Average Error: 0.0 → 0
Time: 3.8s
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 r9753355 = x;
        double r9753356 = y;
        double r9753357 = r9753355 * r9753356;
        double r9753358 = r9753357 - r9753355;
        return r9753358;
}
↓
double f(double x, double y) {
        double r9753359 = x;
        double r9753360 = y;
        double r9753361 = -r9753359;
        double r9753362 = fma(r9753359, r9753360, r9753361);
        return r9753362;
}

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 2019179 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))