Details

analyze2.2s (9.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
0%	0%	0%	100%	0%	0%	0%	2
25%	0%	0%	100%	0%	0%	0%	3
25%	0%	0%	100%	0%	0%	0%	4
25%	0%	0%	100%	0%	0%	0%	5
37.5%	0%	0%	100%	0%	0%	0%	6
56.3%	0%	0%	100%	0%	0%	0%	7
56.3%	0%	0%	100%	0%	0%	0%	8
56.3%	0%	0%	100%	0%	0%	0%	9
65.6%	0%	0%	100%	0%	0%	0%	10
76.6%	0%	0%	100%	0%	0%	0%	11
76.6%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 123 to 87 computations (29.3% saved)

sample13.3s (61.3%)

Results

13.3s

8256×

body

256

valid

Bogosity

preprocess121.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

1196×	`rational_best_45_simplify-84`
1010×	`rational_best_45_simplify-100`
900×	`rational_best_45_simplify-71`
844×	`rational_best_45_simplify-1`
806×	`rational_best_45_simplify-74`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	145	2037
1	348	2037
2	1009	1813
3	3402	1813
0	4	4

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2
3

Outputs
0
1
2
3

Call 2

Inputs
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u1) (-.f32 1 u1)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 u0 u0)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) alphax) (-.f32 1 alphax)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 u0 u0)))) alphay) (-.f32 1 alphay)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32)))))))) (.f32 u1 u1)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32)))))))) (*.f32 u1 u1)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphay alphay)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphax alphax)))) u0) (-.f32 1 u0)))))

Outputs
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2)))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2)))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u0) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u1) (-.f32 1 u1)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u1 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 (.f32 2 (PI.f32)) u0)))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 (.f32 2 (PI.f32)) u0))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 (.f32 2 (PI.f32)) u0)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 (.f32 2 (PI.f32)) u0))))))) (*.f32 alphay alphay))))) (-.f32 1 u1)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u1 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 2 (.f32 u0 (PI.f32)))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 2 (.f32 u0 (PI.f32))))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 2 (.f32 u0 (PI.f32)))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 2 (.f32 u0 (PI.f32))))))))) (*.f32 alphay alphay))))) (-.f32 1 u1)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u1 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u0))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u0)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u0))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u0)))))))) (*.f32 alphay alphay))))) (-.f32 1 u1)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 u0 u0)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay u0) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) alphax) (-.f32 1 alphax)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 alphax (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0))))) (.f32 u0 u0)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0))))) (*.f32 alphay alphay))))) (-.f32 1 alphax)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 alphax (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0))))) (.f32 u0 u0)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphay u0))))) (*.f32 alphay alphay))))) (-.f32 1 alphax)))))
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(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 u0 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 u0 u0)))) alphay) (-.f32 1 alphay)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 alphay (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax))))) (*.f32 u0 u0))))) (-.f32 1 alphay)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 alphay (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 u0 alphax))))) (*.f32 u0 u0))))) (-.f32 1 alphay)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 alphay (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 u0 alphax)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 u0 alphax))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 u0 alphax)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 u0 alphax))))) (*.f32 u0 u0))))) (-.f32 1 alphay)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32)))))))) (.f32 u1 u1)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphax) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u0 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphax (.f32 2 (PI.f32)))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphax (.f32 2 (PI.f32))))))))) (.f32 u1 u1)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphax (.f32 2 (PI.f32)))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphax (.f32 2 (PI.f32))))))))) (*.f32 alphay alphay))))) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u0 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphax 2))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphax 2)))))))) (.f32 u1 u1)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphax 2))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay u1) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphax 2)))))))) (*.f32 alphay alphay))))) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) alphay) (.f32 1/2 (PI.f32)))))))) (*.f32 u1 u1)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u0 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphay (.f32 2 (PI.f32)))))))) (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphay (.f32 2 (PI.f32))))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphay (.f32 2 (PI.f32)))))))) (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (+.f32 (.f32 (PI.f32) 1/2) (.f32 alphay (.f32 2 (PI.f32))))))))) (*.f32 u1 u1))))) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u0 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphay 2))))))) (cos.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphay 2)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphay 2))))))) (sin.f32 (atan.f32 (.f32 (/.f32 u1 alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 alphay 2)))))))) (*.f32 u1 u1))))) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphay alphay)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphax alphay) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphax alphax)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u0 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay))))) (.f32 alphay alphay)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay))))) (*.f32 alphax alphax))))) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u0 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay))))) (.f32 alphay alphay)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))) (/.f32 alphax alphay))))) (*.f32 alphax alphax))))) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 u0 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 alphax alphay)))) (cos.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 alphax alphay))))) (.f32 alphay alphay)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 alphax alphay)))) (sin.f32 (atan.f32 (.f32 (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))) (/.f32 alphax alphay))))) (*.f32 alphax alphax))))) (-.f32 1 u0)))))

