Average Error: 0.0 → 0
Time: 3.5s
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 r174934 = x;
        double r174935 = y;
        double r174936 = r174934 * r174935;
        double r174937 = r174936 - r174934;
        return r174937;
}
↓
double f(double x, double y) {
        double r174938 = x;
        double r174939 = y;
        double r174940 = -r174938;
        double r174941 = fma(r174938, r174939, r174940);
        return r174941;
}

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 2019304 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))