Details

analyze2.3s (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)

sample4.2s (9%)

Results

4.0s

8256×

body

128

valid

Compiler

Compiled 136 to 97 computations (28.7% saved)

simplify49.0ms (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

prune8.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	13.3b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Status

Error

Program

▶

0.5b

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

13.3b

(/.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)

localize89.0ms (0.2%)

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

series490.0ms (1.1%)

Counts

4 → 156

Calls

4 calls:

249.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
139.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
53.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
50.0ms	(/.f32 cos2phi (*.f32 alphax alphax))

rewrite72.0ms (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:

18.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
16.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
6.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
6.0ms	(/.f32 cos2phi (*.f32 alphax alphax))

simplify354.0ms (0.8%)

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

prune497.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	9	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	9	239

Error

Counts

239 → 9

Alt Table

Status	Error	Program
	0.8b	(/.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))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 1 (/.f32 alphax (/.f32 cos2phi alphax))) (/.f32 sin2phi (*.f32 alphay alphay))))
	1.0b	(.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))))))
	2.0b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (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 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	0.9b	(.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 (/.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)))
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	0.7b	(.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))))))
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 7721 to 1897 computations (75.4% saved)

localize128.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay))
	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.2b	(/.f32 (/.f32 sin2phi alphay) alphay)
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))

series443.0ms (1%)

Counts

3 → 132

Calls

3 calls:

222.0ms

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

167.0ms

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

53.0ms

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

rewrite119.0ms (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:

44.0ms

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

37.0ms

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

9.0ms

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

simplify462.0ms (1%)

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

prune585.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	311	3	314
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	315	8	323

Error

Counts

323 → 8

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 (/.f32 sin2phi alphay) alphay)))
	0.6b	(.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)))
	0.9b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	0.9b	(.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))))))
	9.8b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (.f32 (/.f32 (/.f32 sin2phi alphay) alphay) (/.f32 (/.f32 sin2phi alphay) alphay)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	2.0b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (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 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 9566 to 2266 computations (76.3% saved)

localize148.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series420.0ms (0.9%)

Counts

4 → 100

Calls

4 calls:

281.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 (/.f32 sin2phi alphay) alphay)))
71.0ms	(/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))
46.0ms	(/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax)))
21.0ms	(/.f32 (sqrt.f32 cos2phi) alphax)

rewrite1.4s (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1494×	`times-frac_binary32`
767×	`*-un-lft-identity_binary32`
701×	`add-sqr-sqrt_binary32`
701×	`add-cube-cbrt_binary32`
453×	`sqrt-prod_binary32`

Counts

4 → 755

Calls

4 calls:

1.1s	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 (/.f32 sin2phi alphay) alphay)))
34.0ms	(/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax)))
8.0ms	(/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))
3.0ms	(/.f32 (sqrt.f32 cos2phi) alphax)

simplify1.1s (2.3%)

Algorithm

1×	egg-herbie

Rules

848×	`associate-/r/_binary32`
772×	`associate-/l/_binary32`
561×	`associate-/l*_binary32`
499×	`times-frac_binary32`
56×	`fma-def_binary32`

Counts

855 → 988

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	853	28764
1	1918	26546
2	5008	26546

prune2.5s (5.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	988	0	988
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	988	8	996

Error

Counts

996 → 8

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 (/.f32 sin2phi alphay) alphay)))
▶	0.6b	(.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)))
	0.9b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	0.9b	(.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))))))
	9.8b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (.f32 (/.f32 (/.f32 sin2phi alphay) alphay) (/.f32 (/.f32 sin2phi alphay) alphay)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	2.0b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (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 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 34738 to 6635 computations (80.9% saved)

localize112.0ms (0.2%)

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)))
✓	0.4b	(.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)))

series501.0ms (1.1%)

Counts

4 → 192

Calls

4 calls:

212.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
210.0ms	(.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)))
52.0ms	(fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi))
25.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))

rewrite106.0ms (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:

29.0ms	(.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)))
18.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
7.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
1.0ms	(fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi))

simplify422.0ms (0.9%)

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

prune658.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	349	8	357

Error

Counts

357 → 8

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 (sqrt.f32 cos2phi) (/.f32 alphax (/.f32 (sqrt.f32 cos2phi) alphax))) (/.f32 (/.f32 sin2phi alphay) alphay)))
✓	0.6b	(.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)))
	0.9b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	0.9b	(.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))))))
	9.8b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphax alphax))) (.f32 (/.f32 (/.f32 sin2phi alphay) alphay) (/.f32 (/.f32 sin2phi alphay) alphay)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
	2.0b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (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 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	1.5b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 14284 to 2973 computations (79.2% saved)

regimes29.0s (62.7%)

Accuracy

Total 0.5b remaining (91.6%)

Threshold costs 0.5b (91.6%)

Counts

1043 → 1

Compiler

Compiled 570622 to 316449 computations (44.5% saved)

simplify7.0ms (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

end157.0ms (0.3%)

Compiler: Compiled 349 to 167 computations (52.1% 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

analyze2.3s (5%)

sample4.2s (9%)

simplify49.0ms (0.1%)

prune8.0ms (0%)

localize89.0ms (0.2%)

series490.0ms (1.1%)

rewrite72.0ms (0.2%)

simplify354.0ms (0.8%)

prune497.0ms (1.1%)

localize128.0ms (0.3%)

series443.0ms (1%)

rewrite119.0ms (0.3%)

simplify462.0ms (1%)

prune585.0ms (1.3%)

localize148.0ms (0.3%)

series420.0ms (0.9%)

rewrite1.4s (2.9%)

simplify1.1s (2.3%)

prune2.5s (5.4%)

localize112.0ms (0.2%)

series501.0ms (1.1%)

rewrite106.0ms (0.2%)

simplify422.0ms (0.9%)

prune658.0ms (1.4%)

regimes29.0s (62.7%)

simplify7.0ms (0%)

end157.0ms (0.3%)

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