Compiler

Compiled 96 to 68 computations (29.2% saved)

simplify198.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1460×	`rational_best_45_simplify-1`
1280×	`rational_best_45_simplify-84`
990×	`rational_best_45_simplify-98`
928×	`rational_best_45_simplify-25`
744×	`rational_best_45_simplify-96`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	291
1	83	291
2	228	259
3	773	259
4	3447	259
5	7613	259

Stop Event

1×	node limit

Counts

1 → 4

Calls

Call 1

Inputs

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (*.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32)))))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Outputs
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2)))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 (PI.f32) 1/2))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2)))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 2 (.f32 u1 (PI.f32))) (.f32 (PI.f32) 1/2))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

eval10.0ms (0%)

Compiler: Compiled 348 to 225 computations (35.3% saved)

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	1	5

Error

0.2b

Counts

5 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Status

Error

Program

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (*.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Compiler

Compiled 84 to 60 computations (28.6% saved)

localize918.0ms (4.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))
✓	0.5b	(.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))))
✓	12.0b	(tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))
✓	12.6b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))

Compiler

Compiled 741 to 467 computations (37% saved)

series17.0ms (0.1%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
3.0ms	u1	@	0	(.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))
2.0ms	u1	@	0	(tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))
1.0ms	alphax	@	inf	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))
1.0ms	alphay	@	0	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))
1.0ms	u1	@	inf	(.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))))

rewrite341.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

794×	`rational_best_45_simplify-100`
724×	`rational_best_45_simplify-71`
710×	`rational_best-4`
710×	`rational_best-2`
710×	`rational_best-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	186
1	118	186
2	376	186
3	1529	186
4	6604	186

Stop Event

1×	node limit

Counts

4 → 147

Calls

Call 1

Inputs
(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))
(tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))
(.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))))
(.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))) (.f32 (.f32 (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))) (.f32 (neg.f32 (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 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simplify342.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1312×	`rational_best_45_simplify-98`
1302×	`rational_best_45_simplify-25`
944×	`rational_best_45_simplify-100`
776×	`rational_best_45_simplify-37`
734×	`rational_best_45_simplify-91`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	346	12219
1	1185	12131
2	4751	12131

