Average Error: 0.0 → 0.0
Time: 1.2s
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 r84453 = x;
        double r84454 = y;
        double r84455 = r84453 * r84454;
        double r84456 = r84455 + r84453;
        double r84457 = r84456 + r84454;
        return r84457;
}
↓
double f(double x, double y) {
        double r84458 = x;
        double r84459 = y;
        double r84460 = fma(r84458, r84459, r84458);
        double r84461 = r84460 + r84459;
        return r84461;
}

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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))