Average Error: 0.0 → 0.0
Time: 4.9s
Precision: binary32
\[2.328306437 \cdot 10^{-10} \leq ux \land ux \leq 1 \land 2.328306437 \cdot 10^{-10} \leq uy \land uy \leq 1 \land 0 \leq maxCos \land maxCos \leq 1\]
\[\left(1 - ux\right) + ux \cdot maxCos \]
↓
\[1 + ux \cdot \left(-1 + maxCos\right) \]
\left(1 - ux\right) + ux \cdot maxCos
↓
1 + ux \cdot \left(-1 + maxCos\right)

(FPCore (ux uy maxCos) :precision binary32 (+ (- 1.0 ux) (* ux maxCos)))
↓
(FPCore (ux uy maxCos) :precision binary32 (+ 1.0 (* ux (+ -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 * (-1.0f + maxCos));
}

Error

Bits error versus ux

Bits error versus uy

Bits error versus maxCos

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. Using strategy rm

  3. Applied associate-+l-_binary320.0

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

  4. Simplified0.0

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

  5. Taylor expanded around -inf 0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021204 
(FPCore (ux uy maxCos)
  :name "UniformSampleCone, z"
  :precision binary32
  :pre (and (<= 2.328306437e-10 ux 1.0) (<= 2.328306437e-10 uy 1.0) (<= 0.0 maxCos 1.0))
  (+ (- 1.0 ux) (* ux maxCos)))