Average Error: 0.0 → 0.0
Time: 7.2s
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 r194263 = x;
        double r194264 = y;
        double r194265 = r194264 - r194263;
        double r194266 = z;
        double r194267 = r194265 * r194266;
        double r194268 = r194263 + r194267;
        return r194268;
}
↓
double f(double x, double y, double z) {
        double r194269 = z;
        double r194270 = y;
        double r194271 = x;
        double r194272 = r194270 - r194271;
        double r194273 = fma(r194269, r194272, r194271);
        return r194273;
}

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 2019212 +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)))