Details

analyze24.0ms (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)

sample6.3s (26.5%)

Results

6.1s

8256×

body

128

valid

Compiler

Compiled 307 to 220 computations (28.3% saved)

simplify119.0ms (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

prune16.0ms (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)

localize246.0ms (1%)

Local error

Found 4 expressions with local error:

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

series85.0ms (0.4%)

Counts

4 → 72

Calls

4 calls:

43.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
25.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
10.0ms	(*.f32 (-.f32 1 ux) maxCos)
7.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite70.0ms (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:

22.0ms	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
10.0ms	(*.f32 (-.f32 1 ux) maxCos)
7.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
7.0ms	(.f32 (.f32 uy 2) (PI.f32))

simplify239.0ms (1%)

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

prune1.9s (8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	255	11	266
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	257	11	268

Error

0.1b

Counts

268 → 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 (.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)))))
	0.4b	(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))))
	0.7b	(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 (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 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))))
	15.1b	(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 (.f32 (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 yi)) (sqrt.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 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 yi (-.f32 (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))))))))
	0.3b	(fma.f32 ux (.f32 (.f32 (sqrt.f32 (.f32 (-.f32 1 ux) maxCos)) (sqrt.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))))
	0.4b	(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))))
	4.8b	(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 (cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 yi yi) 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	(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 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 14611 to 8350 computations (42.9% saved)

localize219.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))
	0.3b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
	0.3b	(.f32 (.f32 uy 2) (PI.f32))

series18.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

12.0ms	(log1p.f32 (.f32 (.f32 uy 2) (PI.f32)))
6.0ms	(expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary32`
2×	`*-un-lft-identity_binary32`
2×	`add-sqr-sqrt_binary32`
2×	`add-cube-cbrt_binary32`
2×	`add-cbrt-cube_binary32`

Counts

2 → 22

Calls

2 calls:

1.0ms	(expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))
1.0ms	(log1p.f32 (.f32 (.f32 uy 2) (PI.f32)))

simplify133.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-neg_binary32`
627×	`cancel-sign-sub-inv_binary32`
364×	`associate-l_binary32`
350×	`unswap-sqr_binary32`
336×	`associate-r_binary32`

Counts

46 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	774
1	220	712
2	724	701
3	2779	687
4	4960	687
5	5253	687

prune1.3s (5.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	161	13	174

Error

0.1b

Counts

174 → 13

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 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)))))
	0.4b	(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))))
	0.7b	(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 (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 (sqrt.f32 (.f32 (-.f32 1 ux) maxCos)) (sqrt.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))))
	1.4b	(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 (expm1.f32 (fma.f32 8/3 (pow.f32 (.f32 uy (PI.f32)) 3) (.f32 2 (.f32 uy (-.f32 (PI.f32) (.f32 uy (pow.f32 (PI.f32) 2)))))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	1.6b	(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 (expm1.f32 (.f32 2 (.f32 uy (-.f32 (PI.f32) (.f32 uy (pow.f32 (PI.f32) 2))))))) 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 (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 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))))
	15.1b	(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 (.f32 (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 yi)) (sqrt.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 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 yi (-.f32 (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 4/3 (.f32 (pow.f32 uy 3) (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 (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))))
	4.8b	(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 (cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 yi yi) 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 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 9995 to 6016 computations (39.8% saved)

localize298.0ms (1.2%)

Local error

Found 4 expressions with local error:

