Details

analyze8.0ms (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)

sample4.1s (51.5%)

Results

4.1s

8256×

body

128

valid

Compiler

Compiled 236 to 170 computations (28% saved)

preprocess63.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

404×	`distribute-rgt-neg-in_binary32`
374×	`distribute-lft-neg-in_binary32`
320×	`distribute-rgt-in_binary32`
274×	`distribute-lft-in_binary32`
271×	`associate-r_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	191	1584
1	601	1552
2	2217	1120
3	4855	1120
0	6	6

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4
5

Outputs
0
1
2
3
4
5

Call 2

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

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

Compiler

Compiled 71 to 50 computations (29.6% saved)

simplify32.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

362×	`distribute-rgt-in_binary32`
340×	`fma-def_binary32`
335×	`distribute-lft-in_binary32`
255×	`distribute-neg-in_binary32`
228×	`distribute-rgt-neg-out_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	99
1	67	97
2	214	70
3	839	66
4	2903	66
5	4998	66

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs

(+.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))

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

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

0.4b

Counts

3 → 2

Alt Table

Status

Error

Program

0.4b

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

Compiler

Compiled 354 to 245 computations (30.8% saved)

localize95.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (-.f32 1 ux) (.f32 maxCos zi))
✓	0.2b	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))
✓	0.2b	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
✓	0.3b	(.f32 uy (.f32 2 (PI.f32)))

series16.0ms (0.2%)

Counts

4 → 68

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	yi	@	0	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
2.0ms	maxCos	@	inf	(.f32 (-.f32 1 ux) (.f32 maxCos zi))
2.0ms	uy	@	0	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
1.0ms	uy	@	0	(.f32 uy (.f32 2 (PI.f32)))
1.0ms	zi	@	inf	(.f32 (-.f32 1 ux) (.f32 maxCos zi))

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`prod-diff_binary32`
163×	`add-sqr-sqrt_binary32`
159×	`*-un-lft-identity_binary32`
159×	`pow1_binary32`
149×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	322	41
2	3899	41

Stop Event

1×	node limit

Counts

4 → 69

Calls

Call 1

Inputs
(.f32 uy (.f32 2 (PI.f32)))
(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
(sin.f32 (.f32 uy (.f32 2 (PI.f32))))
(.f32 (-.f32 1 ux) (.f32 maxCos zi))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (PI.f32) (.f32 uy 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (PI.f32) (.f32 uy 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (PI.f32) (.f32 uy 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 (exp.f32 2) (PI.f32)) uy))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (PI.f32) (.f32 uy 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 2 (PI.f32)) 3) (pow.f32 uy 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (PI.f32) (.f32 uy 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (PI.f32) (.f32 uy 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (*.f32 uy 2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 yi) (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 3) (pow.f32 yi 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 yi 3) (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2))) yi)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 2) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 maxCos zi) (.f32 (neg.f32 ux) (.f32 maxCos zi)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 maxCos zi) (.f32 (.f32 maxCos zi) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (pow.f32 ux 3)) (.f32 maxCos zi)) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (-.f32 1 (.f32 ux ux)) (.f32 maxCos zi)) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (.f32 maxCos zi) (-.f32 1 (pow.f32 ux 3))) (+.f32 1 (fma.f32 ux ux ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (.f32 maxCos zi) (-.f32 1 (.f32 ux ux))) (+.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 (exp.f32 zi) maxCos) (-.f32 1 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 (.f32 maxCos zi) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 maxCos zi) 3) (pow.f32 (-.f32 1 ux) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (-.f32 1 ux) (.f32 maxCos zi))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (-.f32 1 ux) (*.f32 maxCos zi))) 1))))))

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

954×	`fma-neg_binary32`
628×	`distribute-rgt-neg-in_binary32`
505×	`associate-l_binary32`
416×	`associate-r_binary32`
229×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	902
1	221	894
2	688	880
3	3136	878

Stop Event

1×	node limit

Counts

137 → 97

Calls

Call 1

Inputs
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (*.f32 (PI.f32) yi)))
(-.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3)))))
(-.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))))
(-.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))))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 2 (.f32 uy (PI.f32)))
(-.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.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))))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(*.f32 maxCos zi)
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 -1 (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 -1 (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)

