Details

analyze423.0ms (4.2%)

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)

sample2.2s (21.6%)

Results

2.1s	8256×	body	128	valid
1.0ms	3×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify14.0ms (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)))
	13.6b	(.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)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series208.0ms (2.1%)

Counts

4 → 52

Calls

4 calls:

189.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
13.0ms	(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)

rewrite17.0ms (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)
2.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
2.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))

simplify124.0ms (1.2%)

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

prune214.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	157	11	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

0.1b

Counts

170 → 11

Alt Table

Status	Error	Program
	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)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.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 (.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)))))
	1.2b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	2.9b	(+.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)))))
	0.6b	(.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))))
	1.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (exp.f32 (log.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)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	2.6b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	6.5b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))

Compiler

Compiled 5015 to 3060 computations (39% saved)

localize47.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
✓	0.2b	(cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
✓	0.4b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
✓	1.4b	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series1.2s (12.1%)

Counts

4 → 44

Calls

4 calls:

487.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
247.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))
243.0ms	(cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
236.0ms	(+.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	(cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
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)))))
5.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))
5.0ms	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))

simplify312.0ms (3.1%)

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

prune199.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	149	12	161

Error

0.1b

Counts

161 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.2b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	2.9b	(+.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)))))
	1.9b	(.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))))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))) (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))) (cbrt.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.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))))
	2.7b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
	2.6b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	6.5b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))

Compiler

Compiled 4604 to 2845 computations (38.2% saved)

localize78.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
✓	0.2b	(cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
	0.4b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
✓	1.8b	(pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series1.6s (16.1%)

Counts

3 → 44

Calls

3 calls:

717.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))

461.0ms

(cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))

432.0ms

(pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary32`
15×	`*-un-lft-identity_binary32`
14×	`add-sqr-sqrt_binary32`
13×	`associate-l_binary32`
11×	`sqrt-prod_binary32`

Counts

3 → 67

Calls

3 calls:

9.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))

5.0ms

(pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

3.0ms

(cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))

simplify151.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary32`
472×	`fma-def_binary32`
315×	`associate-l_binary32`
269×	`associate-+l+_binary32`
244×	`associate-r_binary32`

Counts

111 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	3531
1	476	2480
2	1308	2398
3	4571	2394
4	5229	2394

prune204.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Error

0.1b

Counts

174 → 11

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.2b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	2.9b	(+.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)))))
	0.6b	(.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))))
	2.2b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
	1.9b	(.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 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))
	2.7b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
▶	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	2.6b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 4947 to 2943 computations (40.5% saved)

localize58.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
✓	0.2b	(expm1.f32 (log1p.f32 (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))
	0.4b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
	1.8b	(pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series447.0ms (4.5%)

Counts

1 → 12

Calls

1 calls:

447.0ms

(expm1.f32 (log1p.f32 (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary32`
1×	`add-sqr-sqrt_binary32`
1×	`add-cube-cbrt_binary32`
1×	`add-cbrt-cube_binary32`
1×	`add-exp-log_binary32`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f32 (log1p.f32 (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary32`
774×	`fma-def_binary32`
487×	`exp-sum_binary32`
425×	`sub-neg_binary32`
386×	`unswap-sqr_binary32`

Counts

23 → 23

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	39	454
1	69	345
2	119	345
3	279	345
4	817	345
5	2460	345
6	3799	257
7	4631	257
8	4912	257

prune211.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	116	11	127

Error

0.1b

Counts

127 → 11

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))
	0.7b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.2b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	2.9b	(+.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)))))
	0.6b	(.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))))
	2.2b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
	1.9b	(.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 (pow.f32 (E.f32) (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))
	2.7b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
✓	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	2.6b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 2971 to 1747 computations (41.2% saved)

regimes1.9s (19.4%)

Accuracy

Total 0.2b remaining (73.4%)

Threshold costs 0.2b (73.4%)

Counts

171 → 1

Compiler

Compiled 38560 to 31948 computations (17.1% 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	18	69
1	29	69
2	33	69
3	35	69
4	35	69

end194.0ms (1.9%)

Compiler: Compiled 386 to 273 computations (29.3% 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

analyze423.0ms (4.2%)

sample2.2s (21.6%)

simplify14.0ms (0.1%)

prune5.0ms (0%)

localize33.0ms (0.3%)

series208.0ms (2.1%)

rewrite17.0ms (0.2%)

simplify124.0ms (1.2%)

prune214.0ms (2.1%)

localize47.0ms (0.5%)

series1.2s (12.1%)

rewrite29.0ms (0.3%)

simplify312.0ms (3.1%)

prune199.0ms (2%)

localize78.0ms (0.8%)

series1.6s (16.1%)

rewrite22.0ms (0.2%)

simplify151.0ms (1.5%)

prune204.0ms (2%)

localize58.0ms (0.6%)

series447.0ms (4.5%)

rewrite1.0ms (0%)

simplify78.0ms (0.8%)

prune211.0ms (2.1%)

regimes1.9s (19.4%)

simplify3.0ms (0%)

end194.0ms (1.9%)

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