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

prune1.9s (8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	224	12	236

Error

0.1b

Counts

236 → 12

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 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)))))
	0.4b	(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))))
	0.7b	(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 (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 (sqrt.f32 (.f32 (-.f32 1 ux) maxCos)) (sqrt.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))))
	1.4b	(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 (expm1.f32 (fma.f32 8/3 (pow.f32 (.f32 uy (PI.f32)) 3) (.f32 2 (.f32 uy (-.f32 (PI.f32) (.f32 uy (pow.f32 (PI.f32) 2)))))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	4.8b	(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 (cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 yi yi) yi))))))
	0.4b	(fma.f32 ux (.f32 (-.f32 maxCos (.f32 maxCos ux)) 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))))
	1.6b	(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 (expm1.f32 (.f32 2 (.f32 uy (-.f32 (PI.f32) (.f32 uy (pow.f32 (PI.f32) 2))))))) 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 (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))))))
	15.1b	(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 (.f32 (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 yi)) (sqrt.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 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 yi (-.f32 (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))))))))
✓	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 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 12616 to 6382 computations (49.4% saved)

localize187.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (-.f32 1 ux) maxCos) (-.f32 (*.f32 ux maxCos) maxCos))
	0.3b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) yi)
	0.3b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.5b	(.f32 (sqrt.f32 (.f32 (-.f32 1 ux) maxCos)) (sqrt.f32 (*.f32 (-.f32 1 ux) maxCos)))

series46.0ms (0.2%)

Counts

1 → 20

Calls

1 calls:

46.0ms

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

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`pow1_binary32`
28×	`sqrt-pow1_binary32`
20×	`pow-prod-down_binary32`
14×	`associate-*l/_binary32`
12×	`sqrt-div_binary32`

Counts

1 → 59

Calls

1 calls:

26.0ms

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

simplify97.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

883×	`distribute-rgt-in_binary32`
864×	`distribute-lft-in_binary32`
527×	`associate-l_binary32`
410×	`unswap-sqr_binary32`
345×	`associate-r_binary32`

Counts

79 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	905
1	141	803
2	445	753
3	1722	727
4	5083	727

prune2.2s (9.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	254	12	266

Error

0.1b

Counts

266 → 12

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 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)))))
	0.4b	(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))))
	0.7b	(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 (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 (sqrt.f32 (.f32 (-.f32 1 ux) maxCos)) (sqrt.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))))
	1.4b	(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 (expm1.f32 (fma.f32 8/3 (pow.f32 (.f32 uy (PI.f32)) 3) (.f32 2 (.f32 uy (-.f32 (PI.f32) (.f32 uy (pow.f32 (PI.f32) 2)))))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))
	4.8b	(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 (cbrt.f32 (.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) (.f32 (.f32 yi yi) yi))))))
	0.4b	(fma.f32 ux (.f32 (-.f32 maxCos (.f32 maxCos ux)) 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))))
	1.6b	(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 (expm1.f32 (.f32 2 (.f32 uy (-.f32 (PI.f32) (.f32 uy (pow.f32 (PI.f32) 2))))))) 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 (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))))))
	15.1b	(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 (.f32 (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 yi)) (sqrt.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 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 yi (-.f32 (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))))))))
✓	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 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) xi (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) yi))))

Compiler

Compiled 15413 to 9139 computations (40.7% saved)

regimes7.4s (31%)

Accuracy

Total 0.2b remaining (52.3%)

Threshold costs 0.2b (52.3%)

Counts

174 → 1

Compiler

Compiled 96062 to 65758 computations (31.5% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	29	70
1	44	70
2	51	70
3	55	70
4	57	70
5	56	70

end950.0ms (4%)

Compiler: Compiled 826 to 560 computations (32.2% saved)

Details

analyze24.0ms (0.1%)

sample6.3s (26.5%)

simplify119.0ms (0.5%)

prune16.0ms (0.1%)

localize246.0ms (1%)

series85.0ms (0.4%)

rewrite70.0ms (0.3%)

simplify239.0ms (1%)

prune1.9s (8%)

localize219.0ms (0.9%)

series18.0ms (0.1%)

rewrite3.0ms (0%)

simplify133.0ms (0.6%)

prune1.3s (5.5%)

localize298.0ms (1.2%)

prune1.9s (8%)

localize187.0ms (0.8%)

series46.0ms (0.2%)

rewrite37.0ms (0.2%)

simplify97.0ms (0.4%)

prune2.2s (9.3%)

regimes7.4s (31%)

simplify7.0ms (0%)

end950.0ms (4%)

Profiling