Details

analyze9.0ms (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 (30.1%)

Results

4.3s

8256×

body

128

valid

Compiler

Compiled 307 to 220 computations (28.3% saved)

simplify66.0ms (0.5%)

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 (0.1%)

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)

localize102.0ms (0.7%)

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)
✓	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series36.0ms (0.2%)

Counts

4 → 72

Calls

4 calls:

15.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
14.0ms	(.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))

rewrite28.0ms (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))
5.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
4.0ms	(.f32 (.f32 uy 2) (PI.f32))
2.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))

simplify107.0ms (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

prune541.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	194	10	204
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	195	11	206

Error

0.1b

Counts

206 → 11

Alt Table

Status	Error	Program
	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 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 (pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	5.0b	(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 (log.f32 (exp.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))
	16.3b	(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 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	0.8b	(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)))))
	0.4b	(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 (.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))))))
	10.1b	(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 (log.f32 (exp.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	1.5b	(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 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (*.f32 yi (pow.f32 (PI.f32) 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))))
	0.3b	(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 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.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 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))

Compiler

Compiled 11679 to 6790 computations (41.9% saved)

localize148.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(*.f32 uy (PI.f32))
✓	0.8b	(pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3)

series12.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3)
2.0ms	(*.f32 uy (PI.f32))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary32`
10×	`add-exp-log_binary32`
10×	`pow1_binary32`
7×	`add-sqr-sqrt_binary32`
5×	`*-un-lft-identity_binary32`

Counts

2 → 47

Calls

2 calls:

4.0ms	(pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3)
3.0ms	(*.f32 uy (PI.f32))

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

579×	`sqr-pow_binary32`
429×	`exp-prod_binary32`
428×	`log-prod_binary32`
360×	`cube-prod_binary32`
291×	`swap-sqr_binary32`

Counts

71 → 59

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	636
1	139	614
2	514	606
3	1335	606
4	3736	603
5	5243	603

prune536.0ms (3.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	130	12	142

Error

0.1b

Counts

142 → 12

Alt Table

Status	Error	Program
	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))
	0.9b	(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 (cbrt.f32 (log.f32 (exp.f32 (pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3))))) 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 (cbrt.f32 (pow.f32 (.f32 2 (.f32 (sqrt.f32 uy) (.f32 (sqrt.f32 uy) (PI.f32)))) 3))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	0.8b	(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)))))
	16.3b	(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 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.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 (.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))))))
	10.1b	(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 (log.f32 (exp.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	1.5b	(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 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (*.f32 yi (pow.f32 (PI.f32) 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))))
	0.3b	(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 (pow.f32 (.f32 2 (log.f32 (exp.f32 (.f32 uy (PI.f32))))) 3))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	5.0b	(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 (cbrt.f32 (pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3))) xi (.f32 (sin.f32 (log.f32 (exp.f32 (.f32 2 (.f32 uy (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 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))

Compiler

Compiled 8230 to 4881 computations (40.7% saved)

localize140.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f32 (sqrt.f32 uy) (PI.f32))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(.f32 (sqrt.f32 uy) (.f32 (sqrt.f32 uy) (PI.f32)))
✓	0.8b	(pow.f32 (.f32 2 (.f32 (sqrt.f32 uy) (*.f32 (sqrt.f32 uy) (PI.f32)))) 3)

series33.0ms (0.2%)

Counts

3 → 16

Calls

3 calls:

19.0ms	(pow.f32 (.f32 2 (.f32 (sqrt.f32 uy) (*.f32 (sqrt.f32 uy) (PI.f32)))) 3)
7.0ms	(*.f32 (sqrt.f32 uy) (PI.f32))
7.0ms	(.f32 (sqrt.f32 uy) (.f32 (sqrt.f32 uy) (PI.f32)))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary32`
20×	`add-exp-log_binary32`
20×	`pow1_binary32`
13×	`add-sqr-sqrt_binary32`
12×	`associate-l_binary32`

Counts

3 → 77

Calls

3 calls:

20.0ms	(pow.f32 (.f32 2 (.f32 (sqrt.f32 uy) (*.f32 (sqrt.f32 uy) (PI.f32)))) 3)
7.0ms	(.f32 (sqrt.f32 uy) (.f32 (sqrt.f32 uy) (PI.f32)))
4.0ms	(*.f32 (sqrt.f32 uy) (PI.f32))

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

734×	`log-prod_binary32`
429×	`swap-sqr_binary32`
355×	`unswap-sqr_binary32`
344×	`associate-+l+_binary32`
322×	`exp-prod_binary32`

Counts

93 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	895
1	202	833
2	698	825
3	1689	825
4	4983	825
5	5239	825

prune1.2s (8.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	137	12	149

Error

0.1b

Counts

149 → 12

Alt Table

Status	Error	Program
▶	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))
	0.9b	(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 (cbrt.f32 (log.f32 (exp.f32 (pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3))))) 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 (cbrt.f32 (pow.f32 (.f32 2 (.f32 (sqrt.f32 uy) (.f32 (sqrt.f32 uy) (PI.f32)))) 3))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	0.8b	(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)))))
	16.3b	(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 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.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 (.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))))))
	10.1b	(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 (log.f32 (exp.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))))
	1.5b	(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 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (*.f32 yi (pow.f32 (PI.f32) 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))))
	0.3b	(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 (pow.f32 (.f32 2 (log.f32 (exp.f32 (.f32 uy (PI.f32))))) 3))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	5.0b	(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 (cbrt.f32 (pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3))) xi (.f32 (sin.f32 (log.f32 (exp.f32 (.f32 2 (.f32 uy (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 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))

