Details

analyze1.7s (9.5%)

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)

sample145.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
15.0ms	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

0.7b

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))))
	14.1b	(/.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))))

14.1b

(/.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)

localize44.0ms (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))
✓	0.3b	(/.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))))

series286.0ms (1.6%)

Counts

4 → 156

Calls

4 calls:

133.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
97.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
28.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
28.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

rewrite39.0ms (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:

13.0ms	(/.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 cos2phi (*.f32 alphax alphax))
3.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

simplify199.0ms (1.1%)

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

prune232.0ms (1.3%)

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

Counts

239 → 10

Alt Table

Status	Error	Program
	0.7b	(/.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 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
	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 (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)))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	9.4b	(-.f32 (/.f32 (log1p.f32 (neg.f32 u0)) (.f32 (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)) (/.f32 alphax (/.f32 cos2phi alphax)))) (/.f32 (log1p.f32 (neg.f32 u0)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))))
	1.0b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))))
	1.2b	(.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))))))

Compiler

Compiled 7679 to 1917 computations (75% saved)

localize54.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series272.0ms (1.6%)

Counts

4 → 168

Calls

4 calls:

141.0ms	(.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)))
112.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
11.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
8.0ms	(.f32 (.f32 alphay alphay) cos2phi)

rewrite50.0ms (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:

15.0ms	(.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)))

simplify237.0ms (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

prune290.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	347	10	357

Error

Counts

357 → 10

Alt Table

Status	Error	Program
▶	0.7b	(/.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 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
	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 (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)))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	9.4b	(-.f32 (/.f32 (log1p.f32 (neg.f32 u0)) (.f32 (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)) (/.f32 alphax (/.f32 cos2phi alphax)))) (/.f32 (log1p.f32 (neg.f32 u0)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))))
	1.0b	(.f32 (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))) (/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))))
	1.2b	(.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))))))

Compiler

Compiled 14566 to 3186 computations (78.1% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay))
✓	0.3b	(/.f32 (/.f32 sin2phi alphay) alphay)
	0.3b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))

series235.0ms (1.3%)

Counts

3 → 132

Calls

3 calls:

125.0ms

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

83.0ms

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

27.0ms

(/.f32 (/.f32 sin2phi alphay) alphay)

rewrite52.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`times-frac_binary32`
97×	`*-un-lft-identity_binary32`
73×	`add-sqr-sqrt_binary32`
73×	`add-cube-cbrt_binary32`
23×	`associate-/l*_binary32`

Counts

3 → 167

Calls

3 calls:

18.0ms

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

17.0ms

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

4.0ms

(/.f32 (/.f32 sin2phi alphay) alphay)

simplify208.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-/r/_binary32`
322×	`fma-def_binary32`
208×	`fma-neg_binary32`
186×	`associate-/l/_binary32`
184×	`associate-/l*_binary32`

Counts

299 → 286

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	371	9186
1	918	8793
2	2730	8712
3	4940	8712
4	5011	8712

prune281.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	311	3	314
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	315	9	324

Error

Counts

324 → 9

Alt Table

Status	Error	Program
	1.2b	(.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 (/.f32 sin2phi 1) (/.f32 (/.f32 1 alphay) alphay))))
	0.9b	(.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))))))
	1.0b	(/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
▶	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi 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)))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	9.4b	(-.f32 (/.f32 (log1p.f32 (neg.f32 u0)) (.f32 (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)) (/.f32 alphax (/.f32 cos2phi alphax)))) (/.f32 (log1p.f32 (neg.f32 u0)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))))

Compiler

Compiled 9531 to 2295 computations (75.9% saved)

localize44.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 alphax (/.f32 cos2phi alphax))
	0.3b	(/.f32 (/.f32 sin2phi alphay) alphay)
✓	0.3b	(/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax)))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 (/.f32 sin2phi alphay) alphay)))

series153.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

118.0ms

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

26.0ms

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

10.0ms

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

rewrite205.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

553×	`times-frac_binary32`
339×	`*-un-lft-identity_binary32`
262×	`add-sqr-sqrt_binary32`
262×	`add-cube-cbrt_binary32`
63×	`associate-/r*_binary32`

Counts

3 → 373

Calls

3 calls:

152.0ms

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

10.0ms

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

4.0ms

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

simplify309.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary32`
323×	`associate-/r/_binary32`
242×	`associate-/l*_binary32`
225×	`associate-*r/_binary32`
218×	`times-frac_binary32`

Counts

481 → 562

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	14105
1	1069	12503
2	3619	12084
3	4747	12084
4	4981	12084

prune730.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	664	0	664
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	664	9	673

Error

Counts

673 → 9

Alt Table

Status	Error	Program
	1.2b	(.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 (/.f32 sin2phi 1) (/.f32 (/.f32 1 alphay) alphay))))
	0.9b	(.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))))))
	1.0b	(/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
✓	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi 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)))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	9.4b	(-.f32 (/.f32 (log1p.f32 (neg.f32 u0)) (.f32 (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)) (/.f32 alphax (/.f32 cos2phi alphax)))) (/.f32 (log1p.f32 (neg.f32 u0)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))))

Compiler

Compiled 20089 to 5792 computations (71.2% saved)

regimes9.8s (55.8%)

Accuracy

Total 0.5b remaining (92.3%)

Threshold costs 0.5b (92.3%)

Counts

581 → 1

Compiler

Compiled 267917 to 158647 computations (40.8% 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

end0.0ms (0%)

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

sample1.9s (11%)

Algorithm

1×

intervals

Results

756.0ms	8000×	body	128	valid
377.0ms	8000×	pre	128	true

Compiler

Compiled 373 to 213 computations (42.9% 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 (9.5%)

sample145.0ms (0.8%)

simplify28.0ms (0.2%)

prune5.0ms (0%)

localize44.0ms (0.3%)

series286.0ms (1.6%)

rewrite39.0ms (0.2%)

simplify199.0ms (1.1%)

prune232.0ms (1.3%)

localize54.0ms (0.3%)

series272.0ms (1.6%)

rewrite50.0ms (0.3%)

simplify237.0ms (1.4%)

prune290.0ms (1.7%)

localize41.0ms (0.2%)

series235.0ms (1.3%)

rewrite52.0ms (0.3%)

simplify208.0ms (1.2%)

prune281.0ms (1.6%)

localize44.0ms (0.3%)

series153.0ms (0.9%)

rewrite205.0ms (1.2%)

simplify309.0ms (1.8%)

prune730.0ms (4.2%)

regimes9.8s (55.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.9s (11%)

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