Average Error: 0.0 → 0
Time: 1.7s
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 r3255543 = x;
        double r3255544 = y;
        double r3255545 = r3255543 * r3255544;
        double r3255546 = r3255545 - r3255543;
        return r3255546;
}
↓
double f(double x, double y) {
        double r3255547 = x;
        double r3255548 = y;
        double r3255549 = -r3255547;
        double r3255550 = fma(r3255547, r3255548, r3255549);
        return r3255550;
}

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 2019156 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))