Average Error: 0.0 → 0.0
Time: 23.8s
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 r3300584 = x;
        double r3300585 = y;
        double r3300586 = r3300584 * r3300585;
        double r3300587 = r3300586 + r3300584;
        double r3300588 = r3300587 + r3300585;
        return r3300588;
}
↓
double f(double x, double y) {
        double r3300589 = y;
        double r3300590 = x;
        double r3300591 = fma(r3300589, r3300590, r3300590);
        double r3300592 = r3300589 + r3300591;
        return r3300592;
}

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 2019172 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  (+ (+ (* x y) x) y))