Details

analyze6.9s (28.8%)

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 57 to 41 computations (28.1% saved)

sample2.7s (11.5%)

Results

2.7s

8256×

body

128

valid

Compiler

Compiled 136 to 97 computations (28.7% saved)

simplify27.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

195×	`fma-neg_binary32`
112×	`fma-def_binary32`
65×	`cancel-sign-sub-inv_binary32`
40×	`sub-neg_binary32`
40×	`div-sub_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	30	25
2	42	25
3	55	25
4	67	25
5	84	25
6	105	25
7	134	25
8	160	25
9	185	25
10	228	25
11	252	25
12	358	25
13	406	25
14	444	25
15	456	25
16	461	25
17	420	25

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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	12.7b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Status

Error

Program

▶

0.5b

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

12.7b

(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Compiler

Compiled 124 to 77 computations (37.9% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
✓	0.3b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series298.0ms (1.3%)

Counts

4 → 156

Calls

4 calls:

139.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
99.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
30.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
30.0ms	(/.f32 cos2phi (*.f32 alphax alphax))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary32`
49×	`times-frac_binary32`
36×	`add-sqr-sqrt_binary32`
36×	`add-cube-cbrt_binary32`
16×	`associate-/l*_binary32`

Counts

4 → 141

Calls

4 calls:

10.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
9.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
3.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
3.0ms	(/.f32 cos2phi (*.f32 alphax alphax))

simplify241.0ms (1%)

Algorithm

1×	egg-herbie

Rules

415×	`associate-/l/_binary32`
350×	`fma-def_binary32`
208×	`times-frac_binary32`
185×	`associate-/l*_binary32`
185×	`unswap-sqr_binary32`

Counts

297 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	8536
1	790	8175
2	2612	8167
3	4993	8167
4	4982	8167

prune255.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	226	11	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	228	11	239

Error

Counts

239 → 11

Alt Table

Status	Error	Program
	1.4b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	0.8b	(.f32 (/.f32 -1 (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (/.f32 (log1p.f32 (neg.f32 u0)) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
▶	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	0.9b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (.f32 (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))))
	2.4b	(fma.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (fma.f32 1/2 (/.f32 (.f32 u0 u0) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	0.7b	(.f32 (sqrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (sqrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax)))))

Compiler

Compiled 7745 to 1945 computations (74.9% saved)

localize52.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 alphay alphay) cos2phi)
✓	0.3b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
✓	0.3b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
✓	0.3b	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))

series316.0ms (1.3%)

Counts

4 → 168

Calls

4 calls:

164.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
129.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
14.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
9.0ms	(.f32 (.f32 alphay alphay) cos2phi)

rewrite58.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-cbrt-cube_binary32`
64×	`add-exp-log_binary32`
60×	`times-frac_binary32`
55×	`pow1_binary32`
49×	`add-sqr-sqrt_binary32`

Counts

4 → 183

Calls

4 calls:

14.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
10.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
5.0ms	(.f32 (.f32 alphay alphay) cos2phi)
3.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))

simplify279.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary32`
539×	`associate-l_binary32`
358×	`times-frac_binary32`
324×	`associate-/l*_binary32`
299×	`*-commutative_binary32`

Counts

351 → 348

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	415	14309
1	1169	13055
2	4399	13034
3	5151	13034

prune334.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	346	2	348
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	350	9	359

Error

Counts

359 → 9

Alt Table

Status	Error	Program
	0.8b	(.f32 (/.f32 -1 (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (/.f32 (log1p.f32 (neg.f32 u0)) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	1.0b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (cbrt.f32 (.f32 (.f32 (.f32 (.f32 alphax alphax) alphax) (.f32 (.f32 alphax alphax) alphax)) (.f32 (.f32 (.f32 alphay alphay) (.f32 alphay alphay)) (*.f32 alphay alphay)))))
	0.7b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax)))))
	0.9b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (.f32 (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))))
	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (sqrt.f32 (.f32 (.f32 alphay alphay) cos2phi)) (sqrt.f32 (.f32 (.f32 alphay alphay) cos2phi))))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Compiler

Compiled 14553 to 3165 computations (78.3% saved)

localize50.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax)))
✓	0.3b	(/.f32 alphax (/.f32 cos2phi alphax))
	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))

series179.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

135.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))

28.0ms

(/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax)))

17.0ms

(/.f32 alphax (/.f32 cos2phi alphax))

rewrite120.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

521×	`times-frac_binary32`
292×	`*-un-lft-identity_binary32`
259×	`add-sqr-sqrt_binary32`
259×	`add-cube-cbrt_binary32`
62×	`associate-/r*_binary32`

Counts

3 → 362

Calls

3 calls:

58.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))

10.0ms

(/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax)))

4.0ms

(/.f32 alphax (/.f32 cos2phi alphax))

simplify349.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

646×	`fma-def_binary32`
323×	`associate-/r/_binary32`
244×	`associate-/l*_binary32`
227×	`times-frac_binary32`
220×	`associate-*r/_binary32`

Counts

470 → 552

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	13671
1	1069	12159
2	3620	11740
3	4777	11740
4	5033	11740

prune682.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	579	1	580
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	580	9	589

