Details

analyze1.8s (18.7%)

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)

sample2.2s (22.4%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 136 to 97 computations (28.7% saved)

simplify22.0ms (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

prune7.0ms (0.1%)

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))))
	13.1b	(/.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))))

13.1b

(/.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)

localize37.0ms (0.4%)

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 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))))

series246.0ms (2.5%)

Counts

4 → 156

Calls

4 calls:

115.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
77.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
31.0ms	(/.f32 cos2phi (*.f32 alphax alphax))
23.0ms	(/.f32 sin2phi (*.f32 alphay alphay))

rewrite92.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

274×	`expm1-udef_binary32`
274×	`log1p-udef_binary32`
176×	`egg-rr`
173×	`add-sqr-sqrt_binary32`
165×	`expm1-log1p-u_binary32`

Counts

4 → 176

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	55
1	336	47
2	4410	47
3	5151	47
0	0	0
1	0	0

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

684×	`associate-/r*_binary32`
603×	`associate-r_binary32`
497×	`associate-l_binary32`
236×	`fma-def_binary32`
197×	`associate-*r/_binary32`

Counts

332 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	4738
1	369	4542
2	1355	4534
3	5323	4534

prune208.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	211	12	223
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	212	13	225

Error

0.0b

Counts

225 → 13

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 sin2phi alphay) (/.f32 1 alphay))))
	2.2b	(+.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 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) u0) (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) (.f32 alphay alphay)) (.f32 alphax sin2phi)) (.f32 alphax (*.f32 alphay alphay))))
	13.1b	(/.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 1 (/.f32 (pow.f32 (.f32 alphax alphay) 2) (fma.f32 cos2phi (.f32 alphay alphay) (.f32 (.f32 alphax alphax) sin2phi)))))
	22.7b	(neg.f32 (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (log1p.f32 (neg.f32 u0))))
	8.2b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	8.5b	(.f32 (sqrt.f32 (log1p.f32 u0)) (.f32 (sqrt.f32 (log1p.f32 u0)) (/.f32 1 (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))))
	8.6b	(.f32 (pow.f32 (cbrt.f32 (log1p.f32 u0)) 2) (.f32 (cbrt.f32 (log1p.f32 u0)) (/.f32 1 (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))))
	7.8b	(/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (sqrt.f32 cos2phi) (.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (pow.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) 3)))

Compiler

Compiled 6480 to 2471 computations (61.9% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.2b	(fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax)))
	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))

series171.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

110.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))

58.0ms

(fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax)))

3.0ms

(log1p.f32 (neg.f32 u0))

rewrite118.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

355×	`prod-diff_binary32`
258×	`fma-udef_binary32`
248×	`expm1-udef_binary32`
248×	`log1p-udef_binary32`
199×	`fma-neg_binary32`

Counts

3 → 90

Calls

3 calls:

116.0ms

(log1p.f32 (neg.f32 u0))

116.0ms

(fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax)))

116.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	42
1	319	36
2	3403	36
3	4887	36
4	4901	36
5	4886	36
0	0	0
1	0	0

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

689×	`associate-/r*_binary32`
417×	`fma-def_binary32`
247×	`fma-neg_binary32`
196×	`associate-*r/_binary32`
193×	`associate-*l/_binary32`

Counts

210 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	4624
1	478	4412
2	1739	4401
3	4814	4401
4	4970	4401

prune152.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	195	13	208

Error

0.0b

Counts

208 → 13

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 sin2phi alphay) (/.f32 1 alphay))))
	2.2b	(+.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 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) u0) (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) (.f32 alphay alphay)) (.f32 alphax sin2phi)) (.f32 alphax (*.f32 alphay alphay))))
	13.1b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	8.5b	(.f32 (log1p.f32 u0) (/.f32 1 (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (.f32 alphax alphax)))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (/.f32 (pow.f32 (.f32 alphax alphay) 2) (fma.f32 cos2phi (.f32 alphay alphay) (.f32 (.f32 alphax alphax) sin2phi)))))
	22.7b	(neg.f32 (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (log1p.f32 (neg.f32 u0))))
	7.8b	(/.f32 (neg.f32 (neg.f32 u0)) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))
	8.2b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	8.5b	(.f32 (sqrt.f32 (log1p.f32 u0)) (.f32 (sqrt.f32 (log1p.f32 u0)) (/.f32 1 (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))))
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (sqrt.f32 cos2phi) (.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (pow.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) 3)))

Compiler

Compiled 5479 to 2631 computations (52% saved)

localize45.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.3b	(.f32 (sqrt.f32 cos2phi) (.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2)))
✓	0.3b	(*.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (sqrt.f32 cos2phi) (.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))) (/.f32 sin2phi (*.f32 alphay alphay))))

series163.0ms (1.7%)

Counts

3 → 88

Calls

3 calls:

129.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (*.f32 (sqrt.f32 cos2phi) (*.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))) (/.f32 sin2phi (*.f32 alphay alphay))))

21.0ms

(*.f32 (sqrt.f32 cos2phi) (*.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2)))

13.0ms

(*.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))

rewrite97.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

308×	`log1p-udef_binary32`
307×	`expm1-udef_binary32`
194×	`add-sqr-sqrt_binary32`
185×	`expm1-log1p-u_binary32`
184×	`log1p-expm1-u_binary32`

Counts

3 → 67

Calls

3 calls:

95.0ms

(*.f32 (sqrt.f32 cos2phi) (*.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2)))

95.0ms

(*.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))