Outputs
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(.f32 2 (.f32 uy (*.f32 (PI.f32) yi)))
(.f32 2 (.f32 (PI.f32) (*.f32 uy yi)))
(-.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3)))))
(-.f32 (.f32 2 (.f32 uy (.f32 (PI.f32) yi))) (.f32 (.f32 4/3 (pow.f32 uy 3)) (.f32 yi (pow.f32 (PI.f32) 3))))
(fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 (.f32 -4/3 (pow.f32 uy 3)) (*.f32 yi (pow.f32 (PI.f32) 3))))
(.f32 yi (fma.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3 (.f32 (PI.f32) (.f32 2 uy))))
(.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3))))
(-.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))))
(+.f32 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (.f32 -4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3)))))
(fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 yi (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 (.f32 -4/3 (pow.f32 uy 3)) (*.f32 yi (pow.f32 (PI.f32) 3)))))
(fma.f32 4/15 (.f32 yi (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 yi (fma.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3 (.f32 (PI.f32) (.f32 2 uy)))))
(fma.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (.f32 (pow.f32 (PI.f32) 3) (.f32 yi (.f32 (pow.f32 uy 3) -4/3))))
(-.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))))))
(-.f32 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (fma.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3))) (.f32 8/315 (.f32 (.f32 (pow.f32 uy 7) yi) (pow.f32 (PI.f32) 7)))))
(+.f32 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 yi (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 (.f32 -4/3 (pow.f32 uy 3)) (.f32 yi (pow.f32 (PI.f32) 3))))) (.f32 -8/315 (.f32 yi (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))))
(-.f32 (.f32 yi (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (PI.f32) (.f32 2 uy)))) (.f32 yi (fma.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))))
(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 uy 3) (*.f32 (pow.f32 (PI.f32) 3) -4/3)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))) yi)
(.f32 yi (sin.f32 (.f32 (*.f32 2 (PI.f32)) uy)))
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 yi (sin.f32 (.f32 (PI.f32) (*.f32 2 uy))))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 (.f32 2 (PI.f32)) uy)
(.f32 (PI.f32) (.f32 2 uy))
(-.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))
(-.f32 (.f32 (.f32 2 (PI.f32)) uy) (.f32 (.f32 4/3 (pow.f32 uy 3)) (pow.f32 (PI.f32) 3)))
(fma.f32 2 (.f32 uy (PI.f32)) (.f32 (*.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3))
(fma.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3 (.f32 (PI.f32) (*.f32 2 uy)))
(fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 uy 3) (*.f32 (pow.f32 (PI.f32) 3) -4/3)))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.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))))
(+.f32 (fma.f32 2 (.f32 uy (PI.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))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3)))
(fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (fma.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3 (.f32 (PI.f32) (.f32 2 uy))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3))))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))))
(-.f32 (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (fma.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (fma.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3 (.f32 (pow.f32 (PI.f32) 7) (*.f32 (pow.f32 uy 7) -8/315)))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (fma.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315) (.f32 (pow.f32 uy 3) (*.f32 (pow.f32 (PI.f32) 3) -4/3)))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 (.f32 2 (PI.f32)) uy))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 2 uy)))
(*.f32 maxCos zi)
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 -1 (.f32 maxCos (*.f32 ux zi)))
(neg.f32 (.f32 maxCos (.f32 zi ux)))
(.f32 (neg.f32 (.f32 maxCos ux)) zi)
(.f32 zi (neg.f32 (.f32 maxCos ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 -1 (.f32 maxCos (*.f32 ux zi)))
(neg.f32 (.f32 maxCos (.f32 zi ux)))
(.f32 (neg.f32 (.f32 maxCos ux)) zi)
(.f32 zi (neg.f32 (.f32 maxCos ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 maxCos (-.f32 zi (.f32 zi ux)))
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(.f32 maxCos (.f32 zi (-.f32 1 ux)))

prune383.0ms (4.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	12	114
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	13	116

Error

0.2b

Counts

116 → 13

Alt Table

Status	Error	Program
	0.4b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(+.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))
	7.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (sqrt.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 2)))))
	5.0b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) yi))))
	1.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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))))))))
	15.2b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)) 2))))
▶	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (log.f32 (pow.f32 (pow.f32 (exp.f32 2) (PI.f32)) uy))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 2)) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 3)) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2)))) 2)) yi))))
	0.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3))))))))

