Average Error: 0.0 → 0
Time: 5.1s
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 r10980784 = x;
        double r10980785 = y;
        double r10980786 = r10980784 * r10980785;
        double r10980787 = r10980786 - r10980784;
        return r10980787;
}
↓
double f(double x, double y) {
        double r10980788 = x;
        double r10980789 = y;
        double r10980790 = -r10980788;
        double r10980791 = fma(r10980788, r10980789, r10980790);
        return r10980791;
}

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 2019168 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))