Average Error: 0.3 → 0.3
Time: 12.7s
Precision: 64
\[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)
↓
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 r3328645 = x_re;
        double r3328646 = y_re;
        double r3328647 = r3328645 * r3328646;
        double r3328648 = x_im;
        double r3328649 = y_im;
        double r3328650 = r3328648 * r3328649;
        double r3328651 = r3328647 - r3328650;
        return r3328651;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r3328652 = x_re;
        double r3328653 = y_re;
        double r3328654 = r3328652 * r3328653;
        double r3328655 = x_im;
        double r3328656 = y_im;
        double r3328657 = r3328655 * r3328656;
        double r3328658 = r3328654 - r3328657;
        return r3328658;
}

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 2019135 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))