Average Error: 0.0 → 0.0
Time: 5.7s
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 r133398 = x;
        double r133399 = y;
        double r133400 = r133399 - r133398;
        double r133401 = z;
        double r133402 = r133400 * r133401;
        double r133403 = r133398 + r133402;
        return r133403;
}
↓
double f(double x, double y, double z) {
        double r133404 = z;
        double r133405 = y;
        double r133406 = x;
        double r133407 = r133405 - r133406;
        double r133408 = fma(r133404, r133407, r133406);
        return r133408;
}

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 2019306 +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)))