Details

analyze1.7s (10.2%)

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)

sample69.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 84 to 61 computations (27.4% saved)

simplify28.0ms (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

prune5.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	11.9b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Status

Error

Program

▶

0.7b

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

11.9b

(/.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)

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
✓	0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series289.0ms (1.7%)

Counts

4 → 156

Calls

4 calls:

141.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
90.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
29.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
28.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

rewrite34.0ms (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:

9.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
8.0ms	(+.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))

simplify225.0ms (1.4%)

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

prune239.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	227	10	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	10	239

Error

0.0b

Counts

239 → 10

Alt Table

Status	Error	Program
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (sqrt.f32 sin2phi) (/.f32 alphay (/.f32 (sqrt.f32 sin2phi) alphay)))))
▶	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	1.1b	(.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))))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 1 (/.f32 (.f32 alphay alphay) sin2phi))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.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))))
	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))))))
	11.2b	(.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))))
	19.0b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (pow.f32 cos2phi 3) (pow.f32 alphax 6)) (/.f32 (pow.f32 sin2phi 3) (pow.f32 alphay 6)))) (+.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))))))
	0.9b	(/.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 7709 to 1957 computations (74.6% saved)

localize52.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series301.0ms (1.8%)

Counts

4 → 168

Calls

4 calls:

159.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
122.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)))
11.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
8.0ms	(.f32 cos2phi (.f32 alphay alphay))

rewrite62.0ms (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 → 187

Calls

4 calls:

19.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
7.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)))
6.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
4.0ms	(.f32 cos2phi (.f32 alphay alphay))

simplify215.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

720×	`associate-r_binary32`
560×	`associate-l_binary32`
378×	`times-frac_binary32`
319×	`associate-/l*_binary32`
217×	`associate-/r*_binary32`

Counts

355 → 365

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	427	14419
1	1241	13188
2	5443	13188

prune337.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	362	3	365
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	366	9	375

Error

Counts

375 → 9

Alt Table

Status	Error	Program
	1.1b	(.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))))))
▶	0.4b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))) (*.f32 alphay alphay))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.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))))
	2.8b	(.f32 (+.f32 (/.f32 u0 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi))) (fma.f32 1/2 (/.f32 (.f32 u0 u0) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi))) (.f32 1/3 (/.f32 (pow.f32 u0 3) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	11.2b	(.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 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0)))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (sqrt.f32 sin2phi) (/.f32 alphay (/.f32 (sqrt.f32 sin2phi) alphay)))))
	0.9b	(/.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 15571 to 3304 computations (78.8% saved)

localize49.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series431.0ms (2.6%)

Counts

4 → 204

Calls

4 calls:

152.0ms	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))) (*.f32 alphay alphay))
143.0ms	(.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi))))
126.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)))
9.0ms	(.f32 (.f32 alphax alphax) sin2phi)

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-cbrt-cube_binary32`
64×	`add-exp-log_binary32`
61×	`times-frac_binary32`
52×	`add-sqr-sqrt_binary32`
48×	`*-un-lft-identity_binary32`

Counts

4 → 179

Calls

4 calls:

10.0ms	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))) (*.f32 alphay alphay))
10.0ms	(.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi))))
4.0ms	(.f32 (.f32 alphax alphax) sin2phi)
3.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)))

simplify313.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-l_binary32`
504×	`fma-def_binary32`
497×	`times-frac_binary32`
426×	`associate-/l*_binary32`
293×	`associate-/r*_binary32`

Counts

383 → 393

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	478	18517
1	1389	16870
2	4820	16848
3	5295	16848

prune356.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	392	1	393
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	393	9	402

