Details

analyze180.0ms (1.1%)

Algorithm

1×

Search

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

Compiler

Compiled 118 to 85 computations (28% saved)

sample117.0ms (0.7%)

Algorithm

1×

intervals

Results

72.0ms	256×	body	128	valid
15.0ms	256×	pre	128	true

Compiler

Compiled 195 to 141 computations (27.7% saved)

simplify68.0ms (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

prune8.0ms (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)

localize92.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series73.0ms (0.5%)

Counts

4 → 72

Calls

4 calls:

50.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
16.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
3.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
16×	`pow1_binary32`
14×	`add-sqr-sqrt_binary32`
13×	`*-un-lft-identity_binary32`

Counts

4 → 92

Calls

4 calls:

10.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
4.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
1.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))

simplify118.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-l_binary32`
517×	`fma-neg_binary32`
481×	`associate-r_binary32`
301×	`cancel-sign-sub-inv_binary32`
270×	`exp-prod_binary32`

Counts

164 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	278	3041
1	658	2723
2	2786	2610
3	4428	2602
4	4967	2602

prune845.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	193	11	204
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	12	206

Error

0.1b

Counts

206 → 12

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 (fma.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3))))))))
	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 1 ux) maxCos) zi) (.f32 (sqrt.f32 (fma.f32 ux (.f32 ux (.f32 (neg.f32 (.f32 maxCos maxCos)) (.f32 ux ux))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.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 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.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))
	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 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (*.f32 uy 2) (PI.f32))))) 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 (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 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy 2) (.f32 uy 2)) (.f32 uy 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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)))))))))
	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)))))
	0.9b	(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 (exp.f32 (+.f32 (log.f32 (*.f32 uy 2)) (log.f32 (PI.f32))))) yi))))

Compiler

Compiled 11877 to 6922 computations (41.7% saved)

localize143.0ms (0.9%)

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

series17.0ms (0.1%)

Counts

3 → 24

Calls

3 calls:

14.0ms	(.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))

rewrite127.0ms (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:

42.0ms	(.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))

simplify156.0ms (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

prune843.0ms (5.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	198	11	209

Error

0.1b

Counts

209 → 11

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 (neg.f32 (.f32 maxCos maxCos)) (.f32 ux ux))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.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 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32)))) yi)))))
	0.7b	(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 3 (log.f32 (.f32 uy 2)))) (.f32 (*.f32 (PI.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))
	0.4b	(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 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.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 (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3))))))))
	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)))))))))
	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)))))
▶	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 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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))))
	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))))
	0.5b	(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))))))

Compiler

Compiled 14007 to 8032 computations (42.7% saved)

localize177.0ms (1.1%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
3.0ms	(.f32 (.f32 uy uy) uy)

rewrite98.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

648×	`pow1_binary32`
306×	`pow-prod-down_binary32`
222×	`pow-plus_binary32`
222×	`pow-prod-up_binary32`
181×	`add-cbrt-cube_binary32`

Counts

2 → 214

Calls

2 calls:

38.0ms	(.f32 (.f32 (.f32 (.f32 uy uy) uy) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))
5.0ms	(.f32 (.f32 uy uy) uy)

simplify150.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1013×	`fma-def_binary32`
473×	`+-commutative_binary32`
435×	`*-commutative_binary32`
360×	`associate-+l+_binary32`
346×	`sqr-pow_binary32`

Counts

238 → 104

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	134	3650
1	226	2737
2	970	2652
3	2298	2518
4	3881	2456
5	4969	2456
6	5149	2456

prune1.2s (7.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	259	11	270

Error

0.1b

Counts

270 → 11

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 (neg.f32 (.f32 maxCos maxCos)) (.f32 ux ux))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.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 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32)))) yi)))))
	0.7b	(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 3 (log.f32 (.f32 uy 2)))) (.f32 (*.f32 (PI.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))
	0.4b	(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 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.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 (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3))))))))
	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)))))))))
	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)))))
▶	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 (cbrt.f32 (.f32 (.f32 (exp.f32 (.f32 3 (log.f32 uy))) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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))))
	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))))
	0.5b	(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))))))

