Details

analyze426.0ms (3.6%)

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)

sample2.3s (19%)

Results

2.2s	8256×	body	128	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify13.0ms (0.1%)

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

prune5.0ms (0%)

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
▶	0.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	13.6b	(.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 (0.3%)

Local error

Found 4 expressions with local error:

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

series195.0ms (1.6%)

Counts

4 → 52

Calls

4 calls:

177.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
11.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
3.0ms	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))
3.0ms	(.f32 (.f32 2 (PI.f32)) u2)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary32`
18×	`add-sqr-sqrt_binary32`
14×	`associate-l_binary32`
13×	`*-un-lft-identity_binary32`
13×	`add-cube-cbrt_binary32`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
4.0ms	(.f32 (.f32 2 (PI.f32)) u2)
1.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
1.0ms	(sin.f32 (.f32 (.f32 2 (PI.f32)) u2))

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Rules

553×	`cancel-sign-sub-inv_binary32`
510×	`fma-neg_binary32`
360×	`times-frac_binary32`
236×	`associate-l_binary32`
224×	`fma-def_binary32`

Counts

134 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	3674
1	775	3341
2	2559	3238
3	4483	3212
4	5079	3212

prune179.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	151	13	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	153	13	166

Error

0.1b

Counts

166 → 13

Alt Table

Status	Error	Program
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) u2)) (sqrt.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.9b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	13.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
▶	0.7b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (fma.f32 2 (.f32 (PI.f32) u2) (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 u2 7) -8/315) (.f32 (pow.f32 (.f32 (PI.f32) u2) 3) -4/3)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
	5.4b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	1.2b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	0.8b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))

Compiler

Compiled 5136 to 3127 computations (39.1% saved)

localize50.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.5b	(*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))

series1.3s (10.6%)

Counts

3 → 60

Calls

3 calls:

809.0ms

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

402.0ms

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

55.0ms

(*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary32`
29×	`associate-l_binary32`
22×	`cbrt-prod_binary32`
19×	`*-un-lft-identity_binary32`
19×	`add-cube-cbrt_binary32`

Counts

3 → 100

Calls

3 calls:

14.0ms

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

8.0ms

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

5.0ms

(*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))

simplify446.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary32`
365×	`associate-/r*_binary32`
312×	`*-commutative_binary32`
307×	`times-frac_binary32`
183×	`associate-/l*_binary32`

Counts

160 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	760	11532
1	2295	10608
2	4928	10571
3	5074	10571

prune429.0ms (3.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	254	6	260
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	261	12	273

Error

0.0b

Counts

273 → 12

Alt Table

Status	Error	Program
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
	7.2b	(.f32 (sqrt.f32 (cbrt.f32 (.f32 u1 u1))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	1.0b	(.f32 (sqrt.f32 (pow.f32 (.f32 (log1p.f32 (neg.f32 u1)) (log1p.f32 (neg.f32 u1))) 1/3)) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
▶	0.8b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	1.8b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))
	0.9b	(.f32 (sqrt.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	5.4b	(.f32 2 (.f32 u2 (*.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.4b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	1.0b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (fma.f32 2 (.f32 (PI.f32) u2) (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 u2 7) -8/315) (.f32 (pow.f32 (.f32 (PI.f32) u2) 3) -4/3)))))

Compiler

Compiled 17138 to 10259 computations (40.1% saved)

localize46.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series472.0ms (3.9%)

Counts

2 → 40

Calls

2 calls:

245.0ms

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

227.0ms

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

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`sqrt-prod_binary32`
32×	`associate-l_binary32`
19×	`add-sqr-sqrt_binary32`
13×	`*-un-lft-identity_binary32`
13×	`add-cube-cbrt_binary32`

Counts

2 → 68

Calls

2 calls:

12.0ms

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

8.0ms

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

simplify142.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

610×	`cancel-sign-sub-inv_binary32`
486×	`fma-neg_binary32`
393×	`times-frac_binary32`
286×	`associate-r_binary32`
252×	`associate-l_binary32`

