Average Error: 0.0 → 0.0
Time: 7.1s
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 r125053 = x;
        double r125054 = y;
        double r125055 = r125054 - r125053;
        double r125056 = z;
        double r125057 = r125055 * r125056;
        double r125058 = r125053 + r125057;
        return r125058;
}
↓
double f(double x, double y, double z) {
        double r125059 = z;
        double r125060 = y;
        double r125061 = x;
        double r125062 = r125060 - r125061;
        double r125063 = fma(r125059, r125062, r125061);
        return r125063;
}

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 2019198 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))