Details

analyze458.0ms (6%)

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)

sample3.0s (39.4%)

Results

2.9s	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

prune6.0ms (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)))
	14.0b	(.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)

localize77.0ms (1%)

Local error

Found 4 expressions with local error:

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

series168.0ms (2.2%)

Counts

4 → 52

Calls

4 calls:

153.0ms	(.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))

rewrite89.0ms (1.2%)

Algorithm

2×	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:

87.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
87.0ms	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))
87.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
87.0ms	(.f32 (.f32 2 (PI.f32)) u2)

Iterations

Useful iterations: 0 (0.0ms)

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

simplify82.0ms (1.1%)

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 → 142

Iterations

Useful iterations: 3 (0.0ms)

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

prune229.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	128	14	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	130	14	144

Error

0.1b

Counts

144 → 14

Alt Table

Status	Error	Program
	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)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))) 3))
	8.1b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	8.0b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3)))
	5.9b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	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)))
	9.4b	(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)))))
	14.6b	(.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)))))))
	3.3b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.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)))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (pow.f32 (sqrt.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 2)))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (pow.f32 (cbrt.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3)))
	3.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3) 1/3))
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (log.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 4378 to 3039 computations (30.6% saved)

localize52.0ms (0.7%)

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)

series164.0ms (2.2%)

Counts

4 → 44

Calls

4 calls:

148.0ms	(.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)))))
12.0ms	(.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))
4.0ms	(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)

rewrite121.0ms (1.6%)

Algorithm

2×	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:

118.0ms	(sin.f32 (cbrt.f32 (.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))))
118.0ms	(.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 u2 3))
118.0ms	(.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)))))
118.0ms	(pow.f32 (*.f32 2 (PI.f32)) 3)

Iterations

Useful iterations: 0 (0.0ms)

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

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

prune119.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	125	13	138

Error

0.1b

Counts

138 → 13

Alt Table

Status	Error	Program
	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)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))) 3))
✓	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)))))
	1.2b	(.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)))))
	8.1b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	8.0b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3)))
	5.9b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	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)))
	9.4b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 2)
	14.6b	(.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)))))))
▶	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)))))
	3.3b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.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)))
	3.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3) 1/3))

Compiler

Compiled 3703 to 2529 computations (31.7% saved)

localize61.0ms (0.8%)

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)))

series158.0ms (2.1%)

Counts

3 → 32

Calls

3 calls:

145.0ms

(*.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)))))

12.0ms

(*.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)))

rewrite61.0ms (0.8%)

Algorithm

2×	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:

60.0ms

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

60.0ms

(*.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)))))

60.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

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

simplify71.0ms (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

prune134.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	122	13	135

Error

0.1b

Counts

135 → 13

Alt Table

Status	Error	Program
▶	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)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))) 3))
✓	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)))))
	1.2b	(.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)))))
	8.1b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	8.0b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3)))
	5.9b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	14.6b	(.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)))))))
✓	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)))))
	3.3b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.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)))
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (pow.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) 3) 1/3) (pow.f32 u2 3)))))
	9.4b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 2)
	3.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3) 1/3))

Compiler

Compiled 3789 to 2667 computations (29.6% saved)

localize47.0ms (0.6%)

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 (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)))))
✓	0.4b	(*.f32 (PI.f32) u2)

series251.0ms (3.3%)

Counts

3 → 28

Calls

3 calls:

244.0ms	(.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)))))
3.0ms	(*.f32 (PI.f32) u2)
3.0ms	(sin.f32 (*.f32 (PI.f32) u2))

rewrite66.0ms (0.9%)

Algorithm

2×	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 → 62

Calls

3 calls:

65.0ms	(sin.f32 (*.f32 (PI.f32) u2))
65.0ms	(.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)))))
65.0ms	(*.f32 (PI.f32) u2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	309	29
2	3231	29
3	5685	29
0	0	0
1	0	0

simplify80.0ms (1.1%)

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

90 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1670
1	437	1542
2	1552	1427
3	4686	1425
4	5028	1425

prune128.0ms (1.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	158	14	172

Error

0.1b

Counts

172 → 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)))))
	1.2b	(.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)))))
	15.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) u2)))) (cbrt.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) u2)))))) (log.f32 (cbrt.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) u2)))))) (cos.f32 (.f32 (PI.f32) u2)))))
	8.1b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	8.0b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u1) 3/2) (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3)))
	5.9b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))) 3))
	14.6b	(.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)))))))
✓	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)))))
	3.3b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2 (.f32 u2 (PI.f32)) (.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 2 (.f32 (cos.f32 (.f32 u2 (PI.f32))) (.f32 (sin.f32 (*.f32 u2 (PI.f32))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (.f32 (pow.f32 (pow.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) 3) 1/3) (pow.f32 u2 3)))))
	9.4b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))) 2)
	3.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (pow.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)) 3) 1/3))

Compiler

Compiled 5049 to 2540 computations (49.7% saved)

regimes1.7s (22%)

Accuracy

Total 0.4b remaining (82.9%)

Threshold costs 0.4b (82.9%)

Counts

120 → 1

Compiler

Compiled 26158 to 22110 computations (15.5% 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	17	29
1	26	29
2	30	29
3	32	29
4	32	29

end224.0ms (3%)

Compiler: Compiled 363 to 298 computations (17.9% 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

analyze458.0ms (6%)

sample3.0s (39.4%)

simplify14.0ms (0.2%)

prune6.0ms (0.1%)

localize77.0ms (1%)

series168.0ms (2.2%)

rewrite89.0ms (1.2%)

simplify82.0ms (1.1%)

prune229.0ms (3%)

localize52.0ms (0.7%)

series164.0ms (2.2%)

rewrite121.0ms (1.6%)

simplify73.0ms (1%)

prune119.0ms (1.6%)

localize61.0ms (0.8%)

series158.0ms (2.1%)

rewrite61.0ms (0.8%)

simplify71.0ms (0.9%)

prune134.0ms (1.8%)

localize47.0ms (0.6%)

series251.0ms (3.3%)

rewrite66.0ms (0.9%)

simplify80.0ms (1.1%)

prune128.0ms (1.7%)

regimes1.7s (22%)

simplify2.0ms (0%)

end224.0ms (3%)

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