Stop Event

1×	node limit

Counts

243 → 193

Calls

Call 1

Inputs
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32))))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) u1))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (+.f32 (.f32 2 (/.f32 (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (pow.f32 u1 2) (.f32 (PI.f32) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))) (cos.f32 (.f32 1/2 (PI.f32))))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (*.f32 1/2 (PI.f32))) 2)))) u1)))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (+.f32 (.f32 (-.f32 (.f32 -4/3 (pow.f32 (PI.f32) 3)) (+.f32 (.f32 4/3 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (pow.f32 (PI.f32) 3)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (+.f32 (.f32 -4 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 (PI.f32) 2))) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (.f32 -2 (.f32 (pow.f32 (PI.f32) 2) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))))) (pow.f32 u1 3)) (+.f32 (.f32 2 (/.f32 (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (pow.f32 u1 2) (.f32 (PI.f32) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))) (cos.f32 (.f32 1/2 (PI.f32))))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) u1))))
(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))) (cos.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))))
(/.f32 (sin.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))) (cos.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))))
(/.f32 (sin.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))) (cos.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))))
(/.f32 (sin.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))) (cos.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax))) 2)
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(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32))) (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32)))))
(/.f32 (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (PI.f32) (PI.f32))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) (*.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32)))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (/.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32)))) (.f32 (/.f32 (PI.f32) (PI.f32)) (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32))))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (+.f32 1/2 (+.f32 u1 u1)))) (*.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (+.f32 1/2 (+.f32 u1 u1))))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))) (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (.f32 1 (.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1))))))
(neg.f32 (.f32 (/.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1))))))
(neg.f32 (.f32 -1 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (.f32 (neg.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32)))) (PI.f32)))

