Average Error: 0.0 → 0.0
Time: 1.1s
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 r261866 = x;
        double r261867 = y;
        double r261868 = r261866 * r261867;
        double r261869 = 1.0;
        double r261870 = r261869 - r261866;
        double r261871 = z;
        double r261872 = r261870 * r261871;
        double r261873 = r261868 + r261872;
        return r261873;
}
↓
double f(double x, double y, double z) {
        double r261874 = x;
        double r261875 = y;
        double r261876 = 1.0;
        double r261877 = r261876 - r261874;
        double r261878 = z;
        double r261879 = r261877 * r261878;
        double r261880 = fma(r261874, r261875, r261879);
        return r261880;
}

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 2020062 +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)))