Error

Counts

402 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (sqrt.f32 sin2phi) (/.f32 alphay (/.f32 (sqrt.f32 sin2phi) alphay)))))
▶	0.5b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))) (*.f32 alphay alphay))
	1.1b	(.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))))))
✓	0.4b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))) (*.f32 alphay alphay))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.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))))
	2.8b	(.f32 (+.f32 (/.f32 u0 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi))) (fma.f32 1/2 (/.f32 (.f32 u0 u0) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi))) (.f32 1/3 (/.f32 (pow.f32 u0 3) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	11.2b	(.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))))
	0.9b	(/.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 16961 to 4342 computations (74.4% saved)

localize51.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))) (*.f32 alphay alphay))
✓	0.3b	(.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0)))
✓	0.6b	(/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))

series770.0ms (4.7%)

Counts

4 → 240

Calls

4 calls:

356.0ms	(/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0)))
151.0ms	(.f32 (.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))) (*.f32 alphay alphay))
139.0ms	(.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0)))))
122.0ms	(/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))

rewrite72.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary32`
97×	`add-cbrt-cube_binary32`
97×	`add-exp-log_binary32`
95×	`add-sqr-sqrt_binary32`
89×	`*-un-lft-identity_binary32`

Counts

4 → 221

Calls

4 calls:

13.0ms	(.f32 (.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))) (*.f32 alphay alphay))
12.0ms	(.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0)))))
4.0ms	(/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))
2.0ms	(/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (*.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0)))

simplify324.0ms (2%)

Algorithm

1×	egg-herbie

Rules

837×	`times-frac_binary32`
639×	`associate-/l*_binary32`
313×	`associate-/r/_binary32`
304×	`fma-def_binary32`
180×	`*-commutative_binary32`

Counts

461 → 516

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	681	24147
1	2081	21777
2	5214	21777

prune536.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	516	0	516
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	516	9	525

Error

Counts

525 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (sqrt.f32 sin2phi) (/.f32 alphay (/.f32 (sqrt.f32 sin2phi) alphay)))))
✓	0.5b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 -1 (/.f32 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)) (log1p.f32 (neg.f32 u0))))) (*.f32 alphay alphay))
	1.1b	(.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))))))
✓	0.4b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))) (*.f32 alphay alphay))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 cos2phi (/.f32 1 (.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))))
	2.8b	(.f32 (+.f32 (/.f32 u0 (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi))) (fma.f32 1/2 (/.f32 (.f32 u0 u0) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi))) (.f32 1/3 (/.f32 (pow.f32 u0 3) (fma.f32 (.f32 alphay alphay) cos2phi (.f32 (.f32 alphax alphax) sin2phi)))))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay)))
	11.2b	(.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))))
	0.9b	(/.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 24152 to 7499 computations (69% saved)

regimes8.0s (48.2%)

Accuracy

Total 0.5b remaining (92.7%)

Threshold costs 0.5b (92.7%)

Counts

486 → 1

Compiler

Compiled 261257 to 130902 computations (49.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	27	35
2	37	35
3	49	35
4	61	35
5	73	35
6	81	35
7	85	35
8	86	35
9	86	35

end1.0ms (0%)

Compiler: Compiled 28 to 15 computations (46.4% saved)

sample2.0s (12.2%)

Algorithm

1×

intervals

Results

770.0ms	8000×	body	128	valid
370.0ms	8000×	pre	128	true

Compiler

Compiled 394 to 220 computations (44.2% 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

analyze1.7s (10.2%)

sample69.0ms (0.4%)

simplify28.0ms (0.2%)

prune5.0ms (0%)

localize43.0ms (0.3%)

series289.0ms (1.7%)

rewrite34.0ms (0.2%)

simplify225.0ms (1.4%)

prune239.0ms (1.4%)

localize52.0ms (0.3%)

series301.0ms (1.8%)

rewrite62.0ms (0.4%)

simplify215.0ms (1.3%)

prune337.0ms (2%)

localize49.0ms (0.3%)

series431.0ms (2.6%)

rewrite51.0ms (0.3%)

simplify313.0ms (1.9%)

prune356.0ms (2.2%)

localize51.0ms (0.3%)

series770.0ms (4.7%)

rewrite72.0ms (0.4%)

simplify324.0ms (2%)

prune536.0ms (3.2%)

regimes8.0s (48.2%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.0s (12.2%)

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