Average Error: 0.0 → 0.0
Time: 1.4s
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 r151909 = x;
        double r151910 = y;
        double r151911 = r151909 * r151910;
        double r151912 = 1.0;
        double r151913 = r151912 - r151909;
        double r151914 = z;
        double r151915 = r151913 * r151914;
        double r151916 = r151911 + r151915;
        return r151916;
}
↓
double f(double x, double y, double z) {
        double r151917 = x;
        double r151918 = y;
        double r151919 = 1.0;
        double r151920 = r151919 - r151917;
        double r151921 = z;
        double r151922 = r151920 * r151921;
        double r151923 = fma(r151917, r151918, r151922);
        return r151923;
}

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 2019354 +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)))