Outputs
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (-.f32 1/2 (*.f32 u1 -2))))) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (-.f32 1/2 (*.f32 u1 -2))))) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (-.f32 1/2 (*.f32 u1 -2))))) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (-.f32 1/2 (*.f32 u1 -2))))) alphax)))
(/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32))))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) u1))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (.f32 u1 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (+.f32 (.f32 2 (/.f32 (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (pow.f32 u1 2) (.f32 (PI.f32) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))) (cos.f32 (.f32 1/2 (PI.f32))))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (*.f32 1/2 (PI.f32))) 2)))) u1)))
(+.f32 (.f32 2 (/.f32 (.f32 (pow.f32 u1 2) (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (PI.f32) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))) (cos.f32 (.f32 1/2 (PI.f32))))) (+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (.f32 u1 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (*.f32 1/2 (PI.f32))) 2)))))))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (+.f32 (.f32 u1 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))) (.f32 2 (/.f32 (.f32 (PI.f32) (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 u1 2)))) (cos.f32 (*.f32 1/2 (PI.f32)))))))
(+.f32 (+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (.f32 u1 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))))) (.f32 2 (/.f32 (.f32 (PI.f32) (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 u1 2)))) (cos.f32 (*.f32 1/2 (PI.f32))))))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (+.f32 (.f32 (-.f32 (.f32 -4/3 (pow.f32 (PI.f32) 3)) (+.f32 (.f32 4/3 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (pow.f32 (PI.f32) 3)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (+.f32 (.f32 -4 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 (PI.f32) 2))) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (.f32 -2 (.f32 (pow.f32 (PI.f32) 2) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))))) (pow.f32 u1 3)) (+.f32 (.f32 2 (/.f32 (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (pow.f32 u1 2) (.f32 (PI.f32) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))) (cos.f32 (.f32 1/2 (PI.f32))))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) u1))))
(+.f32 (.f32 (-.f32 (.f32 -4/3 (pow.f32 (PI.f32) 3)) (+.f32 (.f32 -4 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 (PI.f32) 2))) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (+.f32 (.f32 4/3 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (pow.f32 (PI.f32) 3)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (.f32 -2 (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 (PI.f32) 2)))))) (pow.f32 u1 3)) (+.f32 (.f32 2 (/.f32 (.f32 (pow.f32 u1 2) (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (PI.f32) (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))) (cos.f32 (.f32 1/2 (PI.f32))))) (+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (.f32 u1 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))))))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (+.f32 (+.f32 (.f32 u1 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))))) (.f32 2 (/.f32 (.f32 (PI.f32) (.f32 (sin.f32 (.f32 1/2 (PI.f32))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 u1 2)))) (cos.f32 (.f32 1/2 (PI.f32)))))) (.f32 (-.f32 (.f32 -4/3 (pow.f32 (PI.f32) 3)) (+.f32 (.f32 -4 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 (PI.f32) 2))) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (+.f32 (.f32 4/3 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (pow.f32 (PI.f32) 3)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2))) (.f32 -2 (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (PI.f32) (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) (pow.f32 (PI.f32) 2)))))) (pow.f32 u1 3))))
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(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))) (cos.f32 (.f32 (+.f32 (.f32 2 u1) 1/2) (PI.f32))))
(/.f32 (sin.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))) (cos.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))))
(/.f32 (sin.f32 (.f32 (PI.f32) (-.f32 1/2 (.f32 u1 -2)))) (cos.f32 (.f32 (PI.f32) (-.f32 1/2 (.f32 u1 -2)))))
(/.f32 (sin.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))) (cos.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))))
(/.f32 (sin.f32 (.f32 (PI.f32) (-.f32 1/2 (.f32 u1 -2)))) (cos.f32 (.f32 (PI.f32) (-.f32 1/2 (.f32 u1 -2)))))
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(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (neg.f32 (PI.f32))))
(-.f32 0 (.f32 (neg.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32)))) (PI.f32)))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 u1 (+.f32 1/2 u1)))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (neg.f32 (PI.f32))))
(-.f32 (.f32 (PI.f32) 1/2) (.f32 (PI.f32) (*.f32 u1 -2)))
(-.f32 (.f32 1/2 (PI.f32)) (.f32 (PI.f32) (*.f32 u1 -2)))
(.f32 (PI.f32) (-.f32 1/2 (.f32 u1 -2)))
(-.f32 (.f32 (PI.f32) (+.f32 u1 u1)) (.f32 (PI.f32) -1/2))
(*.f32 (PI.f32) (-.f32 (+.f32 u1 u1) -1/2))
(-.f32 (.f32 0 (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))) (.f32 (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))) (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1))))))
(.f32 (/.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))) (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))) (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))
(.f32 (PI.f32) (.f32 (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))) (+.f32 1/2 (+.f32 u1 u1))))
(/.f32 (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) 1)
(*.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))
(*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))
(/.f32 (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (PI.f32) (PI.f32)))
(*.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))
(*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))
(/.f32 (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (+.f32 1/2 (+.f32 u1 u1))))
(*.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))
(*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))))
(*.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))
(*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32))) (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32)))))
(/.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))) (/.f32 (.f32 (+.f32 u1 (+.f32 1/2 u1)) (/.f32 (PI.f32) (PI.f32))) (*.f32 (+.f32 u1 (+.f32 1/2 u1)) (/.f32 (PI.f32) (PI.f32)))))
(/.f32 (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (PI.f32) (PI.f32))))
(*.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))
(*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) (*.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32)))))
(/.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))) (/.f32 (.f32 (PI.f32) (/.f32 (+.f32 u1 (+.f32 1/2 u1)) (PI.f32))) (*.f32 (PI.f32) (/.f32 (+.f32 u1 (+.f32 1/2 u1)) (PI.f32)))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (/.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32)))) (.f32 (/.f32 (PI.f32) (PI.f32)) (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32))))))
(/.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))) (/.f32 (.f32 (+.f32 u1 (+.f32 1/2 u1)) (.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (PI.f32) (PI.f32)))) (.f32 (+.f32 u1 (+.f32 1/2 u1)) (*.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (PI.f32) (PI.f32))))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (PI.f32) (PI.f32)))) (.f32 (+.f32 1/2 (+.f32 u1 u1)) (*.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (PI.f32) (PI.f32))))))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (+.f32 1/2 (+.f32 u1 u1)))) (*.f32 (PI.f32) (/.f32 (+.f32 1/2 (+.f32 u1 u1)) (+.f32 1/2 (+.f32 u1 u1))))))
(*.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))
(*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))
(/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (/.f32 (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))) (/.f32 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))) (*.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1))))))
(/.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))) (/.f32 (/.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))) (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1)))) (/.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))) (*.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 u1 (+.f32 1/2 u1)))))
(neg.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (neg.f32 (PI.f32))))
(neg.f32 (.f32 1 (.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1))))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 u1 (+.f32 1/2 u1)))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (neg.f32 (PI.f32))))
(neg.f32 (.f32 (/.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1))))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 u1 (+.f32 1/2 u1)))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (neg.f32 (PI.f32))))
(neg.f32 (.f32 -1 (.f32 (PI.f32) (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 u1 (+.f32 1/2 u1)))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (neg.f32 (PI.f32))))
(neg.f32 (.f32 (neg.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (/.f32 (PI.f32) (PI.f32)))) (PI.f32)))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 u1 (+.f32 1/2 u1)))))
(neg.f32 (*.f32 (PI.f32) (neg.f32 (+.f32 1/2 (+.f32 u1 u1)))))
(neg.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (neg.f32 (PI.f32))))

eval1.5s (7.1%)

