Average Error: 0.0 → 0
Time: 584.0ms
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 r197953 = x;
        double r197954 = y;
        double r197955 = r197953 * r197954;
        double r197956 = r197955 - r197953;
        return r197956;
}
↓
double f(double x, double y) {
        double r197957 = x;
        double r197958 = y;
        double r197959 = -r197957;
        double r197960 = fma(r197957, r197958, r197959);
        return r197960;
}

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 2020001 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))