Average Error: 0.0 → 0.0
Time: 785.0ms
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 r179897 = x;
        double r179898 = y;
        double r179899 = r179898 - r179897;
        double r179900 = z;
        double r179901 = r179899 * r179900;
        double r179902 = r179897 + r179901;
        return r179902;
}
↓
double f(double x, double y, double z) {
        double r179903 = z;
        double r179904 = y;
        double r179905 = x;
        double r179906 = r179904 - r179905;
        double r179907 = fma(r179903, r179906, r179905);
        return r179907;
}

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 2020060 +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)))