Average Error: 0.0 → 0.0
Time: 4.8s
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 r143746 = x;
        double r143747 = y;
        double r143748 = r143747 - r143746;
        double r143749 = z;
        double r143750 = r143748 * r143749;
        double r143751 = r143746 + r143750;
        return r143751;
}
↓
double f(double x, double y, double z) {
        double r143752 = z;
        double r143753 = y;
        double r143754 = x;
        double r143755 = r143753 - r143754;
        double r143756 = fma(r143752, r143755, r143754);
        return r143756;
}

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 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))