Details

analyze424.0ms (4.4%)

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 (22.9%)

Results

2.2s	8256×	body	128	valid
2.0ms	6×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify15.0ms (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

prune4.0ms (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
	13.6b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
▶	0.3b	(.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)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
✓	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)))
✓	0.4b	(.f32 (.f32 2 (PI.f32)) u2)

series200.0ms (2.1%)

Counts

4 → 52

Calls

4 calls:

184.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
10.0ms	(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:

7.0ms	(.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	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
1.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))

simplify115.0ms (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

prune213.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	156	12	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	12	170

Error

0.1b

Counts

170 → 12

Alt Table

Status	Error	Program
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.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 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.5b	(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)))))
	1.4b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.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)))))
▶	0.3b	(.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 (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 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cbrt.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.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))))
	0.4b	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
	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)))))

Compiler

Compiled 5111 to 3134 computations (38.7% saved)

localize45.0ms (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 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
✓	0.3b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
✓	1.5b	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series973.0ms (10%)

Counts

3 → 36

Calls

3 calls:

496.0ms

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

240.0ms

(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

237.0ms

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

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`pow1_binary32`
21×	`*-un-lft-identity_binary32`
16×	`log-pow_binary32`
15×	`add-sqr-sqrt_binary32`
13×	`associate-l_binary32`

Counts

3 → 80

Calls

3 calls:

8.0ms

(+.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)))

simplify102.0ms (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

116 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2737
1	500	2451
2	1494	2373
3	4628	2369
4	4958	2369

prune451.0ms (4.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	172	11	183

Error

0.1b

Counts

183 → 11

Alt Table

Status	Error	Program
	1.3b	(.f32 (exp.f32 (log.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	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.5b	(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)))))
	1.4b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.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)))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.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))))) (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 (log.f32 (.f32 2 (PI.f32))) (log.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 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))
	1.9b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	1.0b	(.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)))))

Compiler

Compiled 5570 to 3529 computations (36.6% saved)

localize53.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
✓	0.2b	(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))
	0.3b	(+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))
	1.5b	(exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))

series939.0ms (9.6%)

Counts

2 → 24

Calls

2 calls:

656.0ms	(log1p.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
283.0ms	(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`
2×	`add-cube-cbrt_binary32`
2×	`add-cbrt-cube_binary32`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))
0.0ms	(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

338×	`fma-def_binary32`
331×	`exp-sum_binary32`
328×	`fma-neg_binary32`
308×	`associate-/l/_binary32`
213×	`associate-l_binary32`

Counts

46 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	800
1	78	453
2	137	453
3	387	453
4	2043	453
5	4465	453
6	5001	453

prune151.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Error

0.1b

Counts

115 → 11

Alt Table

Status	Error	Program
	1.3b	(.f32 (exp.f32 (log.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	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.5b	(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)))))
	1.4b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.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)))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.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))))) (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 (log.f32 (.f32 2 (PI.f32))) (log.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 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2))))))
	1.9b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))
	1.0b	(.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)))))

Compiler

Compiled 2869 to 1803 computations (37.2% saved)

localize44.0ms (0.4%)

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 2 (PI.f32)) u2)))
✓	0.3b	(log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
✓	0.3b	(expm1.f32 (log1p.f32 (.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)

series858.0ms (8.8%)

Counts

2 → 40

Calls

2 calls:

628.0ms

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

229.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`
2×	`add-cube-cbrt_binary32`
2×	`add-cbrt-cube_binary32`

Counts

2 → 22

Calls

2 calls:

0.0ms

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

0.0ms

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

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

616×	`cancel-sign-sub-inv_binary32`
257×	`fma-def_binary32`
249×	`unswap-sqr_binary32`
226×	`associate-r_binary32`
207×	`*-commutative_binary32`

Counts

62 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	4599
1	929	4299
2	3623	4290
3	5229	4290

prune268.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	190	12	202

Error

0.0b

Counts

202 → 12

Alt Table

Status	Error	Program
	3.1b	(expm1.f32 (-.f32 (log1p.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 2 (/.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 u2 u2) (pow.f32 (PI.f32) 2))) (+.f32 1 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))))))
	0.9b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.4b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	1.1b	(expm1.f32 (log1p.f32 (.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 2 (PI.f32)) u2))))))
	6.5b	(-.f32 (fma.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) u2))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) 1) 1)
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.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))))) (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 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2))))))
	1.3b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))
	1.4b	(expm1.f32 (.f32 (sqrt.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (sqrt.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	0.9b	(expm1.f32 (.f32 (.f32 (cbrt.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cbrt.f32 (log1p.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))))
	1.9b	(exp.f32 (log.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (+.f32 (log.f32 (.f32 2 (PI.f32))) (log.f32 u2)))))))

Compiler

Compiled 8543 to 5614 computations (34.3% saved)

regimes2.2s (22.6%)

Accuracy

Total 0.3b remaining (79.6%)

Threshold costs 0.3b (79.6%)

Counts

191 → 1

Compiler

Compiled 45933 to 37813 computations (17.7% saved)

simplify2.0ms (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	17	29
1	26	29
2	30	29
3	32	29
4	32	29

end192.0ms (2%)

Compiler: Compiled 366 to 285 computations (22.1% 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

analyze424.0ms (4.4%)

sample2.2s (22.9%)

simplify15.0ms (0.2%)

prune4.0ms (0%)

localize34.0ms (0.4%)

series200.0ms (2.1%)

rewrite17.0ms (0.2%)

simplify115.0ms (1.2%)

prune213.0ms (2.2%)

localize45.0ms (0.5%)

series973.0ms (10%)

rewrite25.0ms (0.3%)

simplify102.0ms (1%)

prune451.0ms (4.6%)

localize53.0ms (0.5%)

series939.0ms (9.6%)

rewrite1.0ms (0%)

simplify71.0ms (0.7%)

prune151.0ms (1.6%)

localize44.0ms (0.4%)

series858.0ms (8.8%)

rewrite2.0ms (0%)

simplify105.0ms (1.1%)

prune268.0ms (2.8%)

regimes2.2s (22.6%)

simplify2.0ms (0%)

end192.0ms (2%)

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