Average Error: 0.0 → 0.0
Time: 8.4s
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 r152459 = x;
        double r152460 = y;
        double r152461 = r152460 - r152459;
        double r152462 = z;
        double r152463 = r152461 * r152462;
        double r152464 = r152459 + r152463;
        return r152464;
}
↓
double f(double x, double y, double z) {
        double r152465 = z;
        double r152466 = y;
        double r152467 = x;
        double r152468 = r152466 - r152467;
        double r152469 = fma(r152465, r152468, r152467);
        return r152469;
}

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 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))