Details

analyze410.0ms (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample2.6s (34.3%)

Results

2.5s	8256×	body	128	valid
1.0ms	3×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
15×	`fma-def_binary32`
11×	`*-commutative_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	13.4b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize63.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.2b	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))
✓	0.3b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

series208.0ms (2.7%)

Counts

4 → 52

Calls

4 calls:

192.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
9.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
3.0ms	(.f32 (.f32 2 (PI.f32)) u2)
3.0ms	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))

rewrite87.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

573×	`prod-diff_binary32`
559×	`log-prod_binary32`
196×	`expm1-udef_binary32`
196×	`log1p-udef_binary32`
179×	`log-pow_binary32`

Counts

4 → 92

Calls

4 calls:

85.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
85.0ms	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))
85.0ms	(.f32 (.f32 2 (PI.f32)) u2)
85.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	260	40
2	2526	40
3	4939	40
4	5077	40

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Rules

553×	`cancel-sign-sub-inv_binary32`
498×	`fma-neg_binary32`
360×	`times-frac_binary32`
287×	`associate-*l/_binary32`
245×	`associate-/r*_binary32`

Counts

144 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2184
1	587	1984
2	1995	1851
3	4459	1845
4	4990	1845

prune150.0ms (2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	125	16	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	16	143

Error

0.1b

Counts

143 → 16

Alt Table

Status	Error	Program
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) 2)))
	1.8b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (PI.f32) u2) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (pow.f32 (sqrt.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 2)))
	2.5b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (PI.f32) u2) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)))) (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (PI.f32) 3)) (.f32 (pow.f32 u2 3) -4/3)))
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))
	6.1b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))) 2))
	8.7b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 2)
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 u2 3)))))
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (pow.f32 (cbrt.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3)))
	2.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (exp.f32 (log.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 1))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cos.f32 1) (neg.f32 (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (fma.f32 (neg.f32 (sin.f32 1)) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	13.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (log.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 4570 to 3197 computations (30% saved)

localize78.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.1b	(.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))
✓	0.3b	(*.f32 (PI.f32) u2)
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))

series254.0ms (3.3%)

Counts

3 → 32

Calls

3 calls:

245.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 2 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))

7.0ms

(*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))

2.0ms

(*.f32 (PI.f32) u2)

rewrite69.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

714×	`log-prod_binary32`
240×	`expm1-udef_binary32`
240×	`log1p-udef_binary32`
237×	`fma-def_binary32`
217×	`log-pow_binary32`

Counts

3 → 61

Calls

3 calls:

67.0ms

(*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))

67.0ms

(*.f32 (PI.f32) u2)

67.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 2 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	42
1	309	38
2	3231	35
3	5685	35

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary32`
375×	`fma-neg_binary32`
360×	`cancel-sign-sub-inv_binary32`
275×	`times-frac_binary32`
269×	`associate-*l/_binary32`

Counts

93 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1770
1	437	1642
2	1552	1527
3	4686	1525
4	5028	1525

prune189.0ms (2.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	159	16	175

Error

0.1b

Counts

175 → 16

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 u2 3)))))
	8.5b	(.f32 (exp.f32 (.f32 (log.f32 (log1p.f32 u1)) 1/2)) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 1))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (PI.f32) u2)) 2)) (cos.f32 (*.f32 (PI.f32) u2)))))
	12.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1/2))))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cos.f32 1) (neg.f32 (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (fma.f32 (neg.f32 (sin.f32 1)) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))
	1.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (fma.f32 u2 (PI.f32) (fma.f32 (pow.f32 u2 5) (.f32 (pow.f32 (PI.f32) 5) 2/15) (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 u2 7) -4/315) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -2/3)))))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1/2)) 3)))
	1.8b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (PI.f32) u2) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (pow.f32 (sqrt.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 2)))
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (pow.f32 (cbrt.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3)))
	6.1b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	2.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (exp.f32 (log.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	13.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (log.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))))
	14.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (+.f32 (log.f32 (sqrt.f32 (sqrt.f32 (exp.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2))))))) (log.f32 (sqrt.f32 (sqrt.f32 (exp.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2))))))))))

Compiler

Compiled 5491 to 3078 computations (43.9% saved)

localize47.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))))
✓	0.3b	(.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 u2 3)))))
✓	1.0b	(pow.f32 (*.f32 2 (PI.f32)) 3)

series199.0ms (2.6%)

Counts

4 → 44

Calls

4 calls:

183.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 u2 3)))))
11.0ms	(.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))
5.0ms	(sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))))
0.0ms	(pow.f32 (*.f32 2 (PI.f32)) 3)

rewrite118.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

368×	`prod-diff_binary32`
245×	`expm1-udef_binary32`
245×	`log1p-udef_binary32`
236×	`fma-udef_binary32`
233×	`log-pow_binary32`

Counts

4 → 84

Calls

4 calls:

116.0ms	(sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))))
116.0ms	(.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))
116.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 u2 3)))))
116.0ms	(pow.f32 (*.f32 2 (PI.f32)) 3)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	50
1	345	46
2	3273	46
3	4868	46
4	4997	46
5	4853	46

