Details

analyze384.0ms (4.9%)

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)

sample99.0ms (1.3%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify16.0ms (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

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize36.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series197.0ms (2.5%)

Counts

4 → 52

Calls

4 calls:

178.0ms	(.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)

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))))

simplify119.0ms (1.5%)

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

prune220.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	10	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

0.1b

Counts

170 → 11

Alt Table

Status	Error	Program
	0.5b	(.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)))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (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)))))
	2.8b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))
▶	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))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.7b	(.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))))
	0.9b	(.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 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.9b	(.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)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 5031 to 3060 computations (39.2% saved)

localize44.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series159.0ms (2%)

Counts

4 → 32

Calls

4 calls:

126.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
16.0ms	(cos.f32 (.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2)))
10.0ms	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2))
6.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary32`
20×	`add-exp-log_binary32`
20×	`pow1_binary32`
17×	`sqrt-prod_binary32`
17×	`add-sqr-sqrt_binary32`

Counts

4 → 89

Calls

4 calls:

8.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))
6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
5.0ms	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2))
2.0ms	(cos.f32 (.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2)))

simplify157.0ms (2%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-def_binary32`
351×	`cancel-sign-sub-inv_binary32`
316×	`associate-l_binary32`
285×	`fma-neg_binary32`
239×	`associate-r_binary32`

Counts

121 → 159

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	250	2957
1	640	2718
2	2102	2606
3	4634	2602
4	4957	2598
5	4999	2598
6	4947	2598

prune195.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

0.1b

Counts

170 → 11

Alt Table

Status	Error	Program
	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)))))
	2.0b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))) (sqrt.f32 (cos.f32 (.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2)))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))))
	0.9b	(.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)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.7b	(.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))))
	0.9b	(.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 (.f32 (*.f32 2 (PI.f32)) u2))))
▶	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	2.8b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 2 (*.f32 u2 (PI.f32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))

Compiler

Compiled 4802 to 2591 computations (46% saved)

localize63.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series45.0ms (0.6%)

Counts

3 → 28

Calls

3 calls:

23.0ms

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

15.0ms

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

7.0ms

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

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`pow1_binary32`
61×	`sqrt-prod_binary32`
50×	`add-sqr-sqrt_binary32`
32×	`pow-prod-up_binary32`
31×	`*-un-lft-identity_binary32`

Counts

3 → 163

Calls

3 calls:

13.0ms

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

9.0ms

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

5.0ms

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

simplify123.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary32`
321×	`fma-neg_binary32`
218×	`associate-l_binary32`
209×	`associate-r_binary32`
166×	`times-frac_binary32`

Counts

191 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	3349
1	602	2791
2	1902	2650
3	4660	2650
4	4986	2650

prune587.0ms (7.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	318	8	326
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	323	14	337

Error

0.0b

Counts

337 → 14

Alt Table

Status	Error	Program
	0.5b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (log.f32 (exp.f32 (pow.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) 2))) (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 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))))
	2.0b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))) (sqrt.f32 (cos.f32 (.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.9b	(.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 (.f32 (*.f32 2 (PI.f32)) u2))))
▶	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))))) (cbrt.f32 (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2)))))
	0.9b	(cbrt.f32 (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) 4) (pow.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) 4)) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(cbrt.f32 (.f32 (sqrt.f32 (pow.f32 (neg.f32 (log1p.f32 (neg.f32 u1))) 3)) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(cbrt.f32 (.f32 (.f32 (sqrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) 3)) (sqrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) 3))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	1.0b	(cbrt.f32 (.f32 (.f32 (exp.f32 (log.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	1.4b	(cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 15335 to 7686 computations (49.9% saved)

localize78.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.4b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
	0.5b	(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
✓	1.3b	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series472.0ms (6%)

Counts

2 → 16

Calls

2 calls:

240.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))
232.0ms	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary32`
16×	`log-pow_binary32`
15×	`*-un-lft-identity_binary32`
12×	`distribute-lft-out_binary32`
9×	`exp-prod_binary32`

Counts

2 → 49

Calls

2 calls:

7.0ms	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))
5.0ms	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-def_binary32`
390×	`fma-neg_binary32`
272×	`prod-exp_binary32`
242×	`associate-*l/_binary32`
191×	`associate-*r/_binary32`

Counts

65 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	790
1	146	630
2	441	622
3	1728	622
4	4208	622
5	5111	622

prune472.0ms (6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	220	4	224
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	226	12	238

Error

0.0b

Counts

238 → 12

Alt Table

Status	Error	Program
	0.5b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (log.f32 (exp.f32 (pow.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) 2))) (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 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))))
	2.0b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))))) (sqrt.f32 (cos.f32 (.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2)))))
	0.9b	(cbrt.f32 (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) 4) (pow.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) 4)) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (exp.f32 (log.f32 (*.f32 2 (PI.f32)))) (exp.f32 (log.f32 u2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.3b	(cbrt.f32 (.f32 (.f32 (neg.f32 (log1p.f32 (neg.f32 u1))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))))
	0.9b	(.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 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))) (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))))
	0.4b	(cbrt.f32 (.f32 (.f32 (sqrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) 3)) (sqrt.f32 (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) 3))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 11010 to 5308 computations (51.8% saved)

regimes1.8s (22.8%)

Accuracy

Total 0.2b remaining (70.2%)

Threshold costs 0.2b (70.2%)

Counts

145 → 1

Compiler

Compiled 46562 to 33716 computations (27.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary32`
11×	`neg-sub0_binary32`
11×	`neg-mul-1_binary32`
10×	`+-commutative_binary32`
9×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	62
1	35	62
2	42	62
3	52	62
4	60	62
5	73	62
6	84	62
7	91	62
8	95	62
9	96	62
10	96	62

end1.0ms (0%)

Compiler: Compiled 38 to 28 computations (26.3% saved)

sample2.4s (30.6%)

Algorithm

1×

intervals

Results

999.0ms	8000×	body	128	valid
506.0ms	8000×	pre	128	true
0.0ms	2×	pre	128	false

Compiler

Compiled 514 to 360 computations (30% 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

analyze384.0ms (4.9%)

sample99.0ms (1.3%)

simplify16.0ms (0.2%)

prune5.0ms (0.1%)

localize36.0ms (0.5%)

series197.0ms (2.5%)

rewrite17.0ms (0.2%)

simplify119.0ms (1.5%)

prune220.0ms (2.8%)

localize44.0ms (0.6%)

series159.0ms (2%)

rewrite26.0ms (0.3%)

simplify157.0ms (2%)

prune195.0ms (2.5%)

localize63.0ms (0.8%)

series45.0ms (0.6%)

rewrite43.0ms (0.6%)

simplify123.0ms (1.6%)

prune587.0ms (7.5%)

localize78.0ms (1%)

series472.0ms (6%)

rewrite13.0ms (0.2%)

simplify67.0ms (0.9%)

prune472.0ms (6%)

regimes1.8s (22.8%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample2.4s (30.6%)

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