Details

analyze2.4s (20.2%)

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)

sample3.0s (25.8%)

Results

2.9s

8256×

body

128

valid

Compiler

Compiled 136 to 97 computations (28.7% 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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Compiler

Compiled 80 to 47 computations (41.3% saved)

localize44.0ms (0.4%)

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))
✓	0.2b	(/.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))))

series252.0ms (2.1%)

Counts

4 → 156

Calls

4 calls:

117.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
82.0ms	(+.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))

rewrite101.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Counts

4 → 179

Calls

4 calls:

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

Iterations

Useful iterations: 1 (0.0ms)

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

simplify97.0ms (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

335 → 224

Iterations

Useful iterations: 2 (0.0ms)

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

prune273.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	211	13	224
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	212	13	225

Error

0.0b

Counts

225 → 13

Alt Table

Status	Error	Program
	9.0b	(.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))))))
	0.7b	(/.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))))
	9.0b	(expm1.f32 (log1p.f32 (/.f32 (log1p.f32 u0) (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))))
	9.0b	(pow.f32 (cbrt.f32 (/.f32 (log1p.f32 u0) (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))) 3)
▶	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (neg.f32 sin2phi) (/.f32 1 (neg.f32 (*.f32 alphay alphay))))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) alphay) (.f32 alphax (/.f32 sin2phi alphay))) (*.f32 alphax alphay)))
	8.6b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi alphay) (.f32 (.f32 alphax alphax) (/.f32 sin2phi alphay))) (.f32 (*.f32 alphax alphax) alphay)))
	2.7b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (pow.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) 3)))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	2.7b	(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 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	8.9b	(.f32 (log1p.f32 u0) (/.f32 1 (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (.f32 alphay alphay)))))

Compiler

Compiled 6543 to 2521 computations (61.5% saved)

localize57.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (neg.f32 sin2phi) (/.f32 1 (neg.f32 (.f32 alphay alphay))))
	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.3b	(/.f32 1 (neg.f32 (*.f32 alphay alphay)))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (neg.f32 sin2phi) (/.f32 1 (neg.f32 (*.f32 alphay alphay))))))

series133.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

105.0ms

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

25.0ms

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

2.0ms

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

rewrite96.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`expm1-udef_binary32`
280×	`log1p-udef_binary32`
241×	`fma-def_binary32`
202×	`add-sqr-sqrt_binary32`
190×	`expm1-log1p-u_binary32`

Counts

3 → 76

Calls

3 calls:

94.0ms

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

94.0ms

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

94.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	49
1	410	33
2	3757	33
3	4990	33
4	4909	33

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

172 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	3994
1	370	3798
2	1358	3790
3	5330	3790

prune132.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	153	13	166

Error

0.0b

Counts

166 → 13

Alt Table

Status	Error	Program
	9.0b	(.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))))))
	0.7b	(/.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))))
	9.0b	(expm1.f32 (log1p.f32 (/.f32 (log1p.f32 u0) (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))))
	9.0b	(pow.f32 (cbrt.f32 (/.f32 (log1p.f32 u0) (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))) 3)
✓	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (neg.f32 sin2phi) (/.f32 1 (neg.f32 (*.f32 alphay alphay))))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) alphay) (.f32 alphax (/.f32 sin2phi alphay))) (*.f32 alphax alphay)))
	8.6b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi alphay) (.f32 (.f32 alphax alphax) (/.f32 sin2phi alphay))) (.f32 (*.f32 alphax alphax) alphay)))
	2.7b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (pow.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) 3)))
▶	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	2.7b	(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 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))
	8.9b	(.f32 (log1p.f32 u0) (/.f32 1 (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (.f32 alphay alphay)))))

Compiler

Compiled 4803 to 2141 computations (55.4% saved)

localize58.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax)
✓	0.3b	(*.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax))
✓	0.5b	(pow.f32 (cbrt.f32 cos2phi) 2)
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series544.0ms (4.6%)

Counts

4 → 120

Calls

4 calls:

348.0ms	(/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax)
113.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
47.0ms	(pow.f32 (cbrt.f32 cos2phi) 2)
36.0ms	(*.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax))

rewrite78.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

343×	`prod-diff_binary32`
208×	`add-sqr-sqrt_binary32`
198×	`expm1-log1p-u_binary32`
197×	`log1p-expm1-u_binary32`
193×	`add-cbrt-cube_binary32`

Counts

4 → 108

Calls

4 calls:

75.0ms	(/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax)
75.0ms	(*.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax))
75.0ms	(pow.f32 (cbrt.f32 cos2phi) 2)
75.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	47
1	419	41
2	4448	41
3	5090	41

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

692×	`associate-/r*_binary32`
631×	`associate-r_binary32`
527×	`associate-l_binary32`
236×	`fma-def_binary32`
204×	`associate-*r/_binary32`

