Details

analyze1.6s (10.6%)

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)

sample141.0ms (0.9%)

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)

simplify24.0ms (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

0.5b

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))))
	14.1b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Status

Error

Program

▶

0.5b

(/.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)

localize41.0ms (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)))
✓	0.3b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series272.0ms (1.8%)

Counts

4 → 156

Calls

4 calls:

131.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
89.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
26.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
26.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

rewrite33.0ms (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))))
7.0ms	(+.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))

simplify208.0ms (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

prune222.0ms (1.4%)

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

0.0b

Counts

239 → 9

Alt Table

Status	Error	Program
	0.9b	(.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))))))
	2.3b	(+.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))))))))
	12.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (cbrt.f32 (/.f32 (pow.f32 sin2phi 3) (pow.f32 alphay 6)))))
	0.7b	(.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))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 1 (/.f32 (.f32 alphay alphay) sin2phi))))
	0.8b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
	1.1b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	1.0b	(.f32 (/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.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 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (+.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)))

Compiler

Compiled 7731 to 1913 computations (75.3% saved)

localize47.0ms (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 (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)))
✓	0.3b	(.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)))

series298.0ms (1.9%)

Counts

4 → 192

Calls

4 calls:

144.0ms	(.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)))
117.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi)))
25.0ms	(fma.f32 sin2phi (.f32 alphax alphax) (.f32 (*.f32 alphay alphay) cos2phi))
11.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))

rewrite46.0ms (0.3%)

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:

13.0ms	(.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)))
9.0ms	(.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))

simplify255.0ms (1.7%)

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 → 339

Iterations

Useful iterations: 2 (0.0ms)

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

prune284.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	335	4	339
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	340	8	348

Error

Counts

348 → 8

Alt Table

Status	Error	Program
	0.9b	(.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))))))
	2.3b	(+.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))))))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 1 (/.f32 (.f32 alphay alphay) sin2phi))))
	0.8b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
▶	0.5b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (.f32 (.f32 alphax alphax) (.f32 alphay alphay)) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 cos2phi (*.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 (*.f32 alphax alphax) alphay) alphay))
	0.6b	(.f32 (/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (sqrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	0.8b	(.f32 (/.f32 -1 (.f32 (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))))) (.f32 (/.f32 (log1p.f32 (neg.f32 u0)) (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))

Compiler

Compiled 14393 to 3089 computations (78.5% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series232.0ms (1.5%)

Counts

3 → 156

Calls

3 calls:

142.0ms

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

62.0ms

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

28.0ms

(fma.f32 sin2phi (*.f32 alphax alphax) (*.f32 cos2phi (*.f32 alphay alphay)))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary32`
46×	`add-exp-log_binary32`
22×	`cbrt-unprod_binary32`
22×	`prod-exp_binary32`
12×	`add-sqr-sqrt_binary32`

Counts

3 → 82

Calls

3 calls:

10.0ms

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

8.0ms

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

0.0ms

(fma.f32 sin2phi (*.f32 alphax alphax) (*.f32 cos2phi (*.f32 alphay alphay)))

simplify209.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary32`
381×	`associate-r_binary32`
339×	`times-frac_binary32`
332×	`associate-l_binary32`
320×	`associate-/l*_binary32`

Counts

238 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	274	10014
1	830	8918
2	4125	8894
3	4977	8894
4	5001	8894

prune215.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	223	8	231

Error

Counts

231 → 8

Alt Table

Status	Error	Program
	0.9b	(.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))))))
	2.3b	(+.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))))))))
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 1 (/.f32 (.f32 alphay alphay) sin2phi))))
	0.8b	(.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))))
✓	0.5b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (.f32 (.f32 alphax alphax) (.f32 alphay alphay)) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 cos2phi (*.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 (*.f32 alphax alphax) alphay) alphay))
	0.6b	(.f32 (/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (sqrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	0.8b	(.f32 (/.f32 -1 (.f32 (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))))) (.f32 (/.f32 (log1p.f32 (neg.f32 u0)) (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))

