Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.im \cdot y.re + x.re \cdot y.im\]
x.re \cdot y.im + x.im \cdot y.re
↓
x.im \cdot y.re + x.re \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1757635 = x_re;
        double r1757636 = y_im;
        double r1757637 = r1757635 * r1757636;
        double r1757638 = x_im;
        double r1757639 = y_re;
        double r1757640 = r1757638 * r1757639;
        double r1757641 = r1757637 + r1757640;
        return r1757641;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1757642 = x_im;
        double r1757643 = y_re;
        double r1757644 = r1757642 * r1757643;
        double r1757645 = x_re;
        double r1757646 = y_im;
        double r1757647 = r1757645 * r1757646;
        double r1757648 = r1757644 + r1757647;
        return r1757648;
}

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

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019104 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))