Average Error: 0.0 → 0
Time: 8.2s
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 r5423338 = x;
        double r5423339 = y;
        double r5423340 = r5423338 * r5423339;
        double r5423341 = r5423340 - r5423338;
        return r5423341;
}
↓
double f(double x, double y) {
        double r5423342 = x;
        double r5423343 = y;
        double r5423344 = -r5423342;
        double r5423345 = fma(r5423342, r5423343, r5423344);
        return r5423345;
}

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 2019200 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))