Details

analyze10.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 118 to 85 computations (28% saved)

sample4.4s (30.2%)

Results

4.3s

8256×

body

128

valid

Compiler

Compiled 307 to 220 computations (28.3% saved)

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

929×	`unsub-neg_binary32`
384×	`associate--l-_binary32`
362×	`distribute-rgt-in_binary32`
356×	`distribute-neg-in_binary32`
347×	`distribute-rgt-neg-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	99
1	67	97
2	204	70
3	683	66
4	1864	66
5	2617	66
6	4625	66
7	5073	66

prune7.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))

Status

Error

Program

▶

0.3b

(fma.f32 ux (*.f32 (*.f32 (-.f32 1 ux) maxCos) zi) (*.f32 (sqrt.f32 (fma.f32 ux (*.f32 ux (*.f32 (*.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32))) xi (*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) yi))))

0.3b

(+.f32 (+.f32 (*.f32 (*.f32 (cos.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) xi) (*.f32 (*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))

Compiler

Compiled 354 to 242 computations (31.6% saved)

localize105.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 (-.f32 1 ux) maxCos)
✓	0.2b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
✓	0.2b	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
✓	0.3b	(.f32 (.f32 uy 2) (PI.f32))

series42.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

17.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
16.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
6.0ms	(*.f32 (-.f32 1 ux) maxCos)
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary32`
18×	`*-un-lft-identity_binary32`
18×	`add-cbrt-cube_binary32`
18×	`add-exp-log_binary32`
18×	`pow1_binary32`

Counts

4 → 108

Calls

4 calls:

17.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
5.0ms	(*.f32 (-.f32 1 ux) maxCos)
4.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
4.0ms	(.f32 (.f32 uy 2) (PI.f32))

simplify115.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-neg_binary32`
598×	`associate-l_binary32`
505×	`associate-r_binary32`
240×	`cancel-sign-sub-inv_binary32`
228×	`*-commutative_binary32`

Counts

180 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	284	3039
1	655	2722
2	2750	2568
3	4436	2561
4	4934	2561

prune1.0s (7.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	252	14	266
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	253	15	268

Error

0.1b

Counts

268 → 15

Alt Table

Status	Error	Program
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (pow.f32 ux 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 ux ux) (.f32 1 ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	1.2b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 (pow.f32 (PI.f32) 5) yi)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi)))))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))))
	16.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 yi (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (-.f32 (.f32 -4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 (.f32 8/315 (pow.f32 uy 7)) (pow.f32 (PI.f32) 7))))))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))) (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (exp.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	5.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (log.f32 (exp.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (.f32 ux ux))) (+.f32 1 ux)) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (.f32 (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
▶	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) yi))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))

Compiler

Compiled 15203 to 8746 computations (42.5% saved)

localize137.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
✓	0.3b	(.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (*.f32 uy 2))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series19.0ms (0.1%)

Counts

3 → 24

Calls

3 calls:

15.0ms	(.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
3.0ms	(.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (*.f32 uy 2))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite124.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

918×	`pow1_binary32`
450×	`pow-prod-down_binary32`
247×	`add-cbrt-cube_binary32`
238×	`add-exp-log_binary32`
238×	`pow-prod-up_binary32`

Counts

3 → 319

Calls

3 calls:

38.0ms	(.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
12.0ms	(.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (*.f32 uy 2))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify157.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary32`
466×	`sqr-pow_binary32`
386×	`associate-l_binary32`
325×	`associate-r_binary32`
286×	`log-prod_binary32`

Counts

343 → 167

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	5654
1	252	3411
2	1381	3345
3	2207	3256
4	3518	2931
5	4975	2931

prune866.0ms (5.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	198	14	212

Error

0.1b

Counts

212 → 14

Alt Table

Status	Error	Program
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 uy) (log.f32 2)) (log.f32 (.f32 uy 2))) (log.f32 (.f32 uy 2)))) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))) yi))))
	5.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (log.f32 (exp.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (pow.f32 ux 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 ux ux) (.f32 1 ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	1.2b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 (pow.f32 (PI.f32) 5) yi)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi)))))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))))
	16.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 yi (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (-.f32 (.f32 -4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 (.f32 8/315 (pow.f32 uy 7)) (pow.f32 (PI.f32) 7))))))))
▶	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32))))) yi))))
	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (.f32 ux ux))) (+.f32 1 ux)) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (.f32 (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (exp.f32 (.f32 2 (.f32 uy (PI.f32)))))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) yi))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))

Compiler

Compiled 14387 to 8280 computations (42.4% saved)

localize154.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32)))
	0.3b	(.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (*.f32 uy 2))
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	1.0b	(pow.f32 (cbrt.f32 (PI.f32)) 5)

series17.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

16.0ms	(.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32)))
0.0ms	(pow.f32 (cbrt.f32 (PI.f32)) 5)

rewrite75.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

334×	`add-exp-log_binary32`
287×	`prod-exp_binary32`
183×	`add-cbrt-cube_binary32`
159×	`cbrt-unprod_binary32`
120×	`pow1_binary32`

Counts

2 → 145

Calls

2 calls:

29.0ms	(.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32)))
2.0ms	(pow.f32 (cbrt.f32 (PI.f32)) 5)

simplify769.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

982×	`fma-def_binary32`
598×	`associate-l_binary32`
456×	`associate-r_binary32`
379×	`+-commutative_binary32`
272×	`log-prod_binary32`

