Average Error: 0.0 → 0.0
Time: 3.9s
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 r202781 = x;
        double r202782 = y;
        double r202783 = r202782 - r202781;
        double r202784 = z;
        double r202785 = r202783 * r202784;
        double r202786 = r202781 + r202785;
        return r202786;
}
↓
double f(double x, double y, double z) {
        double r202787 = z;
        double r202788 = y;
        double r202789 = x;
        double r202790 = r202788 - r202789;
        double r202791 = fma(r202787, r202790, r202789);
        return r202791;
}

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 2020039 +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)))