Compiler

Compiled 21211 to 11458 computations (46% saved)

localize219.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (exp.f32 (.f32 3 (log.f32 uy))) (.f32 (.f32 2 2) 2)) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)))
✓	0.3b	(*.f32 3 (log.f32 uy))
	1.0b	(*.f32 (PI.f32) (PI.f32))
✓	2.6b	(exp.f32 (*.f32 3 (log.f32 uy)))

series43.0ms (0.3%)

Counts

3 → 32

Calls

3 calls:

26.0ms	(*.f32 3 (log.f32 uy))
14.0ms	(.f32 (.f32 (exp.f32 (.f32 3 (log.f32 uy))) (.f32 (.f32 2 2) 2)) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)))
3.0ms	(exp.f32 (*.f32 3 (log.f32 uy)))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`pow1_binary32`
59×	`add-cbrt-cube_binary32`
50×	`add-exp-log_binary32`
43×	`cbrt-unprod_binary32`
43×	`prod-exp_binary32`

Counts

3 → 93

Calls

3 calls:

17.0ms	(.f32 (.f32 (exp.f32 (.f32 3 (log.f32 uy))) (.f32 (.f32 2 2) 2)) (.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)))
3.0ms	(*.f32 3 (log.f32 uy))
2.0ms	(exp.f32 (*.f32 3 (log.f32 uy)))

simplify130.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary32`
412×	`*-commutative_binary32`
378×	`distribute-rgt-in_binary32`
358×	`distribute-lft-in_binary32`
252×	`log-prod_binary32`

Counts

125 → 110

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	153	1846
1	278	1424
2	945	1363
3	2318	1307
4	4837	1307
5	4989	1287
6	5000	1287
7	4906	1287

prune888.0ms (5.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	180	11	191

Error

0.1b

Counts

191 → 11

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 (neg.f32 (.f32 maxCos maxCos)) (.f32 ux ux))) 1)) (fma.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) xi (.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 (.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32)))) yi)))))
	0.7b	(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 3 (log.f32 (.f32 uy 2)))) (.f32 (*.f32 (PI.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))
	0.4b	(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 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.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 (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 yi (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3))))))))
	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)))))))))
	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)))))
✓	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 (cbrt.f32 (.f32 (.f32 (exp.f32 (.f32 3 (log.f32 uy))) (.f32 (.f32 2 2) 2)) (.f32 (.f32 (PI.f32) (PI.f32)) (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))))
	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))))
	0.5b	(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))))))

Compiler

Compiled 14052 to 8203 computations (41.6% saved)

regimes5.5s (34.4%)

Accuracy

Total 0.2b remaining (51.7%)

Threshold costs 0.2b (51.7%)

Counts

298 → 1

Compiler

Compiled 185188 to 127056 computations (31.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`*-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	37	98
1	56	98
2	63	98
3	67	98
4	69	98
5	68	98

end1.0ms (0%)

Compiler: Compiled 68 to 47 computations (30.9% saved)

sample4.7s (29.5%)

Algorithm

1×

intervals

Results

2.9s	8000×	body	128	valid
532.0ms	8000×	pre	128	true

Compiler

Compiled 910 to 631 computations (30.7% saved)

Details

analyze180.0ms (1.1%)

sample117.0ms (0.7%)

simplify68.0ms (0.4%)

prune8.0ms (0%)

localize92.0ms (0.6%)

series73.0ms (0.5%)

rewrite24.0ms (0.2%)

simplify118.0ms (0.7%)

prune845.0ms (5.3%)

localize143.0ms (0.9%)

series17.0ms (0.1%)

rewrite127.0ms (0.8%)

simplify156.0ms (1%)

prune843.0ms (5.3%)

localize177.0ms (1.1%)

series17.0ms (0.1%)

rewrite98.0ms (0.6%)

simplify150.0ms (0.9%)

prune1.2s (7.5%)

localize219.0ms (1.4%)

series43.0ms (0.3%)

rewrite31.0ms (0.2%)

simplify130.0ms (0.8%)

prune888.0ms (5.6%)

regimes5.5s (34.4%)

simplify4.0ms (0%)

end1.0ms (0%)

sample4.7s (29.5%)

Profiling