Average Error: 0.0 → 0
Time: 724.0ms
Precision: 64
\[x \cdot y - x\]
↓
\[\mathsf{fma}\left(x, y, -x\right)\]
x \cdot y - x
↓
\mathsf{fma}\left(x, y, -x\right)
double f(double x, double y) {
        double r185617 = x;
        double r185618 = y;
        double r185619 = r185617 * r185618;
        double r185620 = r185619 - r185617;
        return r185620;
}
↓
double f(double x, double y) {
        double r185621 = x;
        double r185622 = y;
        double r185623 = -r185621;
        double r185624 = fma(r185621, r185622, r185623);
        return r185624;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))