Compiler

Compiled 6904 to 4103 computations (40.6% saved)

localize113.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
	0.3b	(.f32 uy (.f32 2 (PI.f32)))
✓	0.3b	(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))
✓	1.0b	(pow.f32 (*.f32 2 (PI.f32)) 3)

series3.0ms (0%)

Counts

2 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	uy	@	0	(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))
1.0ms	uy	@	inf	(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))
1.0ms	uy	@	-inf	(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))

rewrite46.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

773×	`pow1_binary32`
718×	`log1p-expm1-u_binary32`
718×	`expm1-log1p-u_binary32`
87×	`add-sqr-sqrt_binary32`
83×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	197	19
2	2097	19

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(pow.f32 (*.f32 2 (PI.f32)) 3)
(.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 8 (pow.f32 (PI.f32) 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (.f32 (PI.f32) (.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (PI.f32) (.f32 2 (.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 2 (PI.f32)) (.f32 4 (pow.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 8 (pow.f32 (PI.f32) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 8 (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 8 (pow.f32 (PI.f32) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 4 (pow.f32 (PI.f32) 2)) (.f32 2 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 2 (PI.f32))) 2) (.f32 (cbrt.f32 (.f32 2 (PI.f32))) (.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 2 (PI.f32))) (.f32 (sqrt.f32 (.f32 2 (PI.f32))) (.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (PI.f32) 3) 8)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (.f32 2 (PI.f32)) 3/2) (pow.f32 (.f32 2 (PI.f32)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 2 (PI.f32))) 2) 3) (.f32 2 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (sqrt.f32 (.f32 2 (PI.f32))) 3) (pow.f32 (sqrt.f32 (.f32 2 (PI.f32))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 4 (pow.f32 (PI.f32) 2)) 2) (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 4 (pow.f32 (PI.f32) 2)) (PI.f32)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 4 (pow.f32 (PI.f32) 2)) 1) (.f32 2 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 4 (pow.f32 (PI.f32) 2)) (pow.f32 (cbrt.f32 (.f32 2 (PI.f32))) 2)) (cbrt.f32 (.f32 2 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (.f32 4 (pow.f32 (PI.f32) 2)) (sqrt.f32 (.f32 2 (PI.f32)))) (sqrt.f32 (.f32 2 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 2 (PI.f32)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 8) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 8 (pow.f32 (PI.f32) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 8 (pow.f32 (PI.f32) 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 8 (pow.f32 (PI.f32) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 8 (pow.f32 (PI.f32) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 3 (log.f32 (.f32 2 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 3 (log.f32 (.f32 2 (PI.f32)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 8 (pow.f32 (PI.f32) 3)) 3) (pow.f32 (pow.f32 uy 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (pow.f32 uy 3) 3) (pow.f32 (.f32 8 (pow.f32 (PI.f32) 3)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 3 (log.f32 (.f32 (.f32 2 (PI.f32)) uy))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 3 (log.f32 (.f32 (.f32 2 (PI.f32)) uy))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (.f32 2 (PI.f32)) uy)) 3))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 8 (pow.f32 (PI.f32) 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 2 (*.f32 (PI.f32) (*.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (PI.f32) (*.f32 2 (*.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 2 (PI.f32)) (*.f32 4 (pow.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 8 (pow.f32 (PI.f32) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 8 (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 8 (pow.f32 (PI.f32) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 4 (pow.f32 (PI.f32) 2)) (*.f32 2 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (*.f32 2 (PI.f32))) 2) (*.f32 (cbrt.f32 (*.f32 2 (PI.f32))) (*.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (*.f32 2 (PI.f32))) (*.f32 (sqrt.f32 (*.f32 2 (PI.f32))) (*.f32 4 (pow.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (PI.f32) 3) 8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 2 (PI.f32)) 3/2) (pow.f32 (*.f32 2 (PI.f32)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (*.f32 2 (PI.f32))) 2) 3) (*.f32 2 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (*.f32 2 (PI.f32))) 3) (pow.f32 (sqrt.f32 (*.f32 2 (PI.f32))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (*.f32 4 (pow.f32 (PI.f32) 2)) 2) (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (*.f32 4 (pow.f32 (PI.f32) 2)) (PI.f32)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (*.f32 4 (pow.f32 (PI.f32) 2)) 1) (*.f32 2 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (*.f32 4 (pow.f32 (PI.f32) 2)) (pow.f32 (cbrt.f32 (*.f32 2 (PI.f32))) 2)) (cbrt.f32 (*.f32 2 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (*.f32 4 (pow.f32 (PI.f32) 2)) (sqrt.f32 (*.f32 2 (PI.f32)))) (sqrt.f32 (*.f32 2 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 2 (PI.f32)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 8) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 8 (pow.f32 (PI.f32) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 8 (pow.f32 (PI.f32) 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 8 (pow.f32 (PI.f32) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 8 (pow.f32 (PI.f32) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 3 (log.f32 (*.f32 2 (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (log.f32 (*.f32 2 (PI.f32)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (*.f32 8 (pow.f32 (PI.f32) 3)) 3) (pow.f32 (pow.f32 uy 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (pow.f32 uy 3) 3) (pow.f32 (*.f32 8 (pow.f32 (PI.f32) 3)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (*.f32 (*.f32 2 (PI.f32)) uy) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 3 (log.f32 (*.f32 (*.f32 2 (PI.f32)) uy))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (log.f32 (*.f32 (*.f32 2 (PI.f32)) uy))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (*.f32 2 (PI.f32)) uy)) 3))))))

