Average Error: 0.0 → 0.0
Time: 681.0ms
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 r148444 = x;
        double r148445 = y;
        double r148446 = r148445 - r148444;
        double r148447 = z;
        double r148448 = r148446 * r148447;
        double r148449 = r148444 + r148448;
        return r148449;
}
↓
double f(double x, double y, double z) {
        double r148450 = z;
        double r148451 = y;
        double r148452 = x;
        double r148453 = r148451 - r148452;
        double r148454 = fma(r148450, r148453, r148452);
        return r148454;
}

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 2020056 +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)))