Compiler

Compiled 8896 to 2145 computations (75.9% saved)

localize46.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (*.f32 alphay alphay) sin2phi)
	0.3b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.3b	(/.f32 1 (/.f32 (*.f32 alphay alphay) sin2phi))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 1 (/.f32 (.f32 alphay alphay) sin2phi))))

series165.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

127.0ms

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

26.0ms

(/.f32 1 (/.f32 (*.f32 alphay alphay) sin2phi))

12.0ms

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

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary32`
83×	`*-un-lft-identity_binary32`
50×	`add-sqr-sqrt_binary32`
50×	`add-cube-cbrt_binary32`
31×	`add-exp-log_binary32`

Counts

3 → 165

Calls

3 calls:

14.0ms

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

5.0ms

(/.f32 1 (/.f32 (*.f32 alphay alphay) sin2phi))

3.0ms

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

simplify165.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

539×	`associate-/l/_binary32`
357×	`fma-def_binary32`
186×	`times-frac_binary32`
180×	`associate-/l*_binary32`
162×	`unswap-sqr_binary32`

Counts

273 → 253

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	305	8772
1	750	8007
2	2644	7948
3	5115	7948

prune267.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	281	8	289

Error

Counts

289 → 8

Alt Table

Status	Error	Program
	0.9b	(.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))))))
	2.3b	(+.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))))))))
	0.8b	(.f32 (/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) 1) (/.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 1 (/.f32 (.f32 alphay alphay) sin2phi)))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 1 (/.f32 (.f32 alphay alphay) sin2phi))))
✓	0.5b	(.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (.f32 (.f32 alphax alphax) (.f32 alphay alphay)) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 cos2phi (*.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 (*.f32 alphax alphax) alphay) alphay))
	0.6b	(.f32 (/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (sqrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	0.8b	(.f32 (/.f32 -1 (.f32 (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))) (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi))))) (.f32 (/.f32 (log1p.f32 (neg.f32 u0)) (cbrt.f32 (fma.f32 sin2phi (.f32 alphax alphax) (.f32 (.f32 alphay alphay) cos2phi)))) (.f32 (.f32 alphax alphax) (*.f32 alphay alphay))))

Compiler

Compiled 8707 to 2671 computations (69.3% saved)

regimes8.5s (55.2%)

Accuracy

Total 0.5b remaining (92.8%)

Threshold costs 0.5b (92.8%)

Counts

528 → 1

Compiler

Compiled 285012 to 149231 computations (47.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	16	26
1	25	26
2	31	26
3	35	26
4	36	26
5	35	26

end1.0ms (0%)

Compiler: Compiled 22 to 15 computations (31.8% saved)

sample2.0s (12.8%)

Algorithm

1×

intervals

Results

760.0ms	8000×	body	128	valid
360.0ms	8000×	pre	128	true

Compiler

Compiled 419 to 210 computations (49.9% 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

analyze1.6s (10.6%)

sample141.0ms (0.9%)

simplify24.0ms (0.2%)

prune4.0ms (0%)

localize41.0ms (0.3%)

series272.0ms (1.8%)

rewrite33.0ms (0.2%)

simplify208.0ms (1.4%)

prune222.0ms (1.4%)

localize47.0ms (0.3%)

series298.0ms (1.9%)

rewrite46.0ms (0.3%)

simplify255.0ms (1.7%)

prune284.0ms (1.8%)

localize47.0ms (0.3%)

series232.0ms (1.5%)

rewrite28.0ms (0.2%)

simplify209.0ms (1.4%)

prune215.0ms (1.4%)

localize46.0ms (0.3%)

series165.0ms (1.1%)

rewrite35.0ms (0.2%)

simplify165.0ms (1.1%)

prune267.0ms (1.7%)

regimes8.5s (55.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.0s (12.8%)

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