Average Error: 0.0 → 0.0
Time: 813.0ms
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 r244911 = x;
        double r244912 = y;
        double r244913 = r244912 - r244911;
        double r244914 = z;
        double r244915 = r244913 * r244914;
        double r244916 = r244911 + r244915;
        return r244916;
}
↓
double f(double x, double y, double z) {
        double r244917 = z;
        double r244918 = y;
        double r244919 = x;
        double r244920 = r244918 - r244919;
        double r244921 = fma(r244917, r244920, r244919);
        return r244921;
}

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 2020057 +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)))