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

974×	`unswap-sqr_binary32`
508×	`*-commutative_binary32`
505×	`associate-l_binary32`
366×	`sqr-pow_binary32`
337×	`associate-r_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	168
1	26	168
2	80	168
3	346	168
4	1586	132
5	2371	132
6	3795	132
7	3900	132
8	4091	132
9	4269	132
10	4458	132
11	4712	132

Stop Event

1×	node limit

Counts

55 → 45

Calls

Call 1

Inputs
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))

Outputs
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))
(.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)))
(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 uy 3)))
(.f32 8 (pow.f32 (.f32 uy (PI.f32)) 3))

prune415.0ms (5.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	88	13	101

Error

0.2b

Counts

101 → 13

Alt Table

Status	Error	Program
	0.4b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(+.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))
	7.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (sqrt.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 2)))))
	0.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (cbrt.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3))) 1))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
▶	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) yi))))
	5.0b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) yi))))
	1.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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))))))))
	15.2b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)) 2))))
✓	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 2)) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 3)) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2)))) 2)) yi))))
	0.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3))))))))

Compiler

Compiled 6009 to 3782 computations (37.1% saved)

localize121.0ms (1.5%)

Local error

Found 4 expressions with local error:

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

series7.0ms (0.1%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	yi	@	0	(.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2))))) yi)
1.0ms	uy	@	0	(.f32 (PI.f32) (.f32 uy 2))
1.0ms	yi	@	inf	(.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2))))) yi)
1.0ms	uy	@	0	(.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2))))) yi)
0.0ms	yi	@	-inf	(.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2))))) yi)

rewrite46.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

844×	`expm1-log1p-u_binary32`
843×	`log1p-expm1-u_binary32`
98×	`add-sqr-sqrt_binary32`
97×	`pow1_binary32`
96×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	200	31
2	2303	31

Stop Event

1×	node limit

Counts

3 → 51

Calls

Call 1

Inputs
(.f32 (PI.f32) (.f32 uy 2))
(.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2))))) yi)
(sin.f32 (.f32 (PI.f32) (.f32 uy 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 2 (*.f32 (PI.f32) uy)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 2 (*.f32 (PI.f32) uy)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 2 (*.f32 (PI.f32) uy)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (*.f32 (PI.f32) uy)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 2 (*.f32 (PI.f32) uy)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 2 (*.f32 (PI.f32) uy)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 uy 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (*.f32 uy 2) 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 2 (*.f32 (PI.f32) uy))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 2 (*.f32 (PI.f32) uy))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 2 (*.f32 (PI.f32) uy))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) yi))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 3) (pow.f32 yi 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 yi 3) (pow.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) yi)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) (pow.f32 (cbrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) 2) (cbrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) (sqrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1) 3) 1) (+.f32 (*.f32 (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1) (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1)) (+.f32 1 (*.f32 (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1) (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1)) 1) (+.f32 (+.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (sin.f32 (*.f32 2 (*.f32 (PI.f32) uy)))) 1))))))

simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

942×	`fma-neg_binary32`
621×	`distribute-rgt-neg-in_binary32`
616×	`distribute-lft-neg-in_binary32`
487×	`associate-l_binary32`
406×	`associate-r_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	710
1	180	702
2	602	688
3	2957	686

