Details

analyze2.0s (9.2%)

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)

sample2.6s (11.9%)

Results

2.5s

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.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

▶

0.4b

(/.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)

localize51.0ms (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))
✓	0.3b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series287.0ms (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))))
92.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
28.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
27.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

rewrite66.0ms (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:

41.0ms	(/.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))

simplify223.0ms (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

prune295.0ms (1.4%)

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
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 (sqrt.f32 sin2phi) alphay) (/.f32 (sqrt.f32 sin2phi) alphay))))
	0.8b	(.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))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 (*.f32 (cbrt.f32 sin2phi) (cbrt.f32 sin2phi)) alphay) (/.f32 (cbrt.f32 sin2phi) alphay))))
	0.6b	(/.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)))))
	0.9b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	10.3b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	2.6b	(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))))))
	0.6b	(.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 (/.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)))
	1.1b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (.f32 (cbrt.f32 sin2phi) (cbrt.f32 sin2phi)) (/.f32 alphay (/.f32 (cbrt.f32 sin2phi) alphay)))))

Compiler

Compiled 7831 to 1969 computations (74.9% saved)

localize55.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series328.0ms (1.5%)

Counts

4 → 192

Calls

4 calls:

155.0ms	(.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)))
132.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
28.0ms	(fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi))
12.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary32`
59×	`add-cbrt-cube_binary32`
59×	`add-exp-log_binary32`
50×	`pow1_binary32`
47×	`*-un-lft-identity_binary32`

Counts

4 → 172

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 (.f32 alphax alphax) (*.f32 alphay alphay))
3.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
0.0ms	(fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi))

simplify289.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-r_binary32`
476×	`associate-l_binary32`
401×	`fma-def_binary32`
322×	`times-frac_binary32`
303×	`associate-/l*_binary32`

Counts

364 → 349

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	395	14713
1	1121	13457
2	4832	13438
3	5181	13438

prune381.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	348	1	349
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	351	9	360

Error

Counts

360 → 9

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	0.6b	(.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))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 (*.f32 (cbrt.f32 sin2phi) (cbrt.f32 sin2phi)) alphay) (/.f32 (cbrt.f32 sin2phi) alphay))))
	0.6b	(/.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)))))
	0.9b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	10.3b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.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)))
	0.8b	(.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))))))
	1.1b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 14617 to 3133 computations (78.6% saved)

localize68.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series800.0ms (3.7%)

Counts

3 → 168

Calls

3 calls:

442.0ms

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

206.0ms

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

151.0ms

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

rewrite570.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

2210×	`times-frac_binary32`
1720×	`sqrt-prod_binary32`
1084×	`*-un-lft-identity_binary32`
1084×	`add-sqr-sqrt_binary32`
1084×	`add-cube-cbrt_binary32`

Counts

3 → 1312

Calls

3 calls:

71.0ms

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

16.0ms

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

4.0ms

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

simplify2.0s (9.2%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-/r/_binary32`
439×	`times-frac_binary32`
401×	`*-commutative_binary32`
346×	`associate-r_binary32`
312×	`fma-def_binary32`

Counts

1480 → 1862

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1331	91643
1	3910	88077
2	4998	88077
3	5018	88077

prune1.1s (4.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1900	1	1901
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	1901	9	1910

Error

Counts

1910 → 9

Alt Table

Status	Error	Program
✓	0.6b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	8.5b	(/.f32 (.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (.f32 alphay alphay)) sin2phi)
▶	0.6b	(.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))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 (*.f32 (cbrt.f32 sin2phi) (cbrt.f32 sin2phi)) alphay) (/.f32 (cbrt.f32 sin2phi) alphay))))
	0.6b	(/.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)))))
	0.9b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	10.3b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.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)))
	1.1b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 107872 to 12248 computations (88.6% saved)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
	0.3b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
✓	0.4b	(.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))))))
✓	1.6b	(sqrt.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))

series877.0ms (4.1%)

Counts

2 → 80

Calls

2 calls:

542.0ms

(*.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))))))

334.0ms

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

rewrite152.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

341×	`*-un-lft-identity_binary32`
313×	`sqrt-prod_binary32`
277×	`times-frac_binary32`
186×	`add-sqr-sqrt_binary32`
137×	`add-cube-cbrt_binary32`

Counts

2 → 290

Calls

2 calls:

51.0ms

(*.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))))))

10.0ms

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

simplify442.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

876×	`times-frac_binary32`
760×	`fma-def_binary32`
298×	`*-commutative_binary32`
130×	`unswap-sqr_binary32`
103×	`cancel-sign-sub-inv_binary32`

Counts

370 → 395

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	829	24550
1	2265	23149
2	4977	23145
3	5350	23145

prune846.0ms (3.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	857	0	857
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	857	9	866

Error

Counts

866 → 9

Alt Table

Status	Error	Program
✓	0.6b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	8.5b	(/.f32 (.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (.f32 alphay alphay)) sin2phi)
✓	0.6b	(.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))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 (*.f32 (cbrt.f32 sin2phi) (cbrt.f32 sin2phi)) alphay) (/.f32 (cbrt.f32 sin2phi) alphay))))
	0.6b	(/.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)))))
	0.9b	(.f32 (.f32 (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	10.3b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.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)))
	1.1b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 53824 to 13437 computations (75% saved)

regimes7.9s (36.9%)

Accuracy

Total 0.5b remaining (94.5%)

Threshold costs 0.5b (94.5%)

Counts

412 → 1

Compiler

Compiled 208175 to 114793 computations (44.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary32`
3×	`*-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	24	25
2	30	25
3	34	25
4	35	25
5	35	25

end125.0ms (0.6%)

Compiler: Compiled 328 to 178 computations (45.7% 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

analyze2.0s (9.2%)

sample2.6s (11.9%)

simplify27.0ms (0.1%)

prune4.0ms (0%)

localize51.0ms (0.2%)

series287.0ms (1.3%)

rewrite66.0ms (0.3%)

simplify223.0ms (1%)

prune295.0ms (1.4%)

localize55.0ms (0.3%)

series328.0ms (1.5%)

rewrite48.0ms (0.2%)

simplify289.0ms (1.3%)

prune381.0ms (1.8%)

localize68.0ms (0.3%)

series800.0ms (3.7%)

rewrite570.0ms (2.7%)

simplify2.0s (9.2%)

prune1.1s (4.9%)

localize48.0ms (0.2%)

series877.0ms (4.1%)

rewrite152.0ms (0.7%)

simplify442.0ms (2.1%)

prune846.0ms (3.9%)

regimes7.9s (36.9%)

simplify2.0ms (0%)

end125.0ms (0.6%)

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