Average Error: 0.0 → 0
Time: 3.3s
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 r9725980 = x;
        double r9725981 = y;
        double r9725982 = r9725980 * r9725981;
        double r9725983 = r9725982 - r9725980;
        return r9725983;
}
↓
double f(double x, double y) {
        double r9725984 = x;
        double r9725985 = y;
        double r9725986 = -r9725984;
        double r9725987 = fma(r9725984, r9725985, r9725986);
        return r9725987;
}

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 2019171 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))