Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
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 r1697782 = x_re;
        double r1697783 = y_re;
        double r1697784 = r1697782 * r1697783;
        double r1697785 = x_im;
        double r1697786 = y_im;
        double r1697787 = r1697785 * r1697786;
        double r1697788 = r1697784 - r1697787;
        return r1697788;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1697789 = x_re;
        double r1697790 = y_re;
        double r1697791 = r1697789 * r1697790;
        double r1697792 = x_im;
        double r1697793 = y_im;
        double r1697794 = r1697792 * r1697793;
        double r1697795 = r1697791 - r1697794;
        return r1697795;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))