Average Error: 0.0 → 0.0
Time: 2.7s
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 r199334 = x;
        double r199335 = y;
        double r199336 = r199335 - r199334;
        double r199337 = z;
        double r199338 = r199336 * r199337;
        double r199339 = r199334 + r199338;
        return r199339;
}
↓
double f(double x, double y, double z) {
        double r199340 = z;
        double r199341 = y;
        double r199342 = x;
        double r199343 = r199341 - r199342;
        double r199344 = fma(r199340, r199343, r199342);
        return r199344;
}

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 2020020 +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)))