Average Error: 0.0 → 0.0
Time: 2.4s
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 r111778 = x_re;
        double r111779 = y_re;
        double r111780 = r111778 * r111779;
        double r111781 = x_im;
        double r111782 = y_im;
        double r111783 = r111781 * r111782;
        double r111784 = r111780 - r111783;
        return r111784;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r111785 = x_re;
        double r111786 = y_re;
        double r111787 = r111785 * r111786;
        double r111788 = x_im;
        double r111789 = y_im;
        double r111790 = r111788 * r111789;
        double r111791 = r111787 - r111790;
        return r111791;
}

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 2020024 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))