Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(y, x, \left(1 - x\right) \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(y, x, \left(1 - x\right) \cdot z\right)
double f(double x, double y, double z) {
        double r10613860 = x;
        double r10613861 = y;
        double r10613862 = r10613860 * r10613861;
        double r10613863 = 1.0;
        double r10613864 = r10613863 - r10613860;
        double r10613865 = z;
        double r10613866 = r10613864 * r10613865;
        double r10613867 = r10613862 + r10613866;
        return r10613867;
}
↓
double f(double x, double y, double z) {
        double r10613868 = y;
        double r10613869 = x;
        double r10613870 = 1.0;
        double r10613871 = r10613870 - r10613869;
        double r10613872 = z;
        double r10613873 = r10613871 * r10613872;
        double r10613874 = fma(r10613868, r10613869, r10613873);
        return r10613874;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))