Details

analyze383.0ms (4.5%)

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)

sample101.0ms (1.2%)

Algorithm

1×

intervals

Results

36.0ms	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

0.4b

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)))
	13.1b	(.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)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series202.0ms (2.4%)

Counts

4 → 52

Calls

4 calls:

183.0ms	(.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)

rewrite18.0ms (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)
3.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
2.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))

simplify116.0ms (1.4%)

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

prune216.0ms (2.6%)

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

0.2b

Counts

170 → 13

Alt Table

Status	Error	Program
	1.2b	(.f32 (exp.f32 (log.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 (.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))))
	1.8b	(.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))))
	2.1b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	13.1b	(.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 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.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)))))
	1.0b	(.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)))))
	2.2b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 u2 u2) -2)))))
	1.0b	(.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 (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)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))

Compiler

Compiled 5171 to 3172 computations (38.7% saved)

localize47.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.7b	(expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))

series181.0ms (2.1%)

Counts

2 → 32

Calls

2 calls:

174.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
7.0ms	(expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`associate-l_binary32`
11×	`sqrt-prod_binary32`
11×	`add-sqr-sqrt_binary32`
7×	`*-un-lft-identity_binary32`
7×	`add-cube-cbrt_binary32`

Counts

2 → 42

Calls

2 calls:

6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
0.0ms	(expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary32`
645×	`fma-def_binary32`
384×	`cancel-sign-sub-inv_binary32`
215×	`associate--l+_binary32`
173×	`associate-/r*_binary32`

Counts

74 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2466
1	528	2302
2	1616	2200
3	4612	2192
4	5397	2192

prune240.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	155	13	168

Error

0.2b

Counts

168 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (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)))
	1.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (exp.f32 (log.f32 (expm1.f32 (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)))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	1.8b	(.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))))
	2.1b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	13.1b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 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)))))
	2.2b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 u2 u2) -2)))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	2.0b	(.f32 (sqrt.f32 (.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sqrt.f32 (.f32 (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))

Compiler

Compiled 4670 to 2865 computations (38.7% saved)

localize50.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
✓	0.2b	(log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
	0.7b	(expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))

series186.0ms (2.2%)

Counts

2 → 32

Calls

2 calls:

180.0ms

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

6.0ms

(log.f32 (exp.f32 (expm1.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`associate-l_binary32`
13×	`add-sqr-sqrt_binary32`
11×	`sqrt-prod_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-cube-cbrt_binary32`

Counts

2 → 49

Calls

2 calls:

10.0ms

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

2.0ms

(log.f32 (exp.f32 (expm1.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))

simplify94.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-neg_binary32`
645×	`fma-def_binary32`
384×	`cancel-sign-sub-inv_binary32`
215×	`associate--l+_binary32`
173×	`associate-/r*_binary32`

Counts

81 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	2763
1	545	2448
2	1635	2346
3	4640	2338
4	5426	2338

prune276.0ms (3.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	165	5	170
Fresh	6	6	12
Picked	0	1	1
Done	0	0	0
Total	171	12	183

Error

0.1b

Counts

183 → 12

Alt Table

Status	Error	Program
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	1.8b	(.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))))
	13.1b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (log.f32 (cbrt.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))))))
▶	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (-.f32 (log.f32 (exp.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))) (log.f32 (exp.f32 1)))))
	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)))))
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (.f32 (cbrt.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (log.f32 (exp.f32 (.f32 (cbrt.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))))
	2.2b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 u2 u2) -2)))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.8b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))) (sqrt.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (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 (PI.f32) u2)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))))) (cbrt.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))

