Average Error: 0.0 → 0.0
Time: 5.8s
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 r94797 = x;
        double r94798 = y;
        double r94799 = r94798 - r94797;
        double r94800 = z;
        double r94801 = r94799 * r94800;
        double r94802 = r94797 + r94801;
        return r94802;
}
↓
double f(double x, double y, double z) {
        double r94803 = z;
        double r94804 = y;
        double r94805 = x;
        double r94806 = r94804 - r94805;
        double r94807 = fma(r94803, r94806, r94805);
        return r94807;
}

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 2019326 +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)))