Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
x.re \cdot y.im + x.im \cdot y.re
↓
x.re \cdot y.im + x.im \cdot y.re
double f(double x_re, double x_im, double y_re, double y_im) {
        double r8551 = x_re;
        double r8552 = y_im;
        double r8553 = r8551 * r8552;
        double r8554 = x_im;
        double r8555 = y_re;
        double r8556 = r8554 * r8555;
        double r8557 = r8553 + r8556;
        return r8557;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r8558 = x_re;
        double r8559 = y_im;
        double r8560 = r8558 * r8559;
        double r8561 = x_im;
        double r8562 = y_re;
        double r8563 = r8561 * r8562;
        double r8564 = r8560 + r8563;
        return r8564;
}

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

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

Reproduce

herbie shell --seed 2019315 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))