Average Error: 0.0 → 0.0
Time: 26.0s
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 r156416 = x;
        double r156417 = y;
        double r156418 = r156417 - r156416;
        double r156419 = z;
        double r156420 = r156418 * r156419;
        double r156421 = r156416 + r156420;
        return r156421;
}
↓
double f(double x, double y, double z) {
        double r156422 = z;
        double r156423 = y;
        double r156424 = x;
        double r156425 = r156423 - r156424;
        double r156426 = fma(r156422, r156425, r156424);
        return r156426;
}

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 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))