Average Error: 0.0 → 0
Time: 4.4s
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 r13240778 = x;
        double r13240779 = y;
        double r13240780 = r13240778 * r13240779;
        double r13240781 = r13240780 - r13240778;
        return r13240781;
}
↓
double f(double x, double y) {
        double r13240782 = x;
        double r13240783 = y;
        double r13240784 = -r13240782;
        double r13240785 = fma(r13240782, r13240783, r13240784);
        return r13240785;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))