Average Error: 0.0 → 0.0
Time: 5.3s
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 r138931 = x;
        double r138932 = y;
        double r138933 = r138932 - r138931;
        double r138934 = z;
        double r138935 = r138933 * r138934;
        double r138936 = r138931 + r138935;
        return r138936;
}
↓
double f(double x, double y, double z) {
        double r138937 = z;
        double r138938 = y;
        double r138939 = x;
        double r138940 = r138938 - r138939;
        double r138941 = fma(r138937, r138940, r138939);
        return r138941;
}

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 2019303 +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)))