Error

Counts

589 → 9

Alt Table

Status	Error	Program
	0.8b	(.f32 (/.f32 -1 (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (/.f32 (log1p.f32 (neg.f32 u0)) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	0.7b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) 1) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (.f32 alphay alphay)))))
	0.9b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (.f32 (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))))
	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (sqrt.f32 (.f32 (.f32 alphay alphay) cos2phi)) (sqrt.f32 (.f32 (.f32 alphay alphay) cos2phi))))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	1.0b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (cbrt.f32 (.f32 (.f32 (.f32 (.f32 alphax alphax) alphax) (.f32 (.f32 alphax alphax) alphax)) (.f32 (.f32 (.f32 alphay alphay) (.f32 alphay alphay)) (*.f32 alphay alphay)))))

Compiler

Compiled 18039 to 5271 computations (70.8% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f32 cos2phi (/.f32 1 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
✓	0.3b	(/.f32 1 (*.f32 alphax alphax))
	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series242.0ms (1%)

Counts

3 → 120

Calls

3 calls:

143.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

96.0ms

(fma.f32 cos2phi (/.f32 1 (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))

2.0ms

(/.f32 1 (*.f32 alphax alphax))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`times-frac_binary32`
28×	`*-un-lft-identity_binary32`
28×	`add-sqr-sqrt_binary32`
28×	`add-cube-cbrt_binary32`
16×	`add-exp-log_binary32`

Counts

3 → 103

Calls

3 calls:

3.0ms

(/.f32 1 (*.f32 alphax alphax))

3.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

0.0ms

(fma.f32 cos2phi (/.f32 1 (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))

simplify178.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

476×	`associate-*l/_binary32`
356×	`associate-/r/_binary32`
329×	`associate-/l/_binary32`
257×	`fma-def_binary32`
183×	`fma-neg_binary32`

Counts

223 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	7608
1	620	7105
2	2062	7093
3	4991	7093
4	5035	7093

prune241.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	232	9	241

Error

Counts

241 → 9

Alt Table

Status	Error	Program
	0.8b	(.f32 (/.f32 -1 (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (/.f32 (log1p.f32 (neg.f32 u0)) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	0.7b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) 1) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (.f32 alphay alphay)))))
	0.9b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (.f32 (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))))
	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (sqrt.f32 (.f32 (.f32 alphay alphay) cos2phi)) (sqrt.f32 (.f32 (.f32 alphay alphay) cos2phi))))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	1.0b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (cbrt.f32 (.f32 (.f32 (.f32 (.f32 alphax alphax) alphax) (.f32 (.f32 alphax alphax) alphax)) (.f32 (.f32 (.f32 alphay alphay) (.f32 alphay alphay)) (*.f32 alphay alphay)))))

Compiler

Compiled 7109 to 2260 computations (68.2% saved)

regimes10.1s (42.2%)

Accuracy

Total 0.4b remaining (90.9%)

Threshold costs 0.4b (90.9%)

Counts

558 → 1

Compiler

Compiled 264375 to 153417 computations (42% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary32`
9×	`+-commutative_binary32`
9×	`sub-neg_binary32`
9×	`neg-sub0_binary32`
9×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	27	35
2	38	35
3	53	35
4	68	35
5	78	35
6	84	35
7	86	35
8	86	35

end121.0ms (0.5%)

Compiler: Compiled 355 to 184 computations (48.2% saved)

Iter	Nodes	Cost
0	16	26
1	30	25
2	42	25
3	55	25
4	67	25
5	84	25
6	105	25
7	134	25
8	160	25
9	185	25
10	228	25
11	252	25
12	358	25
13	406	25
14	444	25
15	456	25
16	461	25
17	420	25

Iter	Nodes	Cost
0	16	26
1	30	25
2	42	25
3	55	25
4	67	25
5	84	25
6	105	25
7	134	25
8	160	25
9	185	25
10	228	25
11	252	25
12	358	25
13	406	25
14	444	25
15	456	25
16	461	25
17	420	25

Details

analyze6.9s (28.8%)

sample2.7s (11.5%)

simplify27.0ms (0.1%)

prune4.0ms (0%)

localize45.0ms (0.2%)

series298.0ms (1.3%)

rewrite36.0ms (0.2%)

simplify241.0ms (1%)

prune255.0ms (1.1%)

localize52.0ms (0.2%)

series316.0ms (1.3%)

rewrite58.0ms (0.2%)

simplify279.0ms (1.2%)

prune334.0ms (1.4%)

localize50.0ms (0.2%)

series179.0ms (0.8%)

rewrite120.0ms (0.5%)

simplify349.0ms (1.5%)

prune682.0ms (2.9%)

localize45.0ms (0.2%)

series242.0ms (1%)

rewrite15.0ms (0.1%)

simplify178.0ms (0.7%)

prune241.0ms (1%)

regimes10.1s (42.2%)

simplify4.0ms (0%)

end121.0ms (0.5%)

Profiling

Iter	Nodes	Cost
0	16	26
1	30	25
2	42	25
3	55	25
4	67	25
5	84	25
6	105	25
7	134	25
8	160	25
9	185	25
10	228	25
11	252	25
12	358	25
13	406	25
14	444	25
15	456	25
16	461	25
17	420	25