Details

analyze430.0ms (6.1%)

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)

sample2.3s (32.6%)

Results

2.3s	8256×	body	128	valid
2.0ms	7×	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`
13×	`fma-def_binary32`
10×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	13.5b	(.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)

localize35.0ms (0.5%)

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 2 (.f32 (PI.f32) u2)))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
✓	0.3b	(*.f32 (PI.f32) u2)

series150.0ms (2.1%)

Counts

4 → 32

Calls

4 calls:

136.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
9.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
3.0ms	(sin.f32 (.f32 2 (.f32 (PI.f32) u2)))
2.0ms	(*.f32 (PI.f32) u2)

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`prod-diff_binary32`
202×	`expm1-udef_binary32`
202×	`log1p-udef_binary32`
131×	`add-sqr-sqrt_binary32`
123×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	265	37
2	3249	37

Stop Event

1×	node limit

Counts

4 → 76

Calls

4 calls:

46.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
46.0ms	(sin.f32 (.f32 2 (.f32 (PI.f32) u2)))
46.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
46.0ms	(*.f32 (PI.f32) u2)

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

538×	`cancel-sign-sub-inv_binary32`
348×	`times-frac_binary32`
276×	`associate-*l/_binary32`
248×	`associate-/r*_binary32`
218×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2008
1	588	1830
2	2199	1690

Stop Event

1×	node limit

Counts

108 → 124

prune132.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	111	13	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	14	126

Error

0.1b

Counts

126 → 14

Alt Table

Status	Error	Program
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (exp.f32 (log.f32 (*.f32 (PI.f32) u2))))))
	2.0b	(-.f32 (.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 (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))))))
	8.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 u1) 3/2)) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))
	13.5b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	8.3b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (log1p.f32 u1))) 3) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 3))
	8.3b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	2.7b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
▶	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 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)))))
	13.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (pow.f32 (sqrt.f32 (*.f32 (PI.f32) u2)) 2))))

Compiler

Compiled 3995 to 2748 computations (31.2% saved)

localize47.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series154.0ms (2.2%)

Counts

4 → 32

Calls

4 calls:

140.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))
9.0ms	(*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))
4.0ms	(sin.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3)))))
0.0ms	(pow.f32 (PI.f32) 3)

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

469×	`prod-diff_binary32`
251×	`log1p-udef_binary32`
163×	`add-sqr-sqrt_binary32`
155×	`expm1-log1p-u_binary32`
154×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	349	40
2	4083	40

Stop Event

1×	node limit

Counts

4 → 73

Calls

4 calls:

56.0ms	(sin.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3)))))
56.0ms	(*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))
56.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 u2 3))))))
56.0ms	(pow.f32 (PI.f32) 3)

simplify36.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary32`
573×	`associate-l_binary32`
366×	`cancel-sign-sub-inv_binary32`
160×	`associate-*l/_binary32`
160×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1528
1	428	1418
2	1508	1320

Stop Event

1×	node limit

Counts

105 → 113

prune112.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	115	12	127

Error

0.1b

Counts

127 → 12

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (exp.f32 (log.f32 (*.f32 (PI.f32) u2))))))
	2.0b	(-.f32 (.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 (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))))))
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (PI.f32)))) (pow.f32 u2 3))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (pow.f32 (cbrt.f32 (*.f32 (PI.f32) u2)) 3))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 3))
	8.3b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	2.7b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (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)))))
	13.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 1))
	8.3b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (log1p.f32 u1))) 3) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Compiler

Compiled 3395 to 2271 computations (33.1% saved)

localize44.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))
✓	0.1b	(sin.f32 (*.f32 (PI.f32) u2))
✓	0.3b	(.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)))))
	0.3b	(*.f32 (PI.f32) u2)

series166.0ms (2.3%)

Counts

3 → 40

Calls

3 calls:

154.0ms

(*.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)))))

6.0ms

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

6.0ms

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

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`expm1-udef_binary32`
240×	`log1p-udef_binary32`
237×	`fma-def_binary32`
155×	`add-sqr-sqrt_binary32`
153×	`fma-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	310	40
2	4007	40

Stop Event

1×	node limit

Counts

3 → 52

Calls

3 calls:

46.0ms

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

46.0ms

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

46.0ms

(*.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)))))

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-def_binary32`
440×	`cancel-sign-sub-inv_binary32`
275×	`times-frac_binary32`
245×	`associate-/l*_binary32`
188×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1908
1	495	1776
2	1835	1659

