Details

analyze1.6s (16.2%)

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)

sample2.2s (22.4%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 114 to 82 computations (28.1% saved)

preprocess51.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

682×	`div-sub_binary32`
604×	`sub-neg_binary32`
450×	`fma-neg_binary32`
303×	`fma-def_binary32`
194×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	286
1	145	275
2	235	275
3	337	275
4	408	275
5	546	275
6	678	275
7	1063	275
8	1640	275
9	2340	275
10	3445	275
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

195×	`fma-neg_binary32`
110×	`fma-def_binary32`
65×	`cancel-sign-sub-inv_binary32`
40×	`div-sub_binary32`
39×	`sub-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	30	25
2	42	25
3	57	25
4	70	25
5	92	25
6	117	25
7	166	25
8	224	25
9	270	25
10	323	25
11	417	25
12	581	25
13	919	25
14	990	25
15	1031	25
16	1036	25

Stop Event

1×

saturated

Counts

1 → 2

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

0.4b

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))))
	13.6b	(/.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))))

13.6b

(/.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)

localize46.0ms (0.5%)

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))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series209.0ms (2.1%)

Counts

4 → 156

Calls

39 calls:

9.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))	sin2phi	-inf
9.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))	alphay	inf
9.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))	alphax	inf
8.0ms	(/.f32 cos2phi (*.f32 alphax alphax))	cos2phi	inf
8.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))	cos2phi	inf

rewrite45.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary32`
174×	`pow1_binary32`
173×	`*-un-lft-identity_binary32`
165×	`expm1-log1p-u_binary32`
164×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	55
1	336	47
0	15	55

Stop Event

1×	saturated
1×	node limit

Counts

4 → 176

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

684×	`associate-/r*_binary32`
598×	`associate-r_binary32`
495×	`associate-l_binary32`
222×	`fma-def_binary32`
197×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	4738
1	372	4542
2	1398	4534

Stop Event

1×	node limit

Counts

332 → 223

prune243.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	213	10	223
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	215	10	225

Error

0.0b

Counts

225 → 10

Alt Table

Status	Error	Program
	7.7b	(.f32 (/.f32 (sqrt.f32 (log1p.f32 u0)) 1) (/.f32 (sqrt.f32 (log1p.f32 u0)) (fma.f32 cos2phi (pow.f32 alphax -2) (.f32 sin2phi (pow.f32 alphay -2)))))
	2.2b	(fma.f32 1/2 (/.f32 u0 (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) u0)) (fma.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 u0 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))
	8.1b	(.f32 (/.f32 (log1p.f32 (neg.f32 u0)) sin2phi) (neg.f32 (.f32 alphay alphay)))
	4.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 alphay (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (/.f32 sin2phi alphay))) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) alphay)))
	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))))
	4.1b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 alphay alphay) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) sin2phi)) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (.f32 alphay alphay))))
▶	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))
	7.1b	(/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))
	29.7b	(-.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 sin2phi (pow.f32 alphax 4))) (.f32 (pow.f32 cos2phi 2) (pow.f32 alphay 2))) (+.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 (pow.f32 sin2phi 2) (pow.f32 alphax 6))) (.f32 (pow.f32 cos2phi 3) (pow.f32 alphay 4))) (/.f32 (*.f32 (log.f32 (-.f32 1 u0)) (pow.f32 alphax 2)) cos2phi)))

Compiler

Compiled 6394 to 2872 computations (55.1% saved)

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f32 alphax -2)
✓	0.2b	(fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2)))
✓	0.3b	(*.f32 cos2phi (pow.f32 alphax -2))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))

series170.0ms (1.7%)

Counts

4 → 144

Calls

36 calls:

9.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))	alphay	-inf
7.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))	alphay	inf
7.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))	alphax	0
7.0ms	(*.f32 cos2phi (pow.f32 alphax -2))	cos2phi	0
7.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))	alphax	-inf

rewrite56.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

298×	`prod-diff_binary32`
244×	`log1p-udef_binary32`
158×	`add-sqr-sqrt_binary32`
156×	`pow1_binary32`
153×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	315	44
2	3992	44
0	15	48

