Average Error: 0.0 → 0.0
Time: 10.3s
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 r98185 = x;
        double r98186 = y;
        double r98187 = r98186 - r98185;
        double r98188 = z;
        double r98189 = r98187 * r98188;
        double r98190 = r98185 + r98189;
        return r98190;
}
↓
double f(double x, double y, double z) {
        double r98191 = z;
        double r98192 = y;
        double r98193 = x;
        double r98194 = r98192 - r98193;
        double r98195 = fma(r98191, r98194, r98193);
        return r98195;
}

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 2019194 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))