Compiler

Compiled 8875 to 4914 computations (44.6% saved)

localize92.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi)
	0.2b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.2b	(.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)
	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series293.0ms (2%)

Counts

2 → 84

Calls

2 calls:

275.0ms

(*.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)

17.0ms

(*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi)

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
16×	`pow1_binary32`
9×	`cbrt-unprod_binary32`
9×	`prod-exp_binary32`

Counts

2 → 47

Calls

2 calls:

11.0ms

(*.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)

9.0ms

(*.f32 (*.f32 (*.f32 (-.f32 1 ux) maxCos) ux) zi)

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-r_binary32`
672×	`associate-l_binary32`
428×	`fma-neg_binary32`
358×	`*-commutative_binary32`
256×	`fma-def_binary32`

Counts

131 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	6397
1	1186	5664
2	4725	5660
3	5052	5660

prune852.0ms (5.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	213	13	226

Error

0.1b

Counts

226 → 13

Alt Table

Status	Error	Program
	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 (cbrt.f32 (log.f32 (exp.f32 (pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3))))) 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 (cbrt.f32 (pow.f32 (.f32 2 (.f32 (sqrt.f32 uy) (.f32 (sqrt.f32 uy) (PI.f32)))) 3))) xi (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi))))
	1.1b	(+.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 (.f32 2 (.f32 (.f32 (PI.f32) (.f32 uy yi)) (sqrt.f32 (-.f32 (+.f32 1 (.f32 2 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 3)))) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 4))))))) (.f32 4/15 (.f32 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))) (sqrt.f32 (-.f32 (+.f32 1 (.f32 2 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 3)))) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 4)))))))) (.f32 4/3 (.f32 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3))) (sqrt.f32 (-.f32 (+.f32 1 (.f32 2 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 3)))) (+.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 4))))))))) (.f32 (.f32 (.f32 (-.f32 1 ux) maxCos) ux) zi))
	1.5b	(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 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (*.f32 yi (pow.f32 (PI.f32) 3))))))))
	16.7b	(+.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) (exp.f32 (log.f32 (.f32 yi (.f32 (sin.f32 (.f32 2 (.f32 (PI.f32) uy))) (sqrt.f32 (-.f32 1 (.f32 (.f32 ux (.f32 maxCos (-.f32 1 ux))) (.f32 ux (.f32 maxCos (-.f32 1 ux))))))))))) (.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 (.f32 (.f32 uy 2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) yi))))
	0.8b	(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)))))
	16.3b	(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 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi)) (sqrt.f32 (.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 (.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	(+.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 maxCos (.f32 ux zi)) (.f32 maxCos (.f32 (pow.f32 ux 2) zi))))
	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 (pow.f32 (.f32 2 (log.f32 (exp.f32 (.f32 uy (PI.f32))))) 3))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	5.0b	(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 (cbrt.f32 (pow.f32 (.f32 2 (.f32 uy (PI.f32))) 3))) xi (.f32 (sin.f32 (log.f32 (exp.f32 (.f32 2 (.f32 uy (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 (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) yi))))

Compiler

Compiled 18625 to 12295 computations (34% saved)

regimes5.2s (35.6%)

Accuracy

Total 0.2b remaining (59.9%)

Threshold costs 0.2b (59.9%)

Counts

252 → 1

Compiler

Compiled 166962 to 116506 computations (30.2% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

56×	`distribute-rgt-neg-in_binary32`
39×	`cancel-sign-sub-inv_binary32`
38×	`distribute-lft-neg-in_binary32`
33×	`neg-sub0_binary32`
33×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	104
1	58	104
2	80	104
3	100	104
4	117	104
5	133	104
6	146	104
7	167	104
8	203	104
9	233	104
10	254	104
11	271	104
12	286	104
13	290	104
14	286	104

end464.0ms (3.2%)

Compiler: Compiled 1044 to 732 computations (29.9% saved)

Iter	Nodes	Cost
0	31	104
1	58	104
2	80	104
3	100	104
4	117	104
5	133	104
6	146	104
7	167	104
8	203	104
9	233	104
10	254	104
11	271	104
12	286	104
13	290	104
14	286	104

Iter	Nodes	Cost
0	31	104
1	58	104
2	80	104
3	100	104
4	117	104
5	133	104
6	146	104
7	167	104
8	203	104
9	233	104
10	254	104
11	271	104
12	286	104
13	290	104
14	286	104

Details

analyze9.0ms (0.1%)

sample4.4s (30.1%)

simplify66.0ms (0.5%)

prune7.0ms (0.1%)

localize102.0ms (0.7%)

series36.0ms (0.2%)

rewrite28.0ms (0.2%)

simplify107.0ms (0.7%)

prune541.0ms (3.7%)

localize148.0ms (1%)

series12.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify56.0ms (0.4%)

prune536.0ms (3.7%)

localize140.0ms (1%)

series33.0ms (0.2%)

rewrite37.0ms (0.3%)

simplify73.0ms (0.5%)

prune1.2s (8.1%)

localize92.0ms (0.6%)

series293.0ms (2%)

rewrite26.0ms (0.2%)

simplify138.0ms (0.9%)

prune852.0ms (5.8%)

regimes5.2s (35.6%)

simplify13.0ms (0.1%)

end464.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	31	104
1	58	104
2	80	104
3	100	104
4	117	104
5	133	104
6	146	104
7	167	104
8	203	104
9	233	104
10	254	104
11	271	104
12	286	104
13	290	104
14	286	104