Stop Event

1×	saturated
1×	node limit

Counts

4 → 92

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

686×	`associate-/r*_binary32`
597×	`associate-r_binary32`
497×	`associate-l_binary32`
229×	`fma-def_binary32`
197×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	4654
1	373	4458
2	1401	4450

Stop Event

1×	node limit

Counts

236 → 141

prune142.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	141	10	151

Error

0.0b

Counts

151 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))
	8.1b	(.f32 (/.f32 (log1p.f32 (neg.f32 u0)) sin2phi) (neg.f32 (.f32 alphay alphay)))
	4.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 alphay (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (/.f32 sin2phi alphay))) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) alphay)))
	2.2b	(fma.f32 1/2 (/.f32 u0 (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) u0)) (fma.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 u0 (+.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))))
	4.1b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 alphay alphay) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) sin2phi)) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (.f32 alphay alphay))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))
	7.1b	(/.f32 u0 (+.f32 (/.f32 sin2phi (pow.f32 alphay 2)) (/.f32 cos2phi (pow.f32 alphax 2))))
	29.7b	(-.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 sin2phi (pow.f32 alphax 4))) (.f32 (pow.f32 cos2phi 2) (pow.f32 alphay 2))) (+.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 (pow.f32 sin2phi 2) (pow.f32 alphax 6))) (.f32 (pow.f32 cos2phi 3) (pow.f32 alphay 4))) (/.f32 (*.f32 (log.f32 (-.f32 1 u0)) (pow.f32 alphax 2)) cos2phi)))
	7.7b	(.f32 (/.f32 (sqrt.f32 (log1p.f32 u0)) 1) (/.f32 (sqrt.f32 (log1p.f32 u0)) (fma.f32 sin2phi (pow.f32 alphay -2) (.f32 cos2phi (pow.f32 alphax -2)))))

Compiler

Compiled 4252 to 2345 computations (44.8% saved)

localize55.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series193.0ms (1.9%)

Counts

4 → 168

Calls

42 calls:

8.0ms	(/.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))))	alphax	0
8.0ms	(/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) (.f32 alphay alphay)) (.f32 alphax sin2phi)) (.f32 alphax (*.f32 alphay alphay)))	alphax	0
8.0ms	(/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) (.f32 alphay alphay)) (.f32 alphax sin2phi)) (.f32 alphax (*.f32 alphay alphay)))	sin2phi	-inf
8.0ms	(/.f32 (+.f32 (.f32 (/.f32 cos2phi alphax) (.f32 alphay alphay)) (.f32 alphax sin2phi)) (.f32 alphax (*.f32 alphay alphay)))	cos2phi	0
7.0ms	(/.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))))	alphay	0

rewrite43.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

197×	`add-sqr-sqrt_binary32`
194×	`pow1_binary32`
193×	`*-un-lft-identity_binary32`
183×	`expm1-log1p-u_binary32`
182×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	72
1	379	68
0	17	76

Stop Event

1×	saturated
1×	node limit

Counts

4 → 117

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-/r*_binary32`
395×	`fma-def_binary32`
267×	`associate-*l/_binary32`
234×	`associate-/r/_binary32`
167×	`unswap-sqr_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	5129
1	445	4919
2	1815	4785

