Average Error: 0.0 → 0.0
Time: 1.4s
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 r139564 = x;
        double r139565 = y;
        double r139566 = r139564 * r139565;
        double r139567 = r139566 + r139564;
        double r139568 = r139567 + r139565;
        return r139568;
}
↓
double f(double x, double y) {
        double r139569 = x;
        double r139570 = y;
        double r139571 = fma(r139569, r139570, r139569);
        double r139572 = r139571 + r139570;
        return r139572;
}

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 2019351 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))