Details

analyze401.0ms (3.5%)

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 (20.2%)

Results

2.2s	8256×	body	128	valid
2.0ms	9×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify15.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize34.0ms (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	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
✓	0.4b	(.f32 (.f32 2 (PI.f32)) u2)

series198.0ms (1.7%)

Counts

4 → 52

Calls

4 calls:

180.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
12.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
3.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
3.0ms	(.f32 (.f32 2 (PI.f32)) u2)

rewrite19.0ms (0.2%)

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

simplify122.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

532×	`cancel-sign-sub-inv_binary32`
449×	`fma-neg_binary32`
324×	`times-frac_binary32`
243×	`associate-/r*_binary32`
229×	`associate-/l*_binary32`

Counts

134 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	3614
1	751	3315
2	2419	3199
3	4597	3191
4	5025	3191

prune222.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	12	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	13	170

Error

0.1b

Counts

170 → 13

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.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)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (+.f32 (log.f32 2) (log.f32 (PI.f32))) (log.f32 u2)))))
	0.6b	(.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))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	2.5b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (PI.f32) 2) (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))

Compiler

Compiled 5079 to 3116 computations (38.6% saved)

localize46.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
✓	0.5b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
✓	1.4b	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series1.3s (11.2%)

Counts

4 → 44

Calls

4 calls:

504.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
267.0ms	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
256.0ms	(cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
246.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary32`
22×	`*-un-lft-identity_binary32`
16×	`log-pow_binary32`
16×	`add-sqr-sqrt_binary32`
13×	`associate-l_binary32`

Counts

4 → 89

Calls

4 calls:

7.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
6.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))
6.0ms	(cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
5.0ms	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))

simplify109.0ms (1%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-def_binary32`
392×	`associate-l_binary32`
307×	`associate-r_binary32`
233×	`fma-neg_binary32`
210×	`distribute-rgt-in_binary32`

Counts

133 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	3009
1	503	2654
2	1496	2576
3	4630	2572
4	4960	2572

prune209.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	151	12	163

Error

0.0b

Counts

163 → 12

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	1.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))
	0.6b	(.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))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	2.5b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (PI.f32) 2) (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))) (sqrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.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)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	14.4b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
▶	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))

Compiler

Compiled 4584 to 2843 computations (38% saved)

localize74.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
	0.5b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
	1.4b	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series291.0ms (2.5%)

Counts

1 → 12

Calls

1 calls:

291.0ms

(*.f32 (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary32`
16×	`cbrt-prod_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-cube-cbrt_binary32`
8×	`pow1_binary32`

Counts

1 → 42

Calls

1 calls:

6.0ms

(*.f32 (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

833×	`distribute-rgt-neg-in_binary32`
637×	`fma-def_binary32`
479×	`cancel-sign-sub-inv_binary32`
413×	`*-commutative_binary32`
366×	`log-prod_binary32`

Counts

54 → 65

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	1251
1	158	1219
2	425	1019
3	1383	983
4	3425	824
5	4506	824
6	4826	824
7	4892	824

prune412.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	178	5	183
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	184	11	195

Error

0.0b

Counts

195 → 11

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (exp.f32 (fma.f32 (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (log.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)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.6b	(.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))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 (sqrt.f32 u2))) (log.f32 (sqrt.f32 u2)))))))
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (exp.f32 (log1p.f32 (expm1.f32 (log.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))
	1.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (.f32 (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	2.5b	(+.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (pow.f32 (PI.f32) 2) (fma.f32 (.f32 2/3 (pow.f32 u2 4)) (pow.f32 (PI.f32) 2) (.f32 (*.f32 u2 u2) -2)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))

Compiler

Compiled 7628 to 5003 computations (34.4% saved)

localize79.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.7b	(fma.f32 (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (log.f32 u2))
✓	1.4b	(exp.f32 (fma.f32 (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (log.f32 u2)))

series1.1s (9.9%)

Counts

2 → 24

Calls

2 calls:

674.0ms

(fma.f32 (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (log.f32 u2))

460.0ms

(exp.f32 (fma.f32 (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (log.f32 u2)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary32`
3×	`*-un-lft-identity_binary32`
3×	`add-sqr-sqrt_binary32`
3×	`exp-prod_binary32`
3×	`add-cube-cbrt_binary32`

Counts

2 → 24

Calls

2 calls:

1.0ms

(exp.f32 (fma.f32 (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (log.f32 u2)))

0.0ms

(fma.f32 (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (log.f32 u2))

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

490×	`distribute-rgt-in_binary32`
485×	`distribute-lft-in_binary32`
419×	`associate-+l+_binary32`
366×	`associate-l_binary32`
322×	`fma-neg_binary32`

Counts

48 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	687
1	80	495
2	177	495
3	671	495
4	4869	495
5	5143	495

prune423.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	170	10	180

Error

0.0b

Counts

180 → 10

Alt Table

Status	Error	Program
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) 2))))) (cbrt.f32 (cos.f32 (exp.f32 (fma.f32 (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (log.f32 u2))))))
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
✓	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (exp.f32 (fma.f32 (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (log.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)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (sqrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (cos.f32 (exp.f32 (fma.f32 (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (log.f32 u2))))))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (.f32 (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (cos.f32 (exp.f32 (fma.f32 (sqrt.f32 (log.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (log.f32 (*.f32 2 (PI.f32)))) (log.f32 u2))))))
	0.6b	(.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))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	1.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (.f32 (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))

Compiler

Compiled 7599 to 5130 computations (32.5% saved)

regimes3.6s (31.5%)

Accuracy

Total 0.3b remaining (81.5%)

Threshold costs 0.3b (81.5%)

Counts

259 → 1

Compiler

Compiled 86969 to 71331 computations (18% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	27	57
1	40	57
2	44	57
3	46	57
4	44	57

end242.0ms (2.1%)

Compiler: Compiled 431 to 343 computations (20.4% 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

analyze401.0ms (3.5%)

sample2.3s (20.2%)

simplify15.0ms (0.1%)

prune5.0ms (0%)

localize34.0ms (0.3%)

series198.0ms (1.7%)

rewrite19.0ms (0.2%)

simplify122.0ms (1.1%)

prune222.0ms (1.9%)

localize46.0ms (0.4%)

series1.3s (11.2%)

rewrite29.0ms (0.3%)

simplify109.0ms (1%)

prune209.0ms (1.8%)

localize74.0ms (0.6%)

series291.0ms (2.5%)

rewrite10.0ms (0.1%)

simplify102.0ms (0.9%)

prune412.0ms (3.6%)

localize79.0ms (0.7%)

series1.1s (9.9%)

rewrite3.0ms (0%)

simplify58.0ms (0.5%)

prune423.0ms (3.7%)

regimes3.6s (31.5%)

simplify3.0ms (0%)

end242.0ms (2.1%)

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