Average Error: 0.0 → 0.0
Time: 5.0s
Precision: binary32
\[\left(\left(2.328306437 \cdot 10^{-10} \leq ux \land ux \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq uy \land uy \leq 1\right)\right) \land \left(0 \leq maxCos \land maxCos \leq 1\right)\]
\[\left(1 - ux\right) + ux \cdot maxCos \]
↓
\[1 - {\left(\sqrt{{\left(ux \cdot \left(1 - maxCos\right)\right)}^{6}}\right)}^{0.3333333333333333} \]
(FPCore (ux uy maxCos) :precision binary32 (+ (- 1.0 ux) (* ux maxCos)))
↓
(FPCore (ux uy maxCos)
 :precision binary32
 (- 1.0 (pow (sqrt (pow (* ux (- 1.0 maxCos)) 6.0)) 0.3333333333333333)))
float code(float ux, float uy, float maxCos) {
	return (1.0f - ux) + (ux * maxCos);
}
↓
float code(float ux, float uy, float maxCos) {
	return 1.0f - powf(sqrtf(powf((ux * (1.0f - maxCos)), 6.0f)), 0.3333333333333333f);
}

real(4) function code(ux, uy, maxcos)
    real(4), intent (in) :: ux
    real(4), intent (in) :: uy
    real(4), intent (in) :: maxcos
    code = (1.0e0 - ux) + (ux * maxcos)
end function
↓
real(4) function code(ux, uy, maxcos)
    real(4), intent (in) :: ux
    real(4), intent (in) :: uy
    real(4), intent (in) :: maxcos
    code = 1.0e0 - (sqrt(((ux * (1.0e0 - maxcos)) ** 6.0e0)) ** 0.3333333333333333e0)
end function

function code(ux, uy, maxCos)
	return Float32(Float32(Float32(1.0) - ux) + Float32(ux * maxCos))
end
↓
function code(ux, uy, maxCos)
	return Float32(Float32(1.0) - (sqrt((Float32(ux * Float32(Float32(1.0) - maxCos)) ^ Float32(6.0))) ^ Float32(0.3333333333333333)))
end

function tmp = code(ux, uy, maxCos)
	tmp = (single(1.0) - ux) + (ux * maxCos);
end
↓
function tmp = code(ux, uy, maxCos)
	tmp = single(1.0) - (sqrt(((ux * (single(1.0) - maxCos)) ^ single(6.0))) ^ single(0.3333333333333333));
end

\left(1 - ux\right) + ux \cdot maxCos
↓
1 - {\left(\sqrt{{\left(ux \cdot \left(1 - maxCos\right)\right)}^{6}}\right)}^{0.3333333333333333}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(1 - ux\right) + ux \cdot maxCos \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{1 - ux \cdot \left(1 - maxCos\right)} \]

  3. Applied egg-rr0.0

    \[\leadsto 1 - \color{blue}{{\left({\left(ux \cdot \left(1 - maxCos\right)\right)}^{3}\right)}^{0.3333333333333333}} \]

  4. Applied egg-rr0.0

    \[\leadsto 1 - {\color{blue}{\left(\sqrt{{\left(ux \cdot \left(1 - maxCos\right)\right)}^{6}}\right)}}^{0.3333333333333333} \]

  5. Final simplification0.0

    \[\leadsto 1 - {\left(\sqrt{{\left(ux \cdot \left(1 - maxCos\right)\right)}^{6}}\right)}^{0.3333333333333333} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (ux uy maxCos)
  :name "UniformSampleCone, z"
  :precision binary32
  :pre (and (and (and (<= 2.328306437e-10 ux) (<= ux 1.0)) (and (<= 2.328306437e-10 uy) (<= uy 1.0))) (and (<= 0.0 maxCos) (<= maxCos 1.0)))
  (+ (- 1.0 ux) (* ux maxCos)))