Details

analyze1.9s (10.5%)

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 57 to 41 computations (28.1% saved)

sample2.6s (14.6%)

Results

2.5s

8256×

body

128

valid

Compiler

Compiled 136 to 97 computations (28.7% saved)

simplify26.0ms (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

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.6b

Counts

3 → 1

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))))

Compiler

Compiled 80 to 47 computations (41.3% saved)

localize45.0ms (0.2%)

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 cos2phi (*.f32 alphax alphax))
✓	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series235.0ms (1.3%)

Counts

4 → 156

Calls

4 calls:

113.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
74.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
27.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
21.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

rewrite38.0ms (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:

14.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
7.0ms	(+.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))

simplify215.0ms (1.2%)

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

prune234.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	9	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

Counts

238 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))))
	15.9b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (/.f32 cos2phi (.f32 alphax alphax)) 3) (pow.f32 (/.f32 sin2phi (.f32 alphay alphay)) 3))) (+.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (-.f32 (.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 sin2phi (.f32 alphay alphay))) (.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 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))))
	2.2b	(+.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 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	0.7b	(/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 7679 to 1927 computations (74.9% saved)

localize52.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series233.0ms (1.3%)

Counts

4 → 168

Calls

4 calls:

120.0ms	(.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)))
93.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
9.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
9.0ms	(.f32 (.f32 alphay alphay) cos2phi)

rewrite54.0ms (0.3%)

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:

18.0ms	(.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)))
6.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
4.0ms	(.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)))

simplify245.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

351 → 347

Iterations

Useful iterations: 2 (0.0ms)

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

prune375.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	345	2	347
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	348	8	356

Error

Counts

356 → 8

Alt Table

Status	Error	Program
▶	0.5b	(/.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)))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.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 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	2.2b	(+.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 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	0.7b	(/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
	0.7b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) 1) (.f32 (/.f32 (sqrt.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))))

Compiler

Compiled 14484 to 3154 computations (78.2% saved)

localize52.0ms (0.3%)

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

series473.0ms (2.7%)

Counts

2 → 96

Calls

2 calls:

356.0ms

(*.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (*.f32 (*.f32 alphax alphax) (*.f32 alphay alphay)))

116.0ms

(/.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)))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary32`
45×	`add-exp-log_binary32`
26×	`cbrt-unprod_binary32`
26×	`prod-exp_binary32`
20×	`pow1_binary32`

Counts

2 → 69

Calls

2 calls:

16.0ms

(/.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)))

9.0ms

(*.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (*.f32 (*.f32 alphax alphax) (*.f32 alphay alphay)))

simplify155.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

427×	`associate-r_binary32`
356×	`associate-l_binary32`
329×	`unswap-sqr_binary32`
267×	`associate-/l*_binary32`
259×	`times-frac_binary32`

Counts

165 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	7729
1	804	6780
2	3808	6764
3	5118	6764

prune211.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	226	8	234

Error

Counts

234 → 8

Alt Table

Status	Error	Program
✓	0.5b	(/.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)))
▶	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.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 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	2.2b	(+.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 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	0.7b	(/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
	0.7b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) 1) (.f32 (/.f32 (sqrt.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))))

Compiler

Compiled 8806 to 2319 computations (73.7% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay)))
✓	0.3b	(/.f32 (/.f32 cos2phi alphax) alphax)
	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))

series204.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

98.0ms

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

84.0ms

(+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay)))

23.0ms

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

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`times-frac_binary32`
130×	`*-un-lft-identity_binary32`
106×	`add-sqr-sqrt_binary32`
106×	`add-cube-cbrt_binary32`
43×	`fma-def_binary32`

Counts

3 → 203

Calls

3 calls:

19.0ms

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

19.0ms

(+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay)))

4.0ms

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

simplify211.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

519×	`associate-/r/_binary32`
322×	`fma-def_binary32`
204×	`fma-neg_binary32`
186×	`associate-/l/_binary32`
184×	`associate-/l*_binary32`

Counts

335 → 322

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	371	9186
1	918	8790
2	2731	8710
3	4935	8710
4	5000	8710

prune411.0ms (2.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	350	8	358

Error

Counts

358 → 8

Alt Table

Status	Error	Program
✓	0.5b	(/.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)))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	1.0b	(.f32 (.f32 (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))) (cbrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.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 (.f32 alphay alphay) cos2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	2.2b	(+.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 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	0.7b	(/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
	0.7b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) 1) (.f32 (/.f32 (sqrt.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))))

Compiler

Compiled 10267 to 2309 computations (77.5% saved)

regimes9.6s (54%)

Accuracy

Total 0.4b remaining (93.3%)

Threshold costs 0.4b (93.3%)

Counts

462 → 1

Compiler

Compiled 233316 to 126665 computations (45.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	27	32
2	37	32
3	45	32
4	56	32
5	66	32
6	73	32
7	77	32
8	78	32
9	78	32

end124.0ms (0.7%)

Compiler: Compiled 334 to 179 computations (46.4% 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

analyze1.9s (10.5%)

sample2.6s (14.6%)

simplify26.0ms (0.1%)

prune4.0ms (0%)

localize45.0ms (0.2%)

series235.0ms (1.3%)

rewrite38.0ms (0.2%)

simplify215.0ms (1.2%)

prune234.0ms (1.3%)

localize52.0ms (0.3%)

series233.0ms (1.3%)

rewrite54.0ms (0.3%)

simplify245.0ms (1.4%)

prune375.0ms (2.1%)

localize52.0ms (0.3%)

series473.0ms (2.7%)

rewrite36.0ms (0.2%)

simplify155.0ms (0.9%)

prune211.0ms (1.2%)

localize42.0ms (0.2%)

series204.0ms (1.1%)

rewrite61.0ms (0.3%)

simplify211.0ms (1.2%)

prune411.0ms (2.3%)

regimes9.6s (54%)

simplify3.0ms (0%)

end124.0ms (0.7%)

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