Average Error: 0.0 → 0
Time: 2.4s
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 r8852724 = x;
        double r8852725 = y;
        double r8852726 = r8852724 * r8852725;
        double r8852727 = r8852726 - r8852724;
        return r8852727;
}
↓
double f(double x, double y) {
        double r8852728 = x;
        double r8852729 = y;
        double r8852730 = -r8852728;
        double r8852731 = fma(r8852728, r8852729, r8852730);
        return r8852731;
}

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 2019163 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))