Average Error: 0.3 → 0.3
Time: 13.0s
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 r2652648 = x_re;
        double r2652649 = y_re;
        double r2652650 = r2652648 * r2652649;
        double r2652651 = x_im;
        double r2652652 = y_im;
        double r2652653 = r2652651 * r2652652;
        double r2652654 = r2652650 - r2652653;
        return r2652654;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2652655 = x_re;
        double r2652656 = y_re;
        double r2652657 = r2652655 * r2652656;
        double r2652658 = x_im;
        double r2652659 = y_im;
        double r2652660 = r2652658 * r2652659;
        double r2652661 = r2652657 - r2652660;
        return r2652661;
}

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 2019132 +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)))