) 1/3)))
▶	0.3b	(*.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (-.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 (pow.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))))) -3) -1) (+.f32 (pow.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))))) -2) (-.f32 1 (.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 8615 to 5105 computations (40.7% saved)

localize92.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (-.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)
✓	0.5b	(/.f32 (-.f32 (pow.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))))) -2) 1) (-.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))

series22.5s (30.2%)

Counts

2 → 48

Calls

2 calls:

21.8s

(*.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (-.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))))

723.0ms

(/.f32 (-.f32 (pow.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))))) -2) 1) (-.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))

rewrite45.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

285×	`log1p-expm1-u_binary32`
285×	`expm1-log1p-u_binary32`
280×	`add-log-exp_binary32`
277×	`add-exp-log_binary32`
275×	`add-cbrt-cube_binary32`

Counts

2 → 36

Calls

2 calls:

44.0ms

(*.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (-.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 (-.f32 (pow.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))))) -2) 1) (-.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	26	167
1	598	167
2	5151	167

simplify812.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1116×	`fma-def_binary32`
836×	`times-frac_binary32`
11×	`unpow2_binary32`
10×	`cube-mult_binary32`
10×	`unpow3_binary32`

Counts

84 → 89

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3537	87059
1	5810	87059

prune1.9s (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	182	9	191

Error

0.1b

Counts

191 → 9

Alt Table

Status	Error	Program
	0.9b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (exp.f32 (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 (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 (pow.f32 (/.f32 s (PI.f32)) -1)))))) -1)))
	17.6b	(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)))
	24.2b	(log.f32 (pow.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)))
	0.8b	(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)
	0.5b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.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) 1/3)))
	31.2b	(exp.f32 (log.f32 (*.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.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 (pow.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))))) -3) -1) (+.f32 (pow.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))))) -2) (-.f32 1 (.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 (pow.f32 (sqrt.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.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)))

Compiler

Compiled 114441 to 62868 computations (45.1% saved)

localize92.0ms (0.1%)

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)
✓	0.5b	(pow.f32 (sqrt.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.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	(/.f32 (-.f32 (pow.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))))) -2) 1) (+.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))

series37.8s (50.8%)

Counts

2 → 48

Calls

2 calls:

37.1s

(pow.f32 (sqrt.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.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)

726.0ms

(/.f32 (-.f32 (pow.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))))) -2) 1) (+.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))

rewrite76.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`log1p-expm1-u_binary32`
273×	`expm1-log1p-u_binary32`
266×	`add-log-exp_binary32`
263×	`add-exp-log_binary32`
260×	`add-cbrt-cube_binary32`

Counts

2 → 40

Calls

2 calls:

74.0ms

(pow.f32 (sqrt.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.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)

74.0ms

(/.f32 (-.f32 (pow.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))))) -2) 1) (+.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	160
1	568	160
2	4970	160
3	5060	160

simplify1.9s (2.6%)

Algorithm

1×	egg-herbie

Rules

1430× fma-def_binary32

Counts

88 → 57

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4332	131734
1	5762	131734

prune3.3s (4.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	150	10	160

Error

0.1b

Counts

160 → 10

Alt Table

Status	Error	Program
	0.9b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (exp.f32 (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 (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 (pow.f32 (/.f32 s (PI.f32)) -1)))))) -1)))
	17.6b	(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)))
	24.2b	(log.f32 (pow.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 (neg.f32 s) (log.f32 (pow.f32 (sqrt.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.f32 1 (/.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)))))))))) 2) 2) (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.f32 1 (/.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)))))))))) 2))) 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)
	0.5b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.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) 1/3)))
	31.2b	(exp.f32 (log.f32 (*.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.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 (pow.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))))) -3) -1) (+.f32 (pow.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))))) -2) (-.f32 1 (.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 (pow.f32 (sqrt.f32 (/.f32 (-.f32 (pow.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))))) -2) 1) (+.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)))

Compiler

Compiled 165877 to 90105 computations (45.7% saved)

regimes477.0ms (0.6%)

Accuracy

Total 0.2b remaining (61.2%)

Threshold costs 0.2b (61.2%)

Counts

82 → 1

Compiler

Compiled 13062 to 9395 computations (28.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	90
1	45	90
2	60	90
3	71	90
4	76	90
5	77	90
6	75	90

end296.0ms (0.4%)

Compiler: Compiled 653 to 471 computations (27.9% saved)

Details

analyze244.0ms (0.3%)

sample2.2s (3%)

simplify72.0ms (0.1%)

prune4.0ms (0%)

localize74.0ms (0.1%)

series740.0ms (1%)

rewrite76.0ms (0.1%)

simplify181.0ms (0.2%)

prune283.0ms (0.4%)

localize82.0ms (0.1%)

series816.0ms (1.1%)

rewrite38.0ms (0.1%)

simplify83.0ms (0.1%)

prune234.0ms (0.3%)

localize92.0ms (0.1%)

series22.5s (30.2%)

rewrite45.0ms (0.1%)

simplify812.0ms (1.1%)

prune1.9s (2.5%)

localize92.0ms (0.1%)

series37.8s (50.8%)

rewrite76.0ms (0.1%)

simplify1.9s (2.6%)

prune3.3s (4.4%)

regimes477.0ms (0.6%)

simplify4.0ms (0%)

end296.0ms (0.4%)

Profiling