Average Error: 0.0 → 0
Time: 3.9s
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 r9071911 = x;
        double r9071912 = y;
        double r9071913 = r9071911 * r9071912;
        double r9071914 = r9071913 - r9071911;
        return r9071914;
}
↓
double f(double x, double y) {
        double r9071915 = x;
        double r9071916 = y;
        double r9071917 = -r9071915;
        double r9071918 = fma(r9071915, r9071916, r9071917);
        return r9071918;
}

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 2019192 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))