Average Error: 0.0 → 0
Time: 5.1s
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 r8340104 = x;
        double r8340105 = y;
        double r8340106 = r8340104 * r8340105;
        double r8340107 = r8340106 - r8340104;
        return r8340107;
}
↓
double f(double x, double y) {
        double r8340108 = x;
        double r8340109 = y;
        double r8340110 = -r8340108;
        double r8340111 = fma(r8340108, r8340109, r8340110);
        return r8340111;
}

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 2019163 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))