Average Error: 0.0 → 0.0
Time: 5.9s
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 r128771 = x;
        double r128772 = y;
        double r128773 = r128772 - r128771;
        double r128774 = z;
        double r128775 = r128773 * r128774;
        double r128776 = r128771 + r128775;
        return r128776;
}
↓
double f(double x, double y, double z) {
        double r128777 = z;
        double r128778 = y;
        double r128779 = x;
        double r128780 = r128778 - r128779;
        double r128781 = fma(r128777, r128780, r128779);
        return r128781;
}

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 2019323 +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)))