Stop Event

1×	node limit

Counts

285 → 168

prune168.0ms (1.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	167	11	178

Error

0.0b

Counts

178 → 11

Alt Table

Status	Error	Program
▶	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))
	8.1b	(.f32 (/.f32 (log1p.f32 (neg.f32 u0)) sin2phi) (neg.f32 (.f32 alphay alphay)))
	1.6b	(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 u0 2) (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (.f32 cos2phi (pow.f32 alphay 2)) alphax)))) (+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 u0 4) (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (.f32 cos2phi (pow.f32 alphay 2)) alphax)))) (+.f32 (.f32 1/3 (/.f32 (.f32 (pow.f32 u0 3) (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (.f32 cos2phi (pow.f32 alphay 2)) alphax)))) (/.f32 (.f32 u0 (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (*.f32 cos2phi (pow.f32 alphay 2)) alphax))))))
	4.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 alphay (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (/.f32 sin2phi alphay))) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) alphay)))
	2.2b	(fma.f32 1/2 (/.f32 u0 (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) u0)) (fma.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 u0 (+.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))))
	4.1b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 alphay alphay) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) sin2phi)) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (.f32 alphay alphay))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))
	29.7b	(-.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 sin2phi (pow.f32 alphax 4))) (.f32 (pow.f32 cos2phi 2) (pow.f32 alphay 2))) (+.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 (pow.f32 sin2phi 2) (pow.f32 alphax 6))) (.f32 (pow.f32 cos2phi 3) (pow.f32 alphay 4))) (/.f32 (*.f32 (log.f32 (-.f32 1 u0)) (pow.f32 alphax 2)) cos2phi)))
	7.7b	(.f32 (/.f32 (sqrt.f32 (log1p.f32 u0)) 1) (/.f32 (sqrt.f32 (log1p.f32 u0)) (fma.f32 sin2phi (pow.f32 alphay -2) (.f32 cos2phi (pow.f32 alphax -2)))))
	2.2b	(fma.f32 1/2 (/.f32 u0 (/.f32 (fma.f32 alphax sin2phi (.f32 (/.f32 (.f32 alphay alphay) alphax) cos2phi)) (.f32 u0 (.f32 alphay (.f32 alphay alphax))))) (fma.f32 1/3 (.f32 (/.f32 (.f32 alphay (.f32 alphay alphax)) (fma.f32 alphax sin2phi (.f32 (/.f32 (.f32 alphay alphay) alphax) cos2phi))) (pow.f32 u0 3)) (.f32 (/.f32 (.f32 alphay (.f32 alphay alphax)) (fma.f32 alphax sin2phi (.f32 (/.f32 (*.f32 alphay alphay) alphax) cos2phi))) u0)))

Compiler

Compiled 6062 to 1979 computations (67.4% saved)

localize51.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
	0.3b	(*.f32 cos2phi (pow.f32 alphax -2))
✓	0.4b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))
✓	0.8b	(pow.f32 (cbrt.f32 (*.f32 cos2phi (pow.f32 alphax -2))) 3)

series133.0ms (1.3%)

Counts

2 → 60

Calls

21 calls:

19.0ms	(pow.f32 (cbrt.f32 (*.f32 cos2phi (pow.f32 alphax -2))) 3)	cos2phi	-inf
8.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))	cos2phi	-inf
8.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))	alphay	inf
7.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))	alphax	0
7.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))	alphay	-inf

rewrite31.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

198×	`add-sqr-sqrt_binary32`
192×	`pow1_binary32`
189×	`*-un-lft-identity_binary32`
187×	`expm1-log1p-u_binary32`
186×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	32
1	417	26
0	19	42

Stop Event

1×	saturated
1×	node limit

Counts

2 → 73

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-/r*_binary32`
599×	`associate-r_binary32`
492×	`associate-l_binary32`
229×	`fma-def_binary32`
197×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	3742
1	372	3546
2	1404	3538