Stop Event

1×	node limit

Counts

92 → 96

prune136.0ms (1.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	123	15	138

Error

0.0b

Counts

138 → 15

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	2.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (exp.f32 (log.f32 (.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 (PI.f32) (*.f32 u2 2)))) 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)))))))
	2.7b	(fma.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (PI.f32) 5)) (.f32 4/15 (pow.f32 u2 5)) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (.f32 (.f32 2 u2) (PI.f32)) (.f32 4/3 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
	8.3b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (PI.f32)))) (pow.f32 u2 3))))))
	13.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2))))))))
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (exp.f32 (log.f32 (*.f32 (PI.f32) u2))))))
	2.7b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2))) 3) (cos.f32 (*.f32 (PI.f32) u2)))))
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))))
	13.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) u2))) (sin.f32 (.f32 (PI.f32) u2))))))
	8.3b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (log1p.f32 u1))) 3) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Compiler

Compiled 4194 to 2192 computations (47.7% saved)

localize50.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))
✓	0.2b	(expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))))
	0.3b	(*.f32 (PI.f32) u2)

series173.0ms (2.5%)

Counts

3 → 44

Calls

3 calls:

158.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 2 (log1p.f32 (expm1.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))))

9.0ms

(expm1.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2))))

6.0ms

(log1p.f32 (expm1.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

911×	`prod-diff_binary32`
161×	`add-sqr-sqrt_binary32`
153×	`expm1-log1p-u_binary32`
151×	`log1p-expm1-u_binary32`
147×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	328	51
2	4137	51

Stop Event

1×	node limit

Counts

3 → 68

Calls

3 calls:

53.0ms

(log1p.f32 (expm1.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))

53.0ms

(expm1.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2))))

53.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 2 (log1p.f32 (expm1.f32 (*.f32 (sin.f32 (*.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))))

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary32`
456×	`cancel-sign-sub-inv_binary32`
275×	`times-frac_binary32`
244×	`associate-/l*_binary32`
195×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	2022
1	522	1890
2	1897	1766

Stop Event

1×	node limit

Counts

112 → 113

prune142.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	144	14	158

Error

0.0b

Counts

158 → 14

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 3) (PI.f32)) (pow.f32 u2 3))))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 u2 2)))) 2))
	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (pow.f32 (cbrt.f32 (cos.f32 (.f32 (PI.f32) u2))) 2)) (cbrt.f32 (cos.f32 (*.f32 (PI.f32) u2))))))
	2.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))))
	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)))))))
	2.7b	(fma.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (PI.f32) 5)) (.f32 4/15 (pow.f32 u2 5)) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (-.f32 (.f32 (.f32 2 u2) (PI.f32)) (.f32 4/3 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))
	8.3b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (log1p.f32 u1)) (sin.f32 (.f32 (PI.f32) (*.f32 u2 2))))) 3)
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2))) 3) (cos.f32 (*.f32 (PI.f32) u2)))))
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log1p.f32 (expm1.f32 (.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (PI.f32) u2)))) (cos.f32 (*.f32 (PI.f32) u2)))))))
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 2 (cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (PI.f32)))) (pow.f32 u2 3))))))
	13.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log.f32 (+.f32 1 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2))))))))
	13.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 2 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) u2)) (cos.f32 (*.f32 (PI.f32) u2)))))))))
	8.3b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (log1p.f32 u1))) 3) (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	2.7b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 u2 3) -4/3)))))

Compiler

Compiled 4367 to 2014 computations (53.9% saved)

regimes2.4s (33.7%)

Accuracy

Total 0.4b remaining (77.9%)

Threshold costs 0.4b (77.9%)

Counts

214 → 1

Compiler

Compiled 47140 to 38494 computations (18.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	21	44
1	32	44
2	36	44
3	38	44

Stop Event

1×

saturated

end216.0ms (3.1%)

Compiler: Compiled 396 to 313 computations (21% saved)

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Details

analyze430.0ms (6.1%)

sample2.3s (32.6%)

simplify14.0ms (0.2%)

prune5.0ms (0.1%)

localize35.0ms (0.5%)

series150.0ms (2.1%)

rewrite47.0ms (0.7%)

simplify41.0ms (0.6%)

prune132.0ms (1.9%)

localize47.0ms (0.7%)

series154.0ms (2.2%)

rewrite57.0ms (0.8%)

simplify36.0ms (0.5%)

prune112.0ms (1.6%)

localize44.0ms (0.6%)

series166.0ms (2.3%)

rewrite47.0ms (0.7%)

simplify43.0ms (0.6%)

prune136.0ms (1.9%)

localize50.0ms (0.7%)

series173.0ms (2.5%)

rewrite54.0ms (0.8%)

simplify45.0ms (0.6%)

prune142.0ms (2%)

regimes2.4s (33.7%)

simplify2.0ms (0%)

end216.0ms (3.1%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21