Average Error: 0.3 → 0.3
Time: 7.6s
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 r715597 = x_re;
        double r715598 = y_re;
        double r715599 = r715597 * r715598;
        double r715600 = x_im;
        double r715601 = y_im;
        double r715602 = r715600 * r715601;
        double r715603 = r715599 - r715602;
        return r715603;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r715604 = x_re;
        double r715605 = y_re;
        double r715606 = r715604 * r715605;
        double r715607 = x_im;
        double r715608 = y_im;
        double r715609 = r715607 * r715608;
        double r715610 = r715606 - r715609;
        return r715610;
}

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 2019119 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))