Compiler: Compiled 59703 to 37454 computations (37.3% saved)

prune335.0ms (1.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	574	1	575
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	575	1	576

Error

0.2b

Counts

576 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Status

Error

Program

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Compiler

Compiled 71 to 53 computations (25.4% saved)

localize796.0ms (3.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2)
	12.0b	(tan.f32 (.f32 (PI.f32) (+.f32 1/2 (.f32 2 u1))))
✓	12.0b	(tan.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32)))
✓	12.6b	(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))

Compiler

Compiled 683 to 447 computations (34.6% saved)

series7.0ms (0%)

Counts

3 → 20

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	u1	@	0	(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
1.0ms	alphay	@	inf	(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
1.0ms	alphax	@	-inf	(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
1.0ms	alphay	@	-inf	(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
1.0ms	alphax	@	inf	(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))

rewrite160.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

838×	`rational_best_45_simplify-73`
670×	`rational_best_45_simplify-100`
642×	`rational_best-4`
642×	`rational_best-2`
642×	`rational_best-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	121
1	114	121
2	320	121
3	1351	121
4	6059	121

Stop Event

1×	node limit

Counts

3 → 83

Calls

Call 1

Inputs
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))
(tan.f32 (.f32 (-.f32 1/2 (.f32 -2 u1)) (PI.f32)))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2)

Inputs

(cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax)))

(tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32)))

(pow.f32 (cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (.f32 0 (/.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 0 (/.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))))) (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (.f32 -1 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (/.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (/.f32 1 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (.f32 (/.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax)))) (/.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 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Outputs

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simplify272.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1352×	`rational_best_45_simplify-84`
1050×	`rational_best_45_simplify-98`
1028×	`rational_best_45_simplify-25`
1022×	`rational_best_45_simplify-1`
626×	`rational_best_45_simplify-100`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	214	5173
1	718	5173
2	3351	5173
3	7904	5173

Stop Event

1×	node limit

Counts

103 → 105

Calls

Call 1

Inputs
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32))))
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(.f32 (neg.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32)))) -1)
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(/.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) 1)
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(/.f32 (neg.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32)))) -1)
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(+.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) 0)
(+.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (.f32 0 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(+.f32 0 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(+.f32 (.f32 0 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(-.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) 0)
(-.f32 0 (.f32 -1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) 1)
(.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (.f32 (.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (.f32 (.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(.f32 1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 1 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))))
(.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))))
(.f32 -1 (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(.f32 (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) -1)
(.f32 (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (neg.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(.f32 (.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(.f32 (.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(.f32 (neg.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) 1)
(/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(neg.f32 (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(neg.f32 (.f32 -1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))

Outputs
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 (*.f32 2 u1) 1/2) (PI.f32))) alphay) alphax)))
(/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32))))
(+.f32 (/.f32 (sin.f32 (.f32 1/2 (PI.f32))) (cos.f32 (.f32 1/2 (PI.f32)))) (.f32 (-.f32 (.f32 2 (PI.f32)) (.f32 -2 (/.f32 (.f32 (pow.f32 (sin.f32 (.f32 1/2 (PI.f32))) 2) (PI.f32)) (pow.f32 (cos.f32 (.f32 1/2 (PI.f32))) 2)))) u1))
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(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(.f32 (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (neg.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(.f32 (.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(.f32 (.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(.f32 (neg.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))) (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) 1)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (/.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)) (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2) (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2))))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(neg.f32 (neg.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)
(neg.f32 (.f32 -1 (pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 (tan.f32 (*.f32 (+.f32 1/2 (+.f32 u1 u1)) (PI.f32))) alphay) alphax))) 2)))
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 1/2 u1))))) alphax))) 2)
(pow.f32 (cos.f32 (atan.f32 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (+.f32 u1 (+.f32 u1 1/2))))) alphax))) 2)

eval561.0ms (2.6%)

