Average Error: 0.0 → 0.0
Time: 6.9s
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 r110800 = x;
        double r110801 = y;
        double r110802 = z;
        double r110803 = r110802 + r110800;
        double r110804 = r110801 * r110803;
        double r110805 = r110800 + r110804;
        return r110805;
}
↓
double f(double x, double y, double z) {
        double r110806 = z;
        double r110807 = x;
        double r110808 = r110806 + r110807;
        double r110809 = y;
        double r110810 = fma(r110808, r110809, r110807);
        return r110810;
}

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 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))