Counts

108 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	4726
1	832	4248
2	2810	4236
3	4907	4234
4	5040	4234

prune259.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	202	13	215

Error

0.0b

Counts

215 → 13

Alt Table

Status	Error	Program
	0.9b	(.f32 (sqrt.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
▶	0.6b	(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
	7.2b	(.f32 (sqrt.f32 (cbrt.f32 (.f32 u1 u1))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.8b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 2) 2) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 u2 u2) u2))))))
	3.0b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.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 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2)))))
	1.4b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.0b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (fma.f32 2 (.f32 (PI.f32) u2) (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 u2 7) -8/315) (.f32 (pow.f32 (.f32 (PI.f32) u2) 3) -4/3)))))
	1.0b	(.f32 (sqrt.f32 (pow.f32 (.f32 (log1p.f32 (neg.f32 u1)) (log1p.f32 (neg.f32 u1))) 1/3)) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.8b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))

Compiler

Compiled 8053 to 4015 computations (50.1% saved)

localize72.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series241.0ms (2%)

Counts

3 → 24

Calls

3 calls:

232.0ms	(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
5.0ms	(*.f32 (PI.f32) u2)
3.0ms	(sin.f32 (.f32 2 (.f32 (PI.f32) u2)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`associate-r_binary32`
16×	`add-sqr-sqrt_binary32`
11×	`sqrt-prod_binary32`
10×	`*-un-lft-identity_binary32`
10×	`add-cube-cbrt_binary32`

Counts

3 → 62

Calls

3 calls:

7.0ms	(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
3.0ms	(*.f32 (PI.f32) u2)
1.0ms	(sin.f32 (.f32 2 (.f32 (PI.f32) u2)))

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary32`
375×	`cancel-sign-sub-inv_binary32`
328×	`fma-neg_binary32`
258×	`times-frac_binary32`
209×	`neg-mul-1_binary32`

Counts

86 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	2560
1	567	2349
2	1834	2224
3	4469	2222
4	4999	2222
5	4961	2222

prune257.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	170	12	182

Error

0.0b

Counts

182 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 2) 2) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))) (.f32 (.f32 u2 u2) u2))))))
	3.0b	(fma.f32 2 (.f32 u2 (.f32 (PI.f32) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.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 (sin.f32 (.f32 2 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (cbrt.f32 (PI.f32)) u2)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.9b	(.f32 (sqrt.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	7.2b	(.f32 (sqrt.f32 (cbrt.f32 (.f32 u1 u1))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.0b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2)))))
	1.0b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (sin.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 4/15 (.f32 (pow.f32 u2 5) (pow.f32 (PI.f32) 5)) (fma.f32 2 (.f32 (PI.f32) u2) (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 u2 7) -8/315) (.f32 (pow.f32 (.f32 (PI.f32) u2) 3) -4/3)))))
	0.6b	(.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) u2))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
	1.0b	(.f32 (sqrt.f32 (pow.f32 (.f32 (log1p.f32 (neg.f32 u1)) (log1p.f32 (neg.f32 u1))) 1/3)) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.8b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))

Compiler

Compiled 4907 to 2782 computations (43.3% saved)

regimes4.6s (38.5%)

Accuracy

Total 0.5b remaining (86.8%)

Threshold costs 0.5b (86.8%)

Counts

310 → 1

Compiler

Compiled 89672 to 62264 computations (30.6% saved)

simplify3.0ms (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	22	37
1	33	37
2	37	37
3	39	37
4	37	37

end220.0ms (1.8%)

Compiler: Compiled 428 to 293 computations (31.5% 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

analyze426.0ms (3.6%)

sample2.3s (19%)

simplify13.0ms (0.1%)

prune5.0ms (0%)

localize35.0ms (0.3%)

series195.0ms (1.6%)

rewrite17.0ms (0.1%)

simplify114.0ms (1%)

prune179.0ms (1.5%)

localize50.0ms (0.4%)

series1.3s (10.6%)

rewrite34.0ms (0.3%)

simplify446.0ms (3.7%)

prune429.0ms (3.6%)

localize46.0ms (0.4%)

series472.0ms (3.9%)

rewrite27.0ms (0.2%)

simplify142.0ms (1.2%)

prune259.0ms (2.2%)

localize72.0ms (0.6%)

series241.0ms (2%)

rewrite16.0ms (0.1%)

simplify110.0ms (0.9%)

prune257.0ms (2.1%)

regimes4.6s (38.5%)

simplify3.0ms (0%)

end220.0ms (1.8%)

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