Average Error: 0.0 → 0.0
Time: 606.0ms
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 r120561 = x;
        double r120562 = y;
        double r120563 = r120561 * r120562;
        double r120564 = r120563 + r120561;
        double r120565 = r120564 + r120562;
        return r120565;
}
↓
double f(double x, double y) {
        double r120566 = y;
        double r120567 = x;
        double r120568 = fma(r120567, r120566, r120567);
        double r120569 = r120566 + r120568;
        return r120569;
}

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 2020033 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))