Average Error: 0.0 → 0
Time: 3.6s
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 r140718 = x;
        double r140719 = y;
        double r140720 = r140718 * r140719;
        double r140721 = r140720 - r140718;
        return r140721;
}
↓
double f(double x, double y) {
        double r140722 = x;
        double r140723 = y;
        double r140724 = -r140722;
        double r140725 = fma(r140722, r140723, r140724);
        return r140725;
}

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 2019235 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))