Average Error: 0.0 → 0.0
Time: 533.0ms
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 r124833 = x;
        double r124834 = y;
        double r124835 = r124833 * r124834;
        double r124836 = r124835 + r124833;
        double r124837 = r124836 + r124834;
        return r124837;
}
↓
double f(double x, double y) {
        double r124838 = y;
        double r124839 = x;
        double r124840 = fma(r124839, r124838, r124839);
        double r124841 = r124838 + r124840;
        return r124841;
}

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 2020021 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))