Average Error: 0.0 → 0
Time: 569.0ms
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 r235854 = x;
        double r235855 = y;
        double r235856 = r235854 * r235855;
        double r235857 = r235856 - r235854;
        return r235857;
}
↓
double f(double x, double y) {
        double r235858 = x;
        double r235859 = y;
        double r235860 = -r235858;
        double r235861 = fma(r235858, r235859, r235860);
        return r235861;
}

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 2020056 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))