Average Error: 0.0 → 0.0
Time: 538.0ms
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[y + \mathsf{fma}\left(x, y, x\right)\]
\left(x \cdot y + x\right) + y
↓
y + \mathsf{fma}\left(x, y, x\right)
double f(double x, double y) {
        double r119767 = x;
        double r119768 = y;
        double r119769 = r119767 * r119768;
        double r119770 = r119769 + r119767;
        double r119771 = r119770 + r119768;
        return r119771;
}
↓
double f(double x, double y) {
        double r119772 = y;
        double r119773 = x;
        double r119774 = fma(r119773, r119772, r119773);
        double r119775 = r119772 + r119774;
        return r119775;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))