Average Error: 0.0 → 0.0
Time: 809.0ms
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 r189743 = x;
        double r189744 = y;
        double r189745 = r189744 - r189743;
        double r189746 = z;
        double r189747 = r189745 * r189746;
        double r189748 = r189743 + r189747;
        return r189748;
}
↓
double f(double x, double y, double z) {
        double r189749 = z;
        double r189750 = y;
        double r189751 = x;
        double r189752 = r189750 - r189751;
        double r189753 = fma(r189749, r189752, r189751);
        return r189753;
}

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 2020064 +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)))