Average Error: 0.0 → 0.0
Time: 7.3s
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 r121428 = x;
        double r121429 = y;
        double r121430 = r121429 - r121428;
        double r121431 = z;
        double r121432 = r121430 * r121431;
        double r121433 = r121428 + r121432;
        return r121433;
}
↓
double f(double x, double y, double z) {
        double r121434 = z;
        double r121435 = y;
        double r121436 = x;
        double r121437 = r121435 - r121436;
        double r121438 = fma(r121434, r121437, r121436);
        return r121438;
}

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 2019305 +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)))