Stop Event

1×	node limit

Counts

99 → 70

Calls

Call 1

Inputs
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (*.f32 (PI.f32) yi)))
(-.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3)))))
(-.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))))
(-.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))))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 2 (.f32 uy (PI.f32)))
(-.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.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))))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))

Outputs
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (PI.f32)))
(.f32 2 (.f32 uy (*.f32 (PI.f32) yi)))
(.f32 (.f32 uy (PI.f32)) (*.f32 2 yi))
(-.f32 (.f32 2 (.f32 uy (.f32 yi (PI.f32)))) (.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3)))))
(+.f32 (.f32 2 (.f32 uy (.f32 (PI.f32) yi))) (.f32 -4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3)))))
(fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 (.f32 (pow.f32 (PI.f32) 3) (*.f32 yi (pow.f32 uy 3))) -4/3))
(.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3))))
(-.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))))
(+.f32 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (.f32 -4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3)))))
(fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 yi (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 (.f32 (pow.f32 (PI.f32) 3) (*.f32 yi (pow.f32 uy 3))) -4/3)))
(fma.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (.f32 yi (pow.f32 uy 5))) (.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3)))))
(fma.f32 yi (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3)))))
(-.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))))))
(-.f32 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (.f32 4/15 (.f32 (pow.f32 uy 5) (.f32 yi (pow.f32 (PI.f32) 5))))) (fma.f32 4/3 (.f32 (pow.f32 uy 3) (.f32 yi (pow.f32 (PI.f32) 3))) (.f32 8/315 (.f32 (pow.f32 uy 7) (.f32 yi (pow.f32 (PI.f32) 7))))))
(+.f32 (fma.f32 2 (.f32 uy (.f32 (PI.f32) yi)) (fma.f32 4/15 (.f32 yi (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))) (.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 yi (pow.f32 uy 3))) -4/3))) (.f32 -8/315 (.f32 (pow.f32 uy 7) (.f32 yi (pow.f32 (PI.f32) 7)))))
(+.f32 (.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 (PI.f32) 5) (.f32 4/15 (pow.f32 uy 5))))) (.f32 yi (fma.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3 (.f32 (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 7) -8/315)))))
(fma.f32 yi (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 uy 7) (.f32 (pow.f32 (PI.f32) 7) -8/315))) (.f32 yi (fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) -4/3)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 (sin.f32 (.f32 2 (*.f32 (PI.f32) uy))) yi)
(.f32 yi (sin.f32 (.f32 2 (*.f32 uy (PI.f32)))))
(.f32 2 (.f32 uy (PI.f32)))
(-.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))
(+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 -4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))))
(fma.f32 2 (.f32 uy (PI.f32)) (.f32 (*.f32 -4/3 (pow.f32 uy 3)) (pow.f32 (PI.f32) 3)))
(fma.f32 2 (.f32 uy (PI.f32)) (.f32 (pow.f32 (PI.f32) 3) (*.f32 (pow.f32 uy 3) -4/3)))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.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))))
(+.f32 (fma.f32 2 (.f32 uy (PI.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))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (.f32 -4/3 (pow.f32 uy 3)) (pow.f32 (PI.f32) 3))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (.f32 (pow.f32 (PI.f32) 3) (.f32 (pow.f32 uy 3) -4/3))))
(-.f32 (+.f32 (.f32 2 (.f32 uy (PI.f32))) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (+.f32 (.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))))
(-.f32 (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (fma.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))))
(-.f32 (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)))) (fma.f32 (.f32 8/315 (pow.f32 uy 7)) (pow.f32 (PI.f32) 7) (.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) 4/3))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (fma.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) -4/3 (.f32 (pow.f32 (PI.f32) 7) (*.f32 (pow.f32 uy 7) -8/315)))))
(fma.f32 2 (.f32 uy (PI.f32)) (fma.f32 4/15 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5)) (fma.f32 (pow.f32 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3) (.f32 (pow.f32 uy 7) (*.f32 (pow.f32 (PI.f32) 7) -8/315)))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))
(sin.f32 (.f32 2 (.f32 (PI.f32) uy)))
(sin.f32 (.f32 2 (.f32 uy (PI.f32))))

