Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)
double f(double x, double y, double z) {
        double r183896 = x;
        double r183897 = y;
        double r183898 = r183896 * r183897;
        double r183899 = 1.0;
        double r183900 = r183899 - r183896;
        double r183901 = z;
        double r183902 = r183900 * r183901;
        double r183903 = r183898 + r183902;
        return r183903;
}
↓
double f(double x, double y, double z) {
        double r183904 = x;
        double r183905 = y;
        double r183906 = 1.0;
        double r183907 = r183906 - r183904;
        double r183908 = z;
        double r183909 = r183907 * r183908;
        double r183910 = fma(r183904, r183905, r183909);
        return r183910;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1 x) z)))