Average Error: 0.0 → 0
Time: 3.0s
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 r120238 = x;
        double r120239 = y;
        double r120240 = r120238 * r120239;
        double r120241 = r120240 - r120238;
        return r120241;
}
↓
double f(double x, double y) {
        double r120242 = x;
        double r120243 = y;
        double r120244 = -r120242;
        double r120245 = fma(r120242, r120243, r120244);
        return r120245;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))