prune359.0ms (4.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	87	13	100

Error

0.2b

Counts

100 → 13

Alt Table

Status	Error	Program
▶	0.4b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(+.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))
	7.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (sqrt.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 2)))))
	0.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (cbrt.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3))) 1))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
✓	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) yi))))
	5.0b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2)))) 1)) yi))))
	1.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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))))))))
	15.2b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)) 2))))
✓	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (expm1.f32 (log1p.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 2 (.f32 (PI.f32) uy))) 2)))) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 3)) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2)))) 2)) yi))))
	0.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3))))))))

Compiler

Compiled 5760 to 3480 computations (39.6% saved)

localize111.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
	0.2b	(sin.f32 (.f32 uy (.f32 2 (PI.f32))))
	0.2b	(.f32 (sin.f32 (.f32 uy (*.f32 2 (PI.f32)))) yi)
	0.3b	(.f32 uy (.f32 2 (PI.f32)))

series14.0ms (0.2%)

Counts

1 → 24

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	maxCos	@	0	(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
4.0ms	ux	@	0	(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
1.0ms	zi	@	inf	(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
1.0ms	zi	@	0	(.f32 (-.f32 zi (.f32 ux zi)) maxCos)
1.0ms	ux	@	inf	(.f32 (-.f32 zi (.f32 ux zi)) maxCos)

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`pow1_binary32`
786×	`log1p-expm1-u_binary32`
786×	`expm1-log1p-u_binary32`
82×	`add-sqr-sqrt_binary32`
81×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	152	10
2	2135	10

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(.f32 (-.f32 zi (.f32 ux zi)) maxCos)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 zi maxCos) (*.f32 (*.f32 zi (neg.f32 ux)) maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 maxCos zi) (*.f32 maxCos (*.f32 zi (neg.f32 ux))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 (pow.f32 zi 3) (pow.f32 (*.f32 zi ux) 3)) maxCos) (fma.f32 zi zi (*.f32 (*.f32 zi ux) (*.f32 (+.f32 ux 1) zi))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (-.f32 (*.f32 zi zi) (pow.f32 (*.f32 zi ux) 2)) maxCos) (*.f32 (+.f32 ux 1) zi))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 maxCos (-.f32 (pow.f32 zi 3) (pow.f32 (*.f32 zi ux) 3))) (fma.f32 zi zi (*.f32 (*.f32 zi ux) (*.f32 (+.f32 ux 1) zi))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 maxCos (-.f32 (*.f32 zi zi) (pow.f32 (*.f32 zi ux) 2))) (*.f32 (+.f32 ux 1) zi))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 maxCos) (-.f32 zi (*.f32 zi ux))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (-.f32 zi (*.f32 zi ux)) 3) (pow.f32 maxCos 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 maxCos 3) (pow.f32 (-.f32 zi (*.f32 zi ux)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (-.f32 zi (*.f32 zi ux)) maxCos)) 1))))))

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary32`
232×	`fma-neg_binary32`
96×	`associate-l_binary32`
94×	`cancel-sign-sub-inv_binary32`
79×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	232
1	56	232
2	152	232
3	321	232
4	576	232
5	1017	232
6	1596	232
7	1799	232

