Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(z, y - x, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(z, y - x, x\right)
double f(double x, double y, double z) {
        double r215875 = x;
        double r215876 = y;
        double r215877 = r215876 - r215875;
        double r215878 = z;
        double r215879 = r215877 * r215878;
        double r215880 = r215875 + r215879;
        return r215880;
}
↓
double f(double x, double y, double z) {
        double r215881 = z;
        double r215882 = y;
        double r215883 = x;
        double r215884 = r215882 - r215883;
        double r215885 = fma(r215881, r215884, r215883);
        return r215885;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))