Average Error: 0.0 → 0
Time: 5.2s
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 r10738820 = x;
        double r10738821 = y;
        double r10738822 = r10738820 * r10738821;
        double r10738823 = r10738822 - r10738820;
        return r10738823;
}
↓
double f(double x, double y) {
        double r10738824 = x;
        double r10738825 = y;
        double r10738826 = -r10738824;
        double r10738827 = fma(r10738824, r10738825, r10738826);
        return r10738827;
}

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 2019169 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))