Average Error: 0.0 → 0.0
Time: 20.9s
Precision: binary32
\[\left(\left(2.328306437 \cdot 10^{-10} \leq ux \land ux \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq uy \land uy \leq 1\right)\right) \land \left(0 \leq maxCos \land maxCos \leq 1\right)\]
\[\left(1 - ux\right) + ux \cdot maxCos \]
↓
\[{e}^{\left(\mathsf{log1p}\left(ux \cdot \left(maxCos + -1\right)\right)\right)} \]
\left(1 - ux\right) + ux \cdot maxCos
↓
{e}^{\left(\mathsf{log1p}\left(ux \cdot \left(maxCos + -1\right)\right)\right)}

(FPCore (ux uy maxCos) :precision binary32 (+ (- 1.0 ux) (* ux maxCos)))
↓
(FPCore (ux uy maxCos)
 :precision binary32
 (pow E (log1p (* ux (+ maxCos -1.0)))))
float code(float ux, float uy, float maxCos) {
	return (1.0f - ux) + (ux * maxCos);
}
↓
float code(float ux, float uy, float maxCos) {
	return powf(((float) M_E), log1pf(ux * (maxCos + -1.0f)));
}

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. Simplified0.0

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

  3. Applied add-exp-log_binary320.0

    \[\leadsto \color{blue}{e^{\log \left(\mathsf{fma}\left(ux, maxCos, 1 - ux\right)\right)}} \]

  4. Simplified0.0

    \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(maxCos \cdot ux - ux\right)}} \]

  5. Applied *-un-lft-identity_binary320.0

    \[\leadsto e^{\color{blue}{1 \cdot \mathsf{log1p}\left(maxCos \cdot ux - ux\right)}} \]

  6. Applied exp-prod_binary320.0

    \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\mathsf{log1p}\left(maxCos \cdot ux - ux\right)\right)}} \]

  7. Simplified0.0

    \[\leadsto {\color{blue}{e}}^{\left(\mathsf{log1p}\left(maxCos \cdot ux - ux\right)\right)} \]

  8. Applied *-un-lft-identity_binary320.0

    \[\leadsto {e}^{\left(\mathsf{log1p}\left(maxCos \cdot ux - \color{blue}{1 \cdot ux}\right)\right)} \]

  9. Applied distribute-rgt-out--_binary320.0

    \[\leadsto {e}^{\left(\mathsf{log1p}\left(\color{blue}{ux \cdot \left(maxCos - 1\right)}\right)\right)} \]

  10. Simplified0.0

    \[\leadsto {e}^{\left(\mathsf{log1p}\left(ux \cdot \color{blue}{\left(maxCos + -1\right)}\right)\right)} \]

  11. Final simplification0.0

    \[\leadsto {e}^{\left(\mathsf{log1p}\left(ux \cdot \left(maxCos + -1\right)\right)\right)} \]

Reproduce

herbie shell --seed 2021313 
(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)))