Average Error: 0.0 → 0.0
Time: 7.0s
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[\mathsf{fma}\left(x, y, x\right) + y\]
\left(x \cdot y + x\right) + y
↓
\mathsf{fma}\left(x, y, x\right) + y
double f(double x, double y) {
        double r127676 = x;
        double r127677 = y;
        double r127678 = r127676 * r127677;
        double r127679 = r127678 + r127676;
        double r127680 = r127679 + r127677;
        return r127680;
}
↓
double f(double x, double y) {
        double r127681 = x;
        double r127682 = y;
        double r127683 = fma(r127681, r127682, r127681);
        double r127684 = r127683 + r127682;
        return r127684;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))