Counts

228 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	4322
1	391	4066
2	1414	4058
3	5504	4058

prune170.0ms (1.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	156	13	169

Error

0.0b

Counts

169 → 13

Alt Table

Status	Error	Program
	9.0b	(pow.f32 (cbrt.f32 (/.f32 (log1p.f32 u0) (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))) 3)
✓	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (neg.f32 sin2phi) (/.f32 1 (neg.f32 (*.f32 alphay alphay))))))
▶	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (expm1.f32 (log1p.f32 (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 sin2phi (.f32 alphay alphay))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) alphay) (.f32 alphax (/.f32 sin2phi alphay))) (*.f32 alphax alphay)))
	8.6b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi alphay) (.f32 (.f32 alphax alphax) (/.f32 sin2phi alphay))) (.f32 (*.f32 alphax alphax) alphay)))
	2.7b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	9.0b	(expm1.f32 (log1p.f32 (/.f32 (log1p.f32 u0) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))))
	9.0b	(.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))))))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (pow.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) 3)))
	8.9b	(.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 (.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	2.7b	(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 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))

Compiler

Compiled 5018 to 2161 computations (56.9% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(expm1.f32 (log1p.f32 (/.f32 cos2phi (*.f32 alphax alphax))))
	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 (expm1.f32 (log1p.f32 (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 sin2phi (.f32 alphay alphay))))

series133.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

106.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (expm1.f32 (log1p.f32 (/.f32 cos2phi (*.f32 alphax alphax)))) (/.f32 sin2phi (*.f32 alphay alphay))))

26.0ms

(expm1.f32 (log1p.f32 (/.f32 cos2phi (*.f32 alphax alphax))))

rewrite85.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

281×	`expm1-udef_binary32`
281×	`log1p-udef_binary32`
177×	`add-sqr-sqrt_binary32`
170×	`expm1-log1p-u_binary32`
168×	`log1p-expm1-u_binary32`

Counts

2 → 90

Calls

2 calls:

83.0ms

(expm1.f32 (log1p.f32 (/.f32 cos2phi (*.f32 alphax alphax))))

83.0ms

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (expm1.f32 (log1p.f32 (/.f32 cos2phi (*.f32 alphax alphax)))) (/.f32 sin2phi (*.f32 alphay alphay))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	350	26
2	4437	26
3	5197	26

simplify81.0ms (0.7%)

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

174 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	3910
1	369	3714
2	1355	3706
3	5323	3706

prune172.0ms (1.5%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	199	13	212

Error

0.0b

Counts

212 → 13

Alt Table

Status	Error	Program
	9.0b	(pow.f32 (cbrt.f32 (/.f32 (log1p.f32 u0) (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (*.f32 alphay alphay))))) 3)
✓	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (.f32 (neg.f32 sin2phi) (/.f32 1 (neg.f32 (*.f32 alphay alphay))))))
✓	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (expm1.f32 (log1p.f32 (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 sin2phi (.f32 alphay alphay))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) alphay) (.f32 alphax (/.f32 sin2phi alphay))) (*.f32 alphax alphay)))
	8.6b	(neg.f32 (.f32 (/.f32 (.f32 alphay alphay) sin2phi) (log1p.f32 (neg.f32 u0))))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 cos2phi alphay) (.f32 (.f32 alphax alphax) (/.f32 sin2phi alphay))) (.f32 (*.f32 alphax alphax) alphay)))
	2.7b	(+.f32 (/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))) (+.f32 (.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))) (.f32 1/2 (/.f32 (pow.f32 u0 2) (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2)))))))
	8.9b	(.f32 (/.f32 1 (fma.f32 cos2phi (pow.f32 alphax -2) (/.f32 sin2phi (.f32 alphay alphay)))) (log1p.f32 u0))
	9.0b	(expm1.f32 (log1p.f32 (/.f32 (log1p.f32 u0) (fma.f32 sin2phi (pow.f32 alphay -2) (/.f32 cos2phi (*.f32 alphax alphax))))))
	9.0b	(.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))))))
	0.8b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (pow.f32 (cbrt.f32 (/.f32 sin2phi (.f32 alphay alphay))) 3)))
✓	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 (/.f32 (pow.f32 (cbrt.f32 cos2phi) 2) alphax) (/.f32 (cbrt.f32 cos2phi) alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	2.7b	(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 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (*.f32 alphax alphax))))))

Compiler

Compiled 5447 to 2122 computations (61% saved)

regimes3.4s (29.1%)

Accuracy

Total 0.4b remaining (86.8%)

Threshold costs 0.4b (86.8%)

Counts

218 → 1

Compiler

Compiled 90949 to 61125 computations (32.8% 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

end165.0ms (1.4%)

Compiler: Compiled 400 to 259 computations (35.3% 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

analyze2.4s (20.2%)

sample3.0s (25.8%)

simplify28.0ms (0.2%)

prune4.0ms (0%)

localize44.0ms (0.4%)

series252.0ms (2.1%)

rewrite101.0ms (0.9%)

simplify97.0ms (0.8%)

prune273.0ms (2.3%)

localize57.0ms (0.5%)

series133.0ms (1.1%)

rewrite96.0ms (0.8%)

simplify83.0ms (0.7%)

prune132.0ms (1.1%)

localize58.0ms (0.5%)

series544.0ms (4.6%)

rewrite78.0ms (0.7%)

simplify90.0ms (0.8%)

prune170.0ms (1.4%)

localize45.0ms (0.4%)

series133.0ms (1.1%)

rewrite85.0ms (0.7%)

simplify81.0ms (0.7%)

prune172.0ms (1.5%)

regimes3.4s (29.1%)

simplify2.0ms (0%)

end165.0ms (1.4%)

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