Average Error: 0.0 → 0
Time: 3.2s
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 r220704 = x;
        double r220705 = y;
        double r220706 = r220704 * r220705;
        double r220707 = r220706 - r220704;
        return r220707;
}
↓
double f(double x, double y) {
        double r220708 = x;
        double r220709 = y;
        double r220710 = -r220708;
        double r220711 = fma(r220708, r220709, r220710);
        return r220711;
}

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))