Average Error: 0.0 → 0
Time: 5.0s
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 r11960037 = x;
        double r11960038 = y;
        double r11960039 = r11960037 * r11960038;
        double r11960040 = r11960039 - r11960037;
        return r11960040;
}
↓
double f(double x, double y) {
        double r11960041 = x;
        double r11960042 = y;
        double r11960043 = -r11960041;
        double r11960044 = fma(r11960041, r11960042, r11960043);
        return r11960044;
}

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 2019170 +o rules:numerics
(FPCore (x y)
  :name "Data.Histogram.Bin.LogBinD:$cbinSizeN from histogram-fill-0.8.4.1"
  (- (* x y) x))