95.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (*.f32 (sqrt.f32 cos2phi) (*.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))) (/.f32 sin2phi (*.f32 alphay alphay))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	390	35
2	4468	35
3	4992	35
4	5242	35
0	0	0
1	0	0

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

690×	`associate-/r*_binary32`
604×	`associate-r_binary32`
499×	`associate-l_binary32`
236×	`fma-def_binary32`
200×	`associate-*r/_binary32`

Counts

155 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	3781
1	375	3565
2	1369	3557
3	5356	3557

prune119.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	145	13	158

Error

0.0b

Counts

158 → 13

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 sin2phi alphay) (/.f32 1 alphay))))
	2.2b	(+.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 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) u0) (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) (.f32 alphay alphay)) (.f32 alphax sin2phi)) (.f32 alphax (*.f32 alphay alphay))))
	13.1b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	8.5b	(.f32 (log1p.f32 u0) (/.f32 1 (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (.f32 alphax alphax)))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (/.f32 (pow.f32 (.f32 alphax alphay) 2) (fma.f32 cos2phi (.f32 alphay alphay) (.f32 (.f32 alphax alphax) sin2phi)))))
	22.7b	(neg.f32 (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (log1p.f32 (neg.f32 u0))))
	7.8b	(/.f32 (neg.f32 (neg.f32 u0)) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))
	8.2b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	8.5b	(.f32 (sqrt.f32 (log1p.f32 u0)) (.f32 (sqrt.f32 (log1p.f32 u0)) (/.f32 1 (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (sqrt.f32 cos2phi) (.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (pow.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) 3)))

Compiler

Compiled 4640 to 2177 computations (53.1% saved)

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 sin2phi alphay) (/.f32 1 alphay)))
	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.4b	(*.f32 (/.f32 sin2phi alphay) (/.f32 1 alphay))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 sin2phi alphay) (/.f32 1 alphay))))

series214.0ms (2.2%)

Counts

3 → 132

Calls

3 calls:

113.0ms

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

77.0ms

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

24.0ms

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

rewrite79.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

852×	`prod-diff_binary32`
185×	`add-sqr-sqrt_binary32`
174×	`expm1-log1p-u_binary32`
173×	`log1p-expm1-u_binary32`
170×	`add-cbrt-cube_binary32`

Counts

3 → 129

Calls

3 calls:

77.0ms

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

77.0ms

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

77.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	48
1	370	40
2	4233	40
3	5860	40
0	0	0
1	0	0

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

684×	`associate-/r*_binary32`
603×	`associate-r_binary32`
497×	`associate-l_binary32`
236×	`fma-def_binary32`
197×	`associate-*r/_binary32`

Counts

261 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	4570
1	369	4374
2	1355	4366
3	5323	4366

prune177.0ms (1.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	209	13	222

Error

0.0b

Counts

222 → 13

Alt Table

Status	Error	Program
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (/.f32 sin2phi alphay) (/.f32 1 alphay))))
	2.2b	(+.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 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) u0) (.f32 1/4 (/.f32 (pow.f32 u0 4) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) (.f32 alphay alphay)) (.f32 alphax sin2phi)) (.f32 alphax (*.f32 alphay alphay))))
	13.1b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	8.5b	(.f32 (log1p.f32 u0) (/.f32 1 (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (.f32 alphax alphax)))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 1 (/.f32 (pow.f32 (.f32 alphax alphay) 2) (fma.f32 cos2phi (.f32 alphay alphay) (.f32 (.f32 alphax alphax) sin2phi)))))
	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (/.f32 alphay (/.f32 1 alphay)))))
	22.7b	(neg.f32 (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (log1p.f32 (neg.f32 u0))))
	7.8b	(/.f32 (neg.f32 (neg.f32 u0)) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))
	8.2b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	8.5b	(*.f32 (/.f32 (sqrt.f32 (log1p.f32 u0)) 1) (/.f32 (sqrt.f32 (log1p.f32 u0)) (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 (/.f32 sin2phi alphay) alphay))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (sqrt.f32 cos2phi) (.f32 (sqrt.f32 cos2phi) (pow.f32 alphax -2))) (/.f32 sin2phi (*.f32 alphay alphay))))

Compiler

Compiled 5696 to 2197 computations (61.4% saved)

regimes3.2s (33%)

Accuracy

Total 0.5b remaining (90.8%)

Threshold costs 0.5b (90.8%)

Counts

203 → 1

Compiler

Compiled 74047 to 50587 computations (31.7% saved)

simplify2.0ms (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	15	23
1	23	23
2	29	23
3	33	23
4	34	23
5	34	23

end141.0ms (1.5%)

Compiler: Compiled 372 to 231 computations (37.9% 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

analyze1.8s (18.7%)

sample2.2s (22.4%)

simplify22.0ms (0.2%)

prune7.0ms (0.1%)

localize37.0ms (0.4%)

series246.0ms (2.5%)

rewrite92.0ms (1%)

simplify84.0ms (0.9%)

prune208.0ms (2.1%)

localize36.0ms (0.4%)

series171.0ms (1.8%)

rewrite118.0ms (1.2%)

simplify103.0ms (1.1%)

prune152.0ms (1.6%)

localize45.0ms (0.5%)

series163.0ms (1.7%)

rewrite97.0ms (1%)

simplify69.0ms (0.7%)

prune119.0ms (1.2%)

localize41.0ms (0.4%)

series214.0ms (2.2%)

rewrite79.0ms (0.8%)

simplify79.0ms (0.8%)

prune177.0ms (1.8%)

regimes3.2s (33%)

simplify2.0ms (0%)

end141.0ms (1.5%)

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