Average Error: 0.0 → 0.0
Time: 1.0s
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 r48115 = x_re;
        double r48116 = y_im;
        double r48117 = r48115 * r48116;
        double r48118 = x_im;
        double r48119 = y_re;
        double r48120 = r48118 * r48119;
        double r48121 = r48117 + r48120;
        return r48121;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r48122 = x_re;
        double r48123 = y_im;
        double r48124 = r48122 * r48123;
        double r48125 = x_im;
        double r48126 = y_re;
        double r48127 = r48125 * r48126;
        double r48128 = r48124 + r48127;
        return r48128;
}

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 2020001 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))