Average Error: 0.0 → 0
Time: 4.2s
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 r146519 = x;
        double r146520 = y;
        double r146521 = r146519 * r146520;
        double r146522 = r146521 - r146519;
        return r146522;
}
↓
double f(double x, double y) {
        double r146523 = x;
        double r146524 = y;
        double r146525 = -r146523;
        double r146526 = fma(r146523, r146524, r146525);
        return r146526;
}

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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  :precision binary64
  (- (* x y) x))