Average Error: 0.0 → 0.0
Time: 44.9s
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[y + \mathsf{fma}\left(y, x, x\right)\]
\left(x \cdot y + x\right) + y
↓
y + \mathsf{fma}\left(y, x, x\right)
double f(double x, double y) {
        double r3145283 = x;
        double r3145284 = y;
        double r3145285 = r3145283 * r3145284;
        double r3145286 = r3145285 + r3145283;
        double r3145287 = r3145286 + r3145284;
        return r3145287;
}
↓
double f(double x, double y) {
        double r3145288 = y;
        double r3145289 = x;
        double r3145290 = fma(r3145288, r3145289, r3145289);
        double r3145291 = r3145288 + r3145290;
        return r3145291;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  (+ (+ (* x y) x) y))