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 r128257 = x;
        double r128258 = y;
        double r128259 = r128258 - r128257;
        double r128260 = z;
        double r128261 = r128259 * r128260;
        double r128262 = r128257 + r128261;
        return r128262;
}
↓
double f(double x, double y, double z) {
        double r128263 = z;
        double r128264 = y;
        double r128265 = x;
        double r128266 = r128264 - r128265;
        double r128267 = fma(r128263, r128266, r128265);
        return r128267;
}

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 2019209 +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)))