Average Error: 0.0 → 0.0
Time: 21.1s
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 r9612705 = x;
        double r9612706 = y;
        double r9612707 = r9612706 - r9612705;
        double r9612708 = z;
        double r9612709 = r9612707 * r9612708;
        double r9612710 = r9612705 + r9612709;
        return r9612710;
}
↓
double f(double x, double y, double z) {
        double r9612711 = z;
        double r9612712 = y;
        double r9612713 = x;
        double r9612714 = r9612712 - r9612713;
        double r9612715 = fma(r9612711, r9612714, r9612713);
        return r9612715;
}

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 2019200 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))