Average Error: 0.0 → 0.0
Time: 6.6s
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 r131408 = x;
        double r131409 = y;
        double r131410 = r131408 * r131409;
        double r131411 = r131410 + r131408;
        double r131412 = r131411 + r131409;
        return r131412;
}
↓
double f(double x, double y) {
        double r131413 = x;
        double r131414 = y;
        double r131415 = fma(r131413, r131414, r131413);
        double r131416 = r131415 + r131414;
        return r131416;
}

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 2020045 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))