Details

analyze2.1s (15.5%)

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)

sample60.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
11.0ms	256×	pre	128	true

Compiler

Compiled 84 to 61 computations (27.4% saved)

simplify23.0ms (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

prune5.0ms (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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
	12.4b	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Status

Error

Program

▶

0.7b

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

12.4b

(/.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)))
✓	0.2b	(/.f32 sin2phi (*.f32 alphay alphay))
✓	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

series250.0ms (1.8%)

Counts

4 → 156

Calls

4 calls:

119.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
81.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
26.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
25.0ms	(/.f32 cos2phi (*.f32 alphax alphax))

rewrite30.0ms (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))))
6.0ms	(+.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))

simplify189.0ms (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

prune217.0ms (1.6%)

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
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	1.1b	(.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))))))
	10.8b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
▶	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 1 alphax) (/.f32 cos2phi alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	1.0b	(/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
	1.3b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	0.9b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))

Compiler

Compiled 7579 to 1883 computations (75.2% saved)

localize49.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series260.0ms (1.9%)

Counts

4 → 168

Calls

4 calls:

134.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
107.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)))
11.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
8.0ms	(.f32 cos2phi (.f32 alphay alphay))

rewrite55.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-cbrt-cube_binary32`
64×	`add-exp-log_binary32`
60×	`times-frac_binary32`
55×	`pow1_binary32`
49×	`add-sqr-sqrt_binary32`

Counts

4 → 187

Calls

4 calls:

16.0ms	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
6.0ms	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi)))
6.0ms	(.f32 (.f32 alphax alphax) (*.f32 alphay alphay))
4.0ms	(.f32 cos2phi (.f32 alphay alphay))

simplify182.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

720×	`associate-r_binary32`
560×	`associate-l_binary32`
378×	`times-frac_binary32`
319×	`associate-/l*_binary32`
217×	`associate-/r*_binary32`

Counts

355 → 348

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	427	14419
1	1241	13188
2	5443	13188

prune266.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	347	1	348
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	348	9	357

Error

Counts

357 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	1.1b	(.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))))))
	10.8b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
✓	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
▶	0.5b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 cos2phi (.f32 alphay alphay))))) (*.f32 alphay alphay))
	1.0b	(/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
	1.3b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	0.9b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))

Compiler

Compiled 15024 to 3186 computations (78.8% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series357.0ms (2.6%)

Counts

3 → 180

Calls

3 calls:

131.0ms

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

119.0ms

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

107.0ms

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

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`times-frac_binary32`
58×	`add-cbrt-cube_binary32`
58×	`add-exp-log_binary32`
49×	`add-sqr-sqrt_binary32`
46×	`*-un-lft-identity_binary32`

Counts

3 → 158

Calls

3 calls:

16.0ms

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

9.0ms

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

3.0ms

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

simplify215.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-r_binary32`
517×	`associate-l_binary32`
482×	`times-frac_binary32`
421×	`associate-/l*_binary32`
290×	`associate-/r*_binary32`

Counts

338 → 305

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	455	18134
1	1340	16514
2	5298	16514

prune263.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	329	9	338

Error

Counts

338 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	1.1b	(.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))))))
	10.8b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
▶	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
✓	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
✓	0.5b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 cos2phi (.f32 alphay alphay))))) (*.f32 alphay alphay))
	1.0b	(/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
	1.3b	(/.f32 -1 (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (log1p.f32 (neg.f32 u0))))
	0.9b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))

Compiler

Compiled 14466 to 4016 computations (72.2% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay))
	0.2b	(/.f32 cos2phi (*.f32 alphax alphax))
✓	0.3b	(/.f32 (/.f32 sin2phi alphay) alphay)
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))

series224.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

118.0ms

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

80.0ms

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

26.0ms

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

rewrite50.0ms (0.4%)

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:

16.0ms

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

16.0ms

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

4.0ms

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

simplify201.0ms (1.5%)

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

prune263.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	313	1	314
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	314	9	323

Error

Counts

323 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 (sqrt.f32 cos2phi) alphax) (/.f32 sin2phi (*.f32 alphay alphay))))
	1.1b	(.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))))))
	0.8b	(/.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (sqrt.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))) (sqrt.f32 (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay))))
	10.8b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (-.f32 (/.f32 (.f32 cos2phi cos2phi) (pow.f32 alphax 4)) (/.f32 (.f32 sin2phi sin2phi) (pow.f32 alphay 4)))) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
✓	0.6b	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 sin2phi alphay) alphay)))
✓	0.5b	(.f32 (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (.f32 cos2phi (.f32 alphay alphay)) (.f32 (.f32 alphax alphax) sin2phi))) (.f32 (.f32 alphax alphax) (.f32 alphay alphay)))
✓	0.5b	(.f32 (.f32 (.f32 alphax alphax) (/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (fma.f32 sin2phi (.f32 alphax alphax) (.f32 cos2phi (.f32 alphay alphay))))) (*.f32 alphay alphay))
	1.0b	(/.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))) (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))))))
	0.9b	(/.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0)))) (/.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u0))))))

Compiler

Compiled 9285 to 2159 computations (76.7% saved)

regimes6.4s (46.3%)

Accuracy

Total 0.5b remaining (95.5%)

Threshold costs 0.5b (95.5%)

Counts

423 → 1

Compiler

Compiled 204441 to 111496 computations (45.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary32`
9×	`+-commutative_binary32`
9×	`sub-neg_binary32`
9×	`neg-sub0_binary32`
9×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	27	35
2	36	35
3	45	35
4	56	35
5	69	35
6	78	35
7	84	35
8	86	35
9	86	35

end1.0ms (0%)

Compiler: Compiled 28 to 15 computations (46.4% saved)

sample1.9s (14%)

Algorithm

1×

intervals

Results

747.0ms	8000×	body	128	valid
357.0ms	8000×	pre	128	true

Compiler

Compiled 382 to 214 computations (44% 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

analyze2.1s (15.5%)

sample60.0ms (0.4%)

simplify23.0ms (0.2%)

prune5.0ms (0%)

localize41.0ms (0.3%)

series250.0ms (1.8%)

rewrite30.0ms (0.2%)

simplify189.0ms (1.4%)

prune217.0ms (1.6%)

localize49.0ms (0.4%)

series260.0ms (1.9%)

rewrite55.0ms (0.4%)

simplify182.0ms (1.3%)

prune266.0ms (1.9%)

localize47.0ms (0.3%)

series357.0ms (2.6%)

rewrite50.0ms (0.4%)

simplify215.0ms (1.6%)

prune263.0ms (1.9%)

localize39.0ms (0.3%)

series224.0ms (1.6%)

rewrite50.0ms (0.4%)

simplify201.0ms (1.5%)

prune263.0ms (1.9%)

regimes6.4s (46.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.9s (14%)

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