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary32`
628×	`associate-l_binary32`
476×	`fma-neg_binary32`
352×	`cancel-sign-sub-inv_binary32`
174×	`associate-/r*_binary32`

Counts

128 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1688
1	431	1613
2	1445	1497
3	4679	1495
4	4981	1495

prune131.0ms (1.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	126	14	140

Error

0.1b

Counts

140 → 14

Alt Table

Status	Error	Program
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 u2 3)))))
	8.5b	(.f32 (exp.f32 (.f32 (log.f32 (log1p.f32 u1)) 1/2)) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 1))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (PI.f32) u2)) 2)) (cos.f32 (*.f32 (PI.f32) u2)))))
	12.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1/2))))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1/2)) 3)))
	1.8b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (PI.f32) u2) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (.f32 2 (PI.f32))))) (pow.f32 u2 3)))))
	6.1b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3))) (pow.f32 u2 3)))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cos.f32 1) (neg.f32 (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (fma.f32 (neg.f32 (sin.f32 1)) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))
	13.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (log.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))))
	14.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (+.f32 (log.f32 (sqrt.f32 (sqrt.f32 (exp.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2))))))) (log.f32 (sqrt.f32 (sqrt.f32 (exp.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2))))))))))

Compiler

Compiled 3879 to 2681 computations (30.9% saved)

localize56.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (expm1.f32 (log1p.f32 (pow.f32 (.f32 2 (PI.f32)) 3))) (pow.f32 u2 3))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3))) (pow.f32 u2 3)))))
	1.0b	(pow.f32 (*.f32 2 (PI.f32)) 3)
✓	1.6b	(expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3)))

series164.0ms (2.1%)

Counts

3 → 32

Calls

3 calls:

151.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3))) (pow.f32 u2 3)))))

13.0ms

(*.f32 (expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3))) (pow.f32 u2 3))

0.0ms

(expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3)))

rewrite62.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

594×	`prod-diff_binary32`
260×	`expm1-udef_binary32`
260×	`log1p-udef_binary32`
168×	`add-sqr-sqrt_binary32`
162×	`expm1-log1p-u_binary32`

Counts

3 → 65

Calls

3 calls:

61.0ms

(*.f32 (expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3))) (pow.f32 u2 3))

61.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3))) (pow.f32 u2 3)))))

61.0ms

(expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	363	36
2	3451	36
3	5074	36

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary32`
501×	`associate-l_binary32`
489×	`associate-r_binary32`
459×	`fma-neg_binary32`
289×	`cancel-sign-sub-inv_binary32`

Counts

97 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1470
1	397	1399
2	1315	1293
3	4700	1291
4	5019	1291

prune123.0ms (1.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	122	14	136

Error

0.1b

Counts

136 → 14

Alt Table

Status	Error	Program
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 u2 3)))))
	8.5b	(.f32 (exp.f32 (.f32 (log.f32 (log1p.f32 u1)) 1/2)) (.f32 2 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 1))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (PI.f32) u2)) 2)) (cos.f32 (*.f32 (PI.f32) u2)))))
	12.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1/2))))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) 1/2)) 3)))
	1.8b	(-.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 (PI.f32) u2) (.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/3 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 u2 7) (pow.f32 (PI.f32) 7))))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (.f32 2 (PI.f32))))) (pow.f32 u2 3)))))
	6.1b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
✓	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (*.f32 2 (PI.f32)) 3))) (pow.f32 u2 3)))))
	12.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cos.f32 1) (neg.f32 (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (fma.f32 (neg.f32 (sin.f32 1)) (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (.f32 (sin.f32 1) (cos.f32 (exp.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))
	13.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (log.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))))
	14.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (+.f32 (log.f32 (sqrt.f32 (sqrt.f32 (exp.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2))))))) (log.f32 (sqrt.f32 (sqrt.f32 (exp.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) u2))))))))))

Compiler

Compiled 3636 to 2540 computations (30.1% saved)

regimes2.1s (26.9%)

Accuracy

Total 0.4b remaining (81.5%)

Threshold costs 0.4b (81.5%)

Counts

187 → 1

Compiler

Compiled 41344 to 34684 computations (16.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	28	26
2	32	26
3	34	26
4	33	26

end245.0ms (3.2%)

Compiler: Compiled 411 to 349 computations (15.1% saved)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Details

analyze410.0ms (5.4%)

sample2.6s (34.3%)

simplify14.0ms (0.2%)

prune8.0ms (0.1%)

localize63.0ms (0.8%)

series208.0ms (2.7%)

rewrite87.0ms (1.1%)

simplify78.0ms (1%)

prune150.0ms (2%)

localize78.0ms (1%)

series254.0ms (3.3%)

rewrite69.0ms (0.9%)

simplify72.0ms (0.9%)

prune189.0ms (2.5%)

localize47.0ms (0.6%)

series199.0ms (2.6%)

rewrite118.0ms (1.5%)

simplify73.0ms (1%)

prune131.0ms (1.7%)

localize56.0ms (0.7%)

series164.0ms (2.1%)

rewrite62.0ms (0.8%)

simplify68.0ms (0.9%)

prune123.0ms (1.6%)

regimes2.1s (26.9%)

simplify2.0ms (0%)

end245.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21