Average Error: 0.0 → 0.0
Time: 10.0s
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 r141579 = x;
        double r141580 = y;
        double r141581 = r141580 - r141579;
        double r141582 = z;
        double r141583 = r141581 * r141582;
        double r141584 = r141579 + r141583;
        return r141584;
}
↓
double f(double x, double y, double z) {
        double r141585 = z;
        double r141586 = y;
        double r141587 = x;
        double r141588 = r141586 - r141587;
        double r141589 = fma(r141585, r141588, r141587);
        return r141589;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))