Average Error: 0.0 → 0.0
Time: 771.0ms
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 r184267 = x;
        double r184268 = y;
        double r184269 = r184268 - r184267;
        double r184270 = z;
        double r184271 = r184269 * r184270;
        double r184272 = r184267 + r184271;
        return r184272;
}
↓
double f(double x, double y, double z) {
        double r184273 = z;
        double r184274 = y;
        double r184275 = x;
        double r184276 = r184274 - r184275;
        double r184277 = fma(r184273, r184276, r184275);
        return r184277;
}

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 2020024 +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)))