Details

analyze1.8s (14.2%)

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 57 to 41 computations (28.1% saved)

sample2.3s (18.1%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 136 to 97 computations (28.7% saved)

simplify23.0ms (0.2%)

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
▶	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	11.8b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Status

Error

Program

▶

0.6b

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

11.8b

(/.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)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
✓	0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series254.0ms (2%)

Counts

4 → 156

Calls

4 calls:

119.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
84.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
25.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
25.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

rewrite31.0ms (0.3%)

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:

8.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
6.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
3.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
3.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

simplify183.0ms (1.5%)

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

prune220.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	9	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	9	239

Error

0.0b

Counts

239 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay)))) (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))))))
	0.6b	(.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)))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (sqrt.f32 sin2phi) (/.f32 (.f32 alphay alphay) (sqrt.f32 sin2phi)))))
	2.3b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (+.f32 (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (*.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))))))
	0.8b	(.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))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	0.8b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))
▶	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 1 alphax) (/.f32 cos2phi alphax) (/.f32 sin2phi (*.f32 alphay alphay))))

Compiler

Compiled 7643 to 1945 computations (74.6% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.1b	(fma.f32 (/.f32 1 alphax) (/.f32 cos2phi alphax) (/.f32 sin2phi (*.f32 alphay alphay)))
	0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 1 alphax) (/.f32 cos2phi alphax) (/.f32 sin2phi (*.f32 alphay alphay))))

series169.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

112.0ms

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

55.0ms

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

3.0ms

(log1p.f32 (neg.f32 u0))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary32`
26×	`*-un-lft-identity_binary32`
26×	`add-sqr-sqrt_binary32`
26×	`add-cube-cbrt_binary32`
12×	`distribute-lft-neg-in_binary32`

Counts

3 → 80

Calls

3 calls:

3.0ms

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

0.0ms

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

0.0ms

(log1p.f32 (neg.f32 u0))

simplify158.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

420×	`fma-def_binary32`
264×	`associate-/l/_binary32`
248×	`fma-neg_binary32`
238×	`associate-/r/_binary32`
155×	`distribute-rgt-in_binary32`

Counts

200 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	7558
1	676	7096
2	2298	7087
3	4853	7087
4	4957	7087

prune190.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	230	9	239

Error

0.0b

Counts

239 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay)))) (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))))))
▶	0.6b	(.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)))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (sqrt.f32 sin2phi) (/.f32 (.f32 alphay alphay) (sqrt.f32 sin2phi)))))
	2.3b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (+.f32 (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (*.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))))))
	0.8b	(.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))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	0.8b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 1 alphax) (/.f32 cos2phi alphax) (/.f32 sin2phi (*.f32 alphay alphay))))

Compiler

Compiled 7509 to 2614 computations (65.2% saved)

localize48.0ms (0.4%)

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)))
✓	0.4b	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
✓	0.4b	(.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)))

series253.0ms (2%)

Counts

4 → 168

Calls

4 calls:

127.0ms	(.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)))
107.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
10.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
8.0ms	(.f32 (.f32 alphay alphay) cos2phi)

rewrite49.0ms (0.4%)

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:

12.0ms	(.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)))
8.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
6.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
4.0ms	(.f32 (.f32 alphay alphay) cos2phi)

simplify225.0ms (1.8%)

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

prune285.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	345	3	348
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	348	9	357

Error

Counts

357 → 9

Alt Table

Status	Error	Program
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
▶	0.6b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 (*.f32 alphax alphax) alphay) alphay))
	0.6b	(/.f32 (.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
	0.8b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 1 alphax) (/.f32 cos2phi alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 alphax (.f32 alphax (*.f32 alphay alphay))))
	2.3b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (+.f32 (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (*.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))))))
	0.8b	(.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))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))

Compiler

Compiled 14541 to 3206 computations (78% saved)

localize51.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series148.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

130.0ms

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

11.0ms

(*.f32 (*.f32 (*.f32 alphax alphax) alphay) alphay)

7.0ms

(*.f32 (*.f32 alphax alphax) alphay)

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-cbrt-cube_binary32`
49×	`add-exp-log_binary32`
36×	`associate-l_binary32`
31×	`pow1_binary32`
30×	`times-frac_binary32`

Counts

3 → 111

Calls

3 calls:

10.0ms

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

5.0ms

(*.f32 (*.f32 (*.f32 alphax alphax) alphay) alphay)

4.0ms

(*.f32 (*.f32 alphax alphax) alphay)

simplify203.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-r_binary32`
583×	`fma-def_binary32`
497×	`associate-l_binary32`
261×	`*-commutative_binary32`
200×	`times-frac_binary32`

Counts

219 → 205

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	291	8019
1	866	7124
2	3916	7104
3	4839	7102
4	4981	7102
5	4978	7102

prune282.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	344	2	346
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	346	9	355

Error

Counts

355 → 9

Alt Table

Status	Error	Program
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
✓	0.6b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 (*.f32 alphax alphax) alphay) alphay))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 1 alphax) (/.f32 cos2phi alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 alphax (.f32 alphax (*.f32 alphay alphay))))
	2.3b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (+.f32 (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (*.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))))))
	0.8b	(.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))))))
	0.8b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))
	0.6b	(.f32 (.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (*.f32 alphax alphax) alphay)) alphay)
	0.9b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (.f32 (/.f32 1 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 (.f32 alphax alphax) alphay) alphay)))

Compiler

Compiled 14147 to 3011 computations (78.7% saved)

regimes5.4s (43.4%)

Accuracy

Total 0.5b remaining (94.9%)

Threshold costs 0.5b (94.9%)

Counts

366 → 1

Compiler

Compiled 191174 to 100704 computations (47.3% 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	36	35
3	45	35
4	56	35
5	69	35
6	78	35
7	84	35
8	86	35
9	86	35

end125.0ms (1%)

Compiler: Compiled 354 to 210 computations (40.7% 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

analyze1.8s (14.2%)

sample2.3s (18.1%)

simplify23.0ms (0.2%)

prune4.0ms (0%)

localize40.0ms (0.3%)

series254.0ms (2%)

rewrite31.0ms (0.3%)

simplify183.0ms (1.5%)

prune220.0ms (1.8%)

localize45.0ms (0.4%)

series169.0ms (1.4%)

rewrite10.0ms (0.1%)

simplify158.0ms (1.3%)

prune190.0ms (1.5%)

localize48.0ms (0.4%)

series253.0ms (2%)

rewrite49.0ms (0.4%)

simplify225.0ms (1.8%)

prune285.0ms (2.3%)

localize51.0ms (0.4%)

series148.0ms (1.2%)

rewrite32.0ms (0.3%)

simplify203.0ms (1.6%)

prune282.0ms (2.3%)

regimes5.4s (43.4%)

simplify4.0ms (0%)

end125.0ms (1%)

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