Details

analyze1.7s (12.3%)

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)

sample138.0ms (1%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 84 to 61 computations (27.4% saved)

simplify25.0ms (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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.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 sin2phi (.f32 alphay alphay))))

Status

Error

Program

13.3b

(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.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 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))))

series276.0ms (2%)

Counts

4 → 156

Calls

4 calls:

128.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
88.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
31.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
28.0ms	(/.f32 cos2phi (*.f32 alphax alphax))

rewrite35.0ms (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:

10.0ms	(/.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))

simplify201.0ms (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

prune238.0ms (1.7%)

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
	1.0b	(/.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))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.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 sin2phi (/.f32 1 (*.f32 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))))))
	0.9b	(/.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))))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 (sqrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
	1.0b	(.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))))))
	3.0b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (cbrt.f32 (.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 sin2phi (.f32 alphay alphay))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
▶	0.6b	(.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)))

Compiler

Compiled 7725 to 1941 computations (74.9% saved)

localize52.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series272.0ms (2%)

Counts

4 → 168

Calls

4 calls:

133.0ms	(.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)))
116.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)))
12.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
9.0ms	(.f32 (.f32 alphax alphax) sin2phi)

rewrite59.0ms (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 (.f32 alphax alphax) sin2phi)

simplify245.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-l_binary32`
402×	`times-frac_binary32`
321×	`associate-/l*_binary32`
295×	`fma-neg_binary32`
231×	`associate-/r*_binary32`

Counts

355 → 359

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	429	14421
1	1250	13199
2	4812	13199
3	5050	13199

prune322.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	357	2	359
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	360	10	370

Error

Counts

370 → 10

Alt Table

Status	Error	Program
	1.0b	(/.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))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.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 (/.f32 sin2phi (.f32 alphay alphay))) (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay)))) (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))))))
	0.7b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (pow.f32 (.f32 alphax alphay) 2))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
	1.0b	(.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))))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (.f32 (/.f32 1 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 sin2phi (/.f32 1 (*.f32 alphay alphay)))))
▶	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
✓	0.6b	(.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)))

Compiler

Compiled 15329 to 3271 computations (78.7% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay)))
	0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.3b	(/.f32 (/.f32 cos2phi alphax) alphax)
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))

series249.0ms (1.8%)

Counts

3 → 132

Calls

3 calls:

124.0ms

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

96.0ms

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

29.0ms

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

rewrite114.0ms (0.8%)

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:

44.0ms

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

27.0ms

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

9.0ms

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

simplify223.0ms (1.6%)

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

prune352.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	346	4	350
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	351	9	360

Error

Counts

360 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (.f32 sin2phi (/.f32 1 (.f32 alphay alphay)))))
✓	0.6b	(.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)))
	1.0b	(/.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))))
	0.9b	(/.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))))))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))
	1.0b	(.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))))))
▶	0.4b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi alphax (.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax)))) (.f32 alphax (*.f32 alphay alphay)))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (.f32 (cbrt.f32 (/.f32 cos2phi alphax)) (cbrt.f32 (/.f32 cos2phi alphax))) (/.f32 (cbrt.f32 (/.f32 cos2phi alphax)) alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (.f32 alphay alphay)))))

Compiler

Compiled 10488 to 2436 computations (76.8% saved)

localize57.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series272.0ms (2%)

Counts

4 → 180

Calls

4 calls:

128.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi alphax (.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax)))) (.f32 alphax (*.f32 alphay alphay)))
108.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi alphax (.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax))))
27.0ms	(.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax))
8.0ms	(.f32 alphax (.f32 alphay alphay))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`times-frac_binary32`
59×	`add-sqr-sqrt_binary32`
55×	`*-un-lft-identity_binary32`
55×	`add-cube-cbrt_binary32`
44×	`add-cbrt-cube_binary32`

Counts

4 → 179

Calls

4 calls:

14.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi alphax (.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax)))) (.f32 alphax (*.f32 alphay alphay)))
6.0ms	(.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax))
4.0ms	(.f32 alphax (.f32 alphay alphay))
3.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi alphax (.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax))))

simplify183.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-r_binary32`
489×	`associate-l_binary32`
358×	`associate-/l*_binary32`
337×	`times-frac_binary32`
217×	`associate-/r*_binary32`

Counts

359 → 363

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	440	13711
1	1285	12695
2	5155	12695

prune324.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	361	2	363
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	363	9	372

Error

Counts

372 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (.f32 sin2phi (/.f32 1 (.f32 alphay alphay)))))
✓	0.6b	(.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)))
	1.0b	(/.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))))
	0.5b	(.f32 (.f32 alphax (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 alphax sin2phi (/.f32 (.f32 cos2phi (.f32 alphay alphay)) alphax)))) (*.f32 alphay alphay))
	0.9b	(/.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 alphax (.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax)))) (.f32 (sqrt.f32 alphax) (.f32 alphay (.f32 alphay (sqrt.f32 alphax)))))
✓	0.4b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi alphax (.f32 (.f32 alphay alphay) (/.f32 cos2phi alphax)))) (.f32 alphax (*.f32 alphay alphay)))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (.f32 (cbrt.f32 (/.f32 cos2phi alphax)) (cbrt.f32 (/.f32 cos2phi alphax))) (/.f32 (cbrt.f32 (/.f32 cos2phi alphax)) alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (+.f32 (/.f32 (/.f32 cos2phi alphax) alphax) (/.f32 sin2phi (.f32 alphay alphay)))))

Compiler

Compiled 13733 to 2947 computations (78.5% saved)

regimes6.2s (45.3%)

Accuracy

Total 0.4b remaining (92.9%)

Threshold costs 0.4b (92.9%)

Counts

382 → 1

Compiler

Compiled 184136 to 106518 computations (42.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`
5×	`+-commutative_binary32`
5×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	37
1	32	37
2	42	37
3	50	37
4	55	37
5	58	37
6	59	37
7	59	37

end1.0ms (0%)

Compiler: Compiled 29 to 20 computations (31% saved)

sample2.0s (14.6%)

Algorithm

1×

intervals

Results

785.0ms	8000×	body	128	valid
354.0ms	8000×	pre	128	true

Compiler

Compiled 344 to 213 computations (38.1% 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 (12.3%)

sample138.0ms (1%)

simplify25.0ms (0.2%)

prune4.0ms (0%)

localize44.0ms (0.3%)

series276.0ms (2%)

rewrite35.0ms (0.3%)

simplify201.0ms (1.5%)

prune238.0ms (1.7%)

localize52.0ms (0.4%)

series272.0ms (2%)

rewrite59.0ms (0.4%)

simplify245.0ms (1.8%)

prune322.0ms (2.4%)

localize47.0ms (0.3%)

series249.0ms (1.8%)

rewrite114.0ms (0.8%)

simplify223.0ms (1.6%)

prune352.0ms (2.6%)

localize57.0ms (0.4%)

series272.0ms (2%)

rewrite47.0ms (0.3%)

simplify183.0ms (1.3%)

prune324.0ms (2.4%)

regimes6.2s (45.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.0s (14.6%)

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