Average Error: 0.0 → 0.0
Time: 910.0ms
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 r235538 = x;
        double r235539 = y;
        double r235540 = r235539 - r235538;
        double r235541 = z;
        double r235542 = r235540 * r235541;
        double r235543 = r235538 + r235542;
        return r235543;
}
↓
double f(double x, double y, double z) {
        double r235544 = z;
        double r235545 = y;
        double r235546 = x;
        double r235547 = r235545 - r235546;
        double r235548 = fma(r235544, r235547, r235546);
        return r235548;
}

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 2019362 +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)))