Compiler

Compiled 5321 to 3374 computations (36.6% saved)

localize64.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.8b	(-.f32 (log.f32 (exp.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (log.f32 (exp.f32 1)))
✓	1.0b	(log.f32 (exp.f32 1))
✓	1.1b	(exp.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))

series18.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

10.0ms	(exp.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
8.0ms	(-.f32 (log.f32 (exp.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (log.f32 (exp.f32 1)))
0.0ms	(log.f32 (exp.f32 1))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`log-pow_binary32`
60×	`exp-prod_binary32`
52×	`*-un-lft-identity_binary32`
49×	`prod-diff_binary32`
42×	`add-sqr-sqrt_binary32`

Counts

3 → 123

Calls

3 calls:

8.0ms	(-.f32 (log.f32 (exp.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (log.f32 (exp.f32 1)))
2.0ms	(exp.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
1.0ms	(log.f32 (exp.f32 1))

simplify131.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1001×	`fma-neg_binary32`
493×	`fma-def_binary32`
354×	`*-commutative_binary32`
329×	`sub-neg_binary32`
256×	`cancel-sign-sub-inv_binary32`

Counts

147 → 153

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	186	2094
1	348	2009
2	1062	1940
3	3129	1919
4	4887	1919
5	4990	1916
6	4906	1916

prune409.0ms (4.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	180	13	193

Error

0.1b

Counts

193 → 13

Alt Table

Status	Error	Program
	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)))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (+.f32 (fma.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (log.f32 (exp.f32 1)) (neg.f32 (.f32 (sqrt.f32 (log.f32 (exp.f32 1))) (sqrt.f32 (log.f32 (exp.f32 1)))))) (fma.f32 (neg.f32 (sqrt.f32 (log.f32 (exp.f32 1)))) (sqrt.f32 (log.f32 (exp.f32 1))) (*.f32 (sqrt.f32 (log.f32 (exp.f32 1))) (sqrt.f32 (log.f32 (exp.f32 1))))))))
	1.8b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))) (sqrt.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))))
	1.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (fma.f32 (cbrt.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (log.f32 (exp.f32 (.f32 (cbrt.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (exp.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) -1)))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))) (cbrt.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2)))))) (cbrt.f32 (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (-.f32 (log.f32 (exp.f32 (exp.f32 (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))) (log.f32 (exp.f32 1)))))
	1.0b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	1.8b	(.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))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (log.f32 (cbrt.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))))))
	1.0b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (.f32 (cbrt.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (log.f32 (exp.f32 (.f32 (cbrt.f32 (expm1.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))))))))
	2.2b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 u2 u2) -2)))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log1p.f32 (log.f32 (exp.f32 (expm1.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	0.7b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))

Compiler

Compiled 6279 to 4569 computations (27.2% saved)

regimes3.4s (40.1%)

Accuracy

Total 0.2b remaining (72.7%)

Threshold costs 0.2b (72.7%)

Counts

208 → 1

Compiler

Compiled 53834 to 45134 computations (16.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	14	22
1	23	22
2	27	22
3	29	22
4	29	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample2.1s (25.1%)

Algorithm

1×

intervals

Results

951.0ms	8000×	body	128	valid
323.0ms	8000×	pre	128	true
0.0ms	6×	pre	128	false

Compiler

Compiled 508 to 415 computations (18.3% 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

analyze383.0ms (4.5%)

sample101.0ms (1.2%)

simplify16.0ms (0.2%)

prune5.0ms (0.1%)

localize37.0ms (0.4%)

series202.0ms (2.4%)

rewrite18.0ms (0.2%)

simplify116.0ms (1.4%)

prune216.0ms (2.6%)

localize47.0ms (0.6%)

series181.0ms (2.1%)

rewrite9.0ms (0.1%)

simplify88.0ms (1.1%)

prune240.0ms (2.9%)

localize50.0ms (0.6%)

series186.0ms (2.2%)

rewrite14.0ms (0.2%)

simplify94.0ms (1.1%)

prune276.0ms (3.3%)

localize64.0ms (0.8%)

series18.0ms (0.2%)

rewrite24.0ms (0.3%)

simplify131.0ms (1.6%)

prune409.0ms (4.9%)

regimes3.4s (40.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.1s (25.1%)

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