Average Error: 0.0 → 0.0
Time: 1.4s
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 r30748 = x_re;
        double r30749 = y_re;
        double r30750 = r30748 * r30749;
        double r30751 = x_im;
        double r30752 = y_im;
        double r30753 = r30751 * r30752;
        double r30754 = r30750 - r30753;
        return r30754;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r30755 = x_re;
        double r30756 = y_re;
        double r30757 = r30755 * r30756;
        double r30758 = x_im;
        double r30759 = y_im;
        double r30760 = r30758 * r30759;
        double r30761 = r30757 - r30760;
        return r30761;
}

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 2019323 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))