Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary32
\[\left(\left(2.328306437 \cdot 10^{-10} \leq ux \land ux \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq uy \land uy \leq 1\right)\right) \land \left(0 \leq maxCos \land maxCos \leq 1\right)\]
\[\left(1 - ux\right) + ux \cdot maxCos \]
↓
\[1 - ux \cdot \left(2 - \left(1 + maxCos\right)\right) \]
(FPCore (ux uy maxCos) :precision binary32 (+ (- 1.0 ux) (* ux maxCos)))
↓
(FPCore (ux uy maxCos)
 :precision binary32
 (- 1.0 (* ux (- 2.0 (+ 1.0 maxCos)))))
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 - (ux * (2.0f - (1.0f + maxCos)));
}

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 - (ux * (2.0e0 - (1.0e0 + maxcos)))
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) - Float32(ux * Float32(Float32(2.0) - Float32(Float32(1.0) + maxCos))))
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) - (ux * (single(2.0) - (single(1.0) + maxCos)));
end

\left(1 - ux\right) + ux \cdot maxCos
↓
1 - ux \cdot \left(2 - \left(1 + maxCos\right)\right)

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-rr0.4

    \[\leadsto \color{blue}{\left({\left(1 - ux\right)}^{2} - {\left(ux \cdot maxCos\right)}^{2}\right) \cdot \frac{1}{1 - \left(ux + ux \cdot maxCos\right)}} \]

  3. Taylor expanded in ux around 0 0.0

    \[\leadsto \color{blue}{-1 \cdot \left(ux \cdot \left(2 + -1 \cdot \left(1 + maxCos\right)\right)\right) + 1} \]

  4. Final simplification0.0

    \[\leadsto 1 - ux \cdot \left(2 - \left(1 + maxCos\right)\right) \]

Reproduce

herbie shell --seed 2022192 
(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)))