Stop Event

1×	node limit

Counts

133 → 113

prune182.0ms (1.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	164	11	175

Error

0.0b

Counts

175 → 11

Alt Table

Status	Error	Program
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (pow.f32 (cbrt.f32 (.f32 cos2phi (pow.f32 alphax -2))) 3) (/.f32 sin2phi (.f32 alphay alphay))))
	8.1b	(.f32 (/.f32 (log1p.f32 (neg.f32 u0)) sin2phi) (neg.f32 (.f32 alphay alphay)))
	1.6b	(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 u0 2) (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (.f32 cos2phi (pow.f32 alphay 2)) alphax)))) (+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 u0 4) (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (.f32 cos2phi (pow.f32 alphay 2)) alphax)))) (+.f32 (.f32 1/3 (/.f32 (.f32 (pow.f32 u0 3) (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (.f32 cos2phi (pow.f32 alphay 2)) alphax)))) (/.f32 (.f32 u0 (.f32 (pow.f32 alphay 2) alphax)) (+.f32 (.f32 sin2phi alphax) (/.f32 (*.f32 cos2phi (pow.f32 alphay 2)) alphax))))))
	4.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 alphay (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (/.f32 sin2phi alphay))) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) alphay)))
	2.2b	(fma.f32 1/2 (/.f32 u0 (/.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))) u0)) (fma.f32 1/3 (/.f32 (pow.f32 u0 3) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax)))) (/.f32 u0 (+.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))))
	4.1b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (/.f32 (+.f32 (.f32 alphay alphay) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) sin2phi)) (.f32 (/.f32 (.f32 alphax alphax) cos2phi) (.f32 alphay alphay))))
✓	0.5b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (pow.f32 alphay -2) (*.f32 cos2phi (pow.f32 alphax -2))))
	29.7b	(-.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 sin2phi (pow.f32 alphax 4))) (.f32 (pow.f32 cos2phi 2) (pow.f32 alphay 2))) (+.f32 (/.f32 (.f32 (log.f32 (-.f32 1 u0)) (.f32 (pow.f32 sin2phi 2) (pow.f32 alphax 6))) (.f32 (pow.f32 cos2phi 3) (pow.f32 alphay 4))) (/.f32 (*.f32 (log.f32 (-.f32 1 u0)) (pow.f32 alphax 2)) cos2phi)))
	7.7b	(.f32 (/.f32 (sqrt.f32 (log1p.f32 u0)) 1) (/.f32 (sqrt.f32 (log1p.f32 u0)) (fma.f32 sin2phi (pow.f32 alphay -2) (.f32 cos2phi (pow.f32 alphax -2)))))
	2.2b	(fma.f32 1/2 (/.f32 u0 (/.f32 (fma.f32 alphax sin2phi (.f32 (/.f32 (.f32 alphay alphay) alphax) cos2phi)) (.f32 u0 (.f32 alphay (.f32 alphay alphax))))) (fma.f32 1/3 (.f32 (/.f32 (.f32 alphay (.f32 alphay alphax)) (fma.f32 alphax sin2phi (.f32 (/.f32 (.f32 alphay alphay) alphax) cos2phi))) (pow.f32 u0 3)) (.f32 (/.f32 (.f32 alphay (.f32 alphay alphax)) (fma.f32 alphax sin2phi (.f32 (/.f32 (*.f32 alphay alphay) alphax) cos2phi))) u0)))

Compiler

Compiled 4919 to 2442 computations (50.4% saved)

regimes3.7s (37.5%)

Accuracy

Total 0.5b remaining (91.8%)

Threshold costs 0.5b (91.8%)

Counts

239 → 1

Compiler

Compiled 98900 to 65893 computations (33.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Stop Event

1×

saturated

end187.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 483 to 287 computations (40.6% saved)

Details

analyze1.6s (16.2%)

sample2.2s (22.4%)

preprocess51.0ms (0.5%)

simplify20.0ms (0.2%)

prune4.0ms (0%)

localize46.0ms (0.5%)

series209.0ms (2.1%)

rewrite45.0ms (0.5%)

simplify78.0ms (0.8%)

prune243.0ms (2.4%)

localize41.0ms (0.4%)

series170.0ms (1.7%)

rewrite56.0ms (0.6%)

simplify76.0ms (0.8%)

prune142.0ms (1.4%)

localize55.0ms (0.6%)

series193.0ms (1.9%)

rewrite43.0ms (0.4%)

simplify87.0ms (0.9%)

prune168.0ms (1.7%)

localize51.0ms (0.5%)

series133.0ms (1.3%)

rewrite31.0ms (0.3%)

simplify65.0ms (0.6%)

prune182.0ms (1.8%)

regimes3.7s (37.5%)

simplify2.0ms (0%)

end187.0ms (1.9%)

Profiling