Average Error: 0.0 → 0.0
Time: 5.3s
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 r102637 = x;
        double r102638 = y;
        double r102639 = r102638 - r102637;
        double r102640 = z;
        double r102641 = r102639 * r102640;
        double r102642 = r102637 + r102641;
        return r102642;
}
↓
double f(double x, double y, double z) {
        double r102643 = z;
        double r102644 = y;
        double r102645 = x;
        double r102646 = r102644 - r102645;
        double r102647 = fma(r102643, r102646, r102645);
        return r102647;
}

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)))