Average Error: 0.0 → 0.0
Time: 4.5s
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 r116680 = x;
        double r116681 = y;
        double r116682 = r116681 - r116680;
        double r116683 = z;
        double r116684 = r116682 * r116683;
        double r116685 = r116680 + r116684;
        return r116685;
}
↓
double f(double x, double y, double z) {
        double r116686 = z;
        double r116687 = y;
        double r116688 = x;
        double r116689 = r116687 - r116688;
        double r116690 = fma(r116686, r116689, r116688);
        return r116690;
}

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 2019304 +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)))