Average Error: 0.3 → 0.3
Time: 6.9s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
double f(double x_re, double x_im, double y_re, double y_im) {
        double r991146 = x_re;
        double r991147 = y_re;
        double r991148 = r991146 * r991147;
        double r991149 = x_im;
        double r991150 = y_im;
        double r991151 = r991149 * r991150;
        double r991152 = r991148 - r991151;
        return r991152;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r991153 = x_re;
        double r991154 = y_re;
        double r991155 = r991153 * r991154;
        double r991156 = x_im;
        double r991157 = y_im;
        double r991158 = r991156 * r991157;
        double r991159 = r991155 - r991158;
        return r991159;
}


x.re \cdot y.re - x.im \cdot y.im
↓
x.re \cdot y.re - x.im \cdot y.im

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

  1. Initial program 0.3

    \[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]

  2. Final simplification0.3

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))