Average Error: 0.0 → 0.0
Time: 749.0ms
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 r206137 = x;
        double r206138 = y;
        double r206139 = r206138 - r206137;
        double r206140 = z;
        double r206141 = r206139 * r206140;
        double r206142 = r206137 + r206141;
        return r206142;
}
↓
double f(double x, double y, double z) {
        double r206143 = z;
        double r206144 = y;
        double r206145 = x;
        double r206146 = r206144 - r206145;
        double r206147 = fma(r206143, r206146, r206145);
        return r206147;
}

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 2020062 +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)))