Average Error: 0.0 → 0.0
Time: 1.9s
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 r2232132 = x_re;
        double r2232133 = y_im;
        double r2232134 = r2232132 * r2232133;
        double r2232135 = x_im;
        double r2232136 = y_re;
        double r2232137 = r2232135 * r2232136;
        double r2232138 = r2232134 + r2232137;
        return r2232138;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2232139 = x_im;
        double r2232140 = y_re;
        double r2232141 = r2232139 * r2232140;
        double r2232142 = x_re;
        double r2232143 = y_im;
        double r2232144 = r2232142 * r2232143;
        double r2232145 = r2232141 + r2232144;
        return r2232145;
}

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 2019120 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))