Average Error: 0.0 → 0.0
Time: 5.6s
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 r162346 = x;
        double r162347 = y;
        double r162348 = r162347 - r162346;
        double r162349 = z;
        double r162350 = r162348 * r162349;
        double r162351 = r162346 + r162350;
        return r162351;
}
↓
double f(double x, double y, double z) {
        double r162352 = z;
        double r162353 = y;
        double r162354 = x;
        double r162355 = r162353 - r162354;
        double r162356 = fma(r162352, r162355, r162354);
        return r162356;
}

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 2019323 +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)))