Average Error: 0.0 → 0
Time: 5.5s
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 r26727567 = x;
        double r26727568 = y;
        double r26727569 = r26727567 * r26727568;
        double r26727570 = r26727569 - r26727567;
        return r26727570;
}
↓
double f(double x, double y) {
        double r26727571 = x;
        double r26727572 = y;
        double r26727573 = -r26727571;
        double r26727574 = fma(r26727571, r26727572, r26727573);
        return r26727574;
}

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 2019173 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))