Average Error: 0.0 → 0.0
Time: 767.0ms
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 r172817 = x;
        double r172818 = y;
        double r172819 = r172818 - r172817;
        double r172820 = z;
        double r172821 = r172819 * r172820;
        double r172822 = r172817 + r172821;
        return r172822;
}
↓
double f(double x, double y, double z) {
        double r172823 = z;
        double r172824 = y;
        double r172825 = x;
        double r172826 = r172824 - r172825;
        double r172827 = fma(r172823, r172826, r172825);
        return r172827;
}

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 2020001 +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)))