Compiler: Compiled 18959 to 12704 computations (33% saved)

prune189.0ms (0.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	189	1	190

Error

0.2b

Counts

190 → 1

Alt Table

Click to see full alt table

Status

Error

Program

✓

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Compiler

Compiled 71 to 53 computations (25.4% saved)

regimes164.0ms (0.8%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

3 → 1

Calls

Call 1

Inputs

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (*.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (*.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32)))))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (*.f32 (*.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Outputs

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Calls

13 calls:

74.0ms	(.f32 (.f32 2 (PI.f32)) u1)
10.0ms	(+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphay alphay)))
9.0ms	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
8.0ms	(/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphay alphay))))
8.0ms	u1

Results

Error	Segments	Branch
0.2b	1	`u0`
0.2b	1	`u1`
0.2b	1	`alphax`
0.2b	1	`alphay`
0.2b	1	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))
0.2b	1	(sqrt.f32 (+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0))))
0.2b	1	(+.f32 1 (/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))
0.2b	1	(/.f32 (.f32 (/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0))
0.2b	1	(/.f32 1 (+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphay alphay))))
0.2b	1	(+.f32 (/.f32 (.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32))))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (.f32 1/2 (PI.f32)))))))) (.f32 alphay alphay)))
0.2b	1	`(tan.f32 (+.f32 (.f32 (.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32))))`
0.2b	1	`(+.f32 (.f32 (.f32 2 (PI.f32)) u1) (*.f32 1/2 (PI.f32)))`
0.2b	1	`(.f32 (.f32 2 (PI.f32)) u1)`

Compiler

Compiled 813 to 562 computations (30.9% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	215

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Outputs

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (*.f32 (/.f32 1 (+.f32 (/.f32 (pow.f32 (cos.f32 (atan.f32 (/.f32 (*.f32 (tan.f32 (*.f32 (-.f32 1/2 (*.f32 -2 u1)) (PI.f32))) alphay) alphax))) 2) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1))))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (+.f32 1/2 (*.f32 2 u1)))))))) (*.f32 alphay alphay)))) u0) (-.f32 1 u0)))))

Compiler

Compiled 71 to 53 computations (25.4% saved)

soundness190.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1460×	`rational_best_45_simplify-1`
1280×	`rational_best_45_simplify-84`
990×	`rational_best_45_simplify-98`
928×	`rational_best_45_simplify-25`
744×	`rational_best_45_simplify-96`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	291
1	83	291
2	228	259
3	773	259
4	3447	259
5	7613	259

Stop Event

1×	node limit

Compiler

Compiled 92 to 64 computations (30.4% saved)

end71.0ms (0.3%)

Compiler: Compiled 71 to 53 computations (25.4% saved)

Details

analyze2.2s (9.9%)

sample13.3s (61.3%)

preprocess121.0ms (0.6%)

simplify198.0ms (0.9%)

eval10.0ms (0%)

prune4.0ms (0%)

localize918.0ms (4.2%)

series17.0ms (0.1%)

rewrite341.0ms (1.6%)

simplify342.0ms (1.6%)

eval1.5s (7.1%)

prune335.0ms (1.5%)

localize796.0ms (3.7%)

series7.0ms (0%)

rewrite160.0ms (0.7%)

simplify272.0ms (1.3%)

eval561.0ms (2.6%)

prune189.0ms (0.9%)

regimes164.0ms (0.8%)

simplify7.0ms (0%)

soundness190.0ms (0.9%)

end71.0ms (0.3%)

Profiling