Average Error: 0.0 → 0.0
Time: 894.0ms
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 r210982 = x;
        double r210983 = y;
        double r210984 = r210983 - r210982;
        double r210985 = z;
        double r210986 = r210984 * r210985;
        double r210987 = r210982 + r210986;
        return r210987;
}
↓
double f(double x, double y, double z) {
        double r210988 = z;
        double r210989 = y;
        double r210990 = x;
        double r210991 = r210989 - r210990;
        double r210992 = fma(r210988, r210991, r210990);
        return r210992;
}

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 2020083 +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)))