Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(z + x, y, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(z + x, y, x\right)
double f(double x, double y, double z) {
        double r98872 = x;
        double r98873 = y;
        double r98874 = z;
        double r98875 = r98874 + r98872;
        double r98876 = r98873 * r98875;
        double r98877 = r98872 + r98876;
        return r98877;
}
↓
double f(double x, double y, double z) {
        double r98878 = z;
        double r98879 = x;
        double r98880 = r98878 + r98879;
        double r98881 = y;
        double r98882 = fma(r98880, r98881, r98879);
        return r98882;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z + x\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z + x, y, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z + x, y, x\right)\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))