Average Error: 0.0 → 0.0
Time: 3.7s
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 r5515745 = x;
        double r5515746 = y;
        double r5515747 = r5515745 * r5515746;
        double r5515748 = r5515747 + r5515745;
        double r5515749 = r5515748 + r5515746;
        return r5515749;
}
↓
double f(double x, double y) {
        double r5515750 = y;
        double r5515751 = x;
        double r5515752 = fma(r5515751, r5515750, r5515751);
        double r5515753 = r5515750 + r5515752;
        return r5515753;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  (+ (+ (* x y) x) y))