Average Error: 0.0 → 0
Time: 3.7s
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 r18935 = x;
        double r18936 = y;
        double r18937 = r18935 * r18936;
        double r18938 = r18937 - r18935;
        return r18938;
}
↓
double f(double x, double y) {
        double r18939 = x;
        double r18940 = y;
        double r18941 = -r18939;
        double r18942 = fma(r18939, r18940, r18941);
        return r18942;
}

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 2019310 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))