Counts

157 → 126

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	202	5261
1	359	2958
2	1943	2355
3	2472	2355
4	3870	1958
5	5000	1958
6	5036	1958

prune1.0s (6.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	203	14	217

Error

0.1b

Counts

217 → 14

Alt Table

Status	Error	Program
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 uy) (log.f32 2)) (log.f32 (.f32 uy 2))) (log.f32 (.f32 uy 2)))) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))) yi))))
	5.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (log.f32 (exp.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (pow.f32 ux 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 ux ux) (.f32 1 ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	1.2b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 (pow.f32 (PI.f32) 5) yi)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi)))))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))))
	16.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 yi (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (-.f32 (.f32 -4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 (.f32 8/315 (pow.f32 uy 7)) (pow.f32 (PI.f32) 7))))))))
✓	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32))))) yi))))
	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (.f32 ux ux))) (+.f32 1 ux)) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (.f32 (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
▶	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (exp.f32 (.f32 2 (.f32 uy (PI.f32)))))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) yi))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))

Compiler

Compiled 16117 to 9667 computations (40% saved)

localize183.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (*.f32 uy 2))
✓	0.3b	(*.f32 uy (PI.f32))
	1.0b	(*.f32 (PI.f32) (PI.f32))
✓	12.5b	(log.f32 (exp.f32 (.f32 2 (.f32 uy (PI.f32)))))

series7.0ms (0%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(*.f32 uy (PI.f32))
3.0ms	(log.f32 (exp.f32 (.f32 2 (.f32 uy (PI.f32)))))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-cube-cbrt_binary32`
5×	`pow1_binary32`
4×	`add-cbrt-cube_binary32`

Counts

2 → 36

Calls

2 calls:

3.0ms	(*.f32 uy (PI.f32))
1.0ms	(log.f32 (exp.f32 (.f32 2 (.f32 uy (PI.f32)))))

simplify111.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

956×	`fma-def_binary32`
718×	`times-frac_binary32`
464×	`log-prod_binary32`
406×	`distribute-rgt-out_binary32`
217×	`log-pow_binary32`

Counts

60 → 48

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	520
1	89	470
2	236	470
3	581	470
4	801	470
5	1864	470
6	3925	470
7	4487	470
8	4946	470
9	4943	470

prune626.0ms (4.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	130	14	144

Error

0.1b

Counts

144 → 14

Alt Table

Status	Error	Program
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 uy) (log.f32 2)) (log.f32 (.f32 uy 2))) (log.f32 (.f32 uy 2)))) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32))))) yi))))
	5.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (log.f32 (exp.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (pow.f32 ux 3))) (+.f32 (.f32 1 1) (+.f32 (.f32 ux ux) (.f32 1 ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	1.2b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 (pow.f32 (PI.f32) 5) yi)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi)))))))
	0.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (.f32 (cbrt.f32 yi) (cbrt.f32 yi))) (cbrt.f32 yi)))))
	16.5b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (fma.f32 yi (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (-.f32 (.f32 -4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 (.f32 8/315 (pow.f32 uy 7)) (pow.f32 (PI.f32) 7))))))))
✓	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32))))) yi))))
	0.3b	(+.f32 (+.f32 (.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) xi) (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) (.f32 (.f32 (-.f32 1 ux) maxCos) ux))))) yi)) (.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi))
	0.3b	(fma.f32 ux (.f32 (/.f32 (.f32 maxCos (-.f32 1 (.f32 ux ux))) (+.f32 1 ux)) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	0.4b	(fma.f32 ux (.f32 (.f32 (.f32 (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) (cbrt.f32 (-.f32 maxCos (.f32 maxCos ux)))) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
✓	0.3b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (log.f32 (exp.f32 (.f32 2 (.f32 uy (PI.f32)))))) xi (.f32 (sin.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))) yi))))
	1.0b	(fma.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (.f32 ux maxCos) maxCos))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (-.f32 (+.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) yi))) (.f32 8/315 (.f32 (pow.f32 uy 7) (*.f32 yi (pow.f32 (PI.f32) 7)))))))))

Compiler

Compiled 9110 to 5268 computations (42.2% saved)

regimes4.0s (27.4%)

Accuracy

Total 0.2b remaining (54.6%)

Threshold costs 0.2b (54.6%)

Counts

189 → 1

Compiler

Compiled 112127 to 76958 computations (31.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary32`
4×	`+-commutative_binary32`
4×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	102
1	56	102
2	63	102
3	67	102
4	69	102
5	68	102

end539.0ms (3.7%)

Compiler: Compiled 1046 to 705 computations (32.6% saved)

Details

analyze10.0ms (0.1%)

sample4.4s (30.2%)

simplify66.0ms (0.4%)

prune7.0ms (0%)

localize105.0ms (0.7%)

series42.0ms (0.3%)

rewrite38.0ms (0.3%)

simplify115.0ms (0.8%)

prune1.0s (7.1%)

localize137.0ms (0.9%)

series19.0ms (0.1%)

rewrite124.0ms (0.8%)

simplify157.0ms (1.1%)

prune866.0ms (5.9%)

localize154.0ms (1%)

series17.0ms (0.1%)

rewrite75.0ms (0.5%)

simplify769.0ms (5.2%)

prune1.0s (6.9%)

localize183.0ms (1.2%)

series7.0ms (0%)

rewrite6.0ms (0%)

simplify111.0ms (0.8%)

prune626.0ms (4.3%)

regimes4.0s (27.4%)

simplify5.0ms (0%)

end539.0ms (3.7%)

Profiling