Stop Event

1×

saturated

Counts

45 → 29

Calls

Call 1

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

Outputs
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 (-.f32 1 ux) (.f32 maxCos zi))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 (-.f32 1 ux) (.f32 maxCos zi))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 (-.f32 1 ux) (.f32 maxCos zi))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 (-.f32 1 ux) (.f32 maxCos zi))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 -1 (.f32 (-.f32 ux 1) (*.f32 maxCos zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 -1 (.f32 (-.f32 ux 1) (*.f32 maxCos zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 -1 (.f32 (-.f32 ux 1) (*.f32 maxCos zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 -1 (.f32 (-.f32 ux 1) (*.f32 maxCos zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(*.f32 maxCos zi)
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 -1 (.f32 maxCos (*.f32 ux zi)))
(neg.f32 (.f32 maxCos (.f32 ux zi)))
(.f32 (.f32 maxCos (neg.f32 ux)) zi)
(.f32 maxCos (.f32 zi (neg.f32 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(.f32 -1 (.f32 maxCos (*.f32 ux zi)))
(neg.f32 (.f32 maxCos (.f32 ux zi)))
(.f32 (.f32 maxCos (neg.f32 ux)) zi)
(.f32 maxCos (.f32 zi (neg.f32 ux)))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))
(-.f32 (.f32 maxCos zi) (.f32 maxCos (*.f32 ux zi)))
(.f32 (-.f32 maxCos (.f32 maxCos ux)) zi)
(.f32 zi (-.f32 maxCos (.f32 maxCos ux)))
(*.f32 maxCos (fma.f32 zi (neg.f32 ux) zi))

prune399.0ms (5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	8	10
Picked	1	0	1
Done	0	2	2
Total	116	12	128

Error

0.2b

Counts

128 → 12

Alt Table

Status	Error	Program
	0.4b	(+.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))
	7.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (sqrt.f32 (pow.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi) 2)))))
	0.4b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (PI.f32) (.f32 uy 2))))) yi))))
	15.2b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))) yi)) 2))))
	0.5b	(fma.f32 ux (.f32 (-.f32 zi (.f32 ux zi)) maxCos) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 uy 2))) 3)) yi))))
✓	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2))))) yi))))
	0.8b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (cbrt.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) uy) 3))) 1))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	1.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 (.f32 2 (PI.f32)) 3)))) xi (.f32 (sin.f32 (.f32 uy (.f32 2 (PI.f32)))) yi))))
	0.4b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (expm1.f32 (log1p.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 2 (.f32 (PI.f32) uy))) 2)))) yi))))
	0.5b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) xi (.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 uy 2)))) (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (*.f32 uy 2)))) 2)) yi))))
	0.9b	(fma.f32 ux (.f32 (-.f32 1 ux) (.f32 maxCos zi)) (.f32 (sqrt.f32 (fma.f32 (-.f32 1 ux) (.f32 (.f32 ux (.f32 maxCos (.f32 ux maxCos))) (+.f32 ux -1)) 1)) (fma.f32 (cos.f32 (.f32 uy (.f32 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 uy 3) (.f32 (pow.f32 (PI.f32) 3) -4/3))))))))

Compiler

Compiled 6195 to 3289 computations (46.9% saved)

regimes972.0ms (12.2%)

Accuracy

Total 0.2b remaining (47.9%)

Threshold costs 0.2b (47.9%)

Counts

133 → 1

Compiler

Compiled 6501 to 3605 computations (44.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	66
1	48	66
2	51	66
3	53	66
4	54	66

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

Outputs

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

end369.0ms (4.6%)

Stop Event

1×

fuel

Compiler

Compiled 788 to 558 computations (29.2% saved)

Details

analyze8.0ms (0.1%)

sample4.1s (51.5%)

preprocess63.0ms (0.8%)

simplify32.0ms (0.4%)

prune7.0ms (0.1%)

localize95.0ms (1.2%)

series16.0ms (0.2%)

rewrite58.0ms (0.7%)

simplify43.0ms (0.5%)

prune383.0ms (4.8%)

localize113.0ms (1.4%)

series3.0ms (0%)

rewrite46.0ms (0.6%)

simplify71.0ms (0.9%)

prune415.0ms (5.2%)

localize121.0ms (1.5%)

series7.0ms (0.1%)

rewrite46.0ms (0.6%)

simplify37.0ms (0.5%)

prune359.0ms (4.5%)

localize111.0ms (1.4%)

series14.0ms (0.2%)

rewrite40.0ms (0.5%)

simplify25.0ms (0.3%)

prune399.0ms (5%)

regimes972.0ms (12.2%)

simplify3.0ms (0%)

end369.0ms (4.6%)

Profiling