Average Error: 0.0 → 0.0
Time: 1.7s
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 r188785 = x;
        double r188786 = y;
        double r188787 = r188786 - r188785;
        double r188788 = z;
        double r188789 = r188787 * r188788;
        double r188790 = r188785 + r188789;
        return r188790;
}
↓
double f(double x, double y, double z) {
        double r188791 = z;
        double r188792 = y;
        double r188793 = x;
        double r188794 = r188792 - r188793;
        double r188795 = fma(r188791, r188794, r188793);
        return r188795;
}

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 2020036 +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)))