Average Error: 0.0 → 0
Time: 4.5s
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 r7138078 = x;
        double r7138079 = y;
        double r7138080 = r7138078 * r7138079;
        double r7138081 = r7138080 - r7138078;
        return r7138081;
}
↓
double f(double x, double y) {
        double r7138082 = x;
        double r7138083 = y;
        double r7138084 = -r7138082;
        double r7138085 = fma(r7138082, r7138083, r7138084);
        return r7138085;
}

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 2019172 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))