Average Error: 0.0 → 0.0
Time: 7.7s
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 r53133 = x_re;
        double r53134 = y_re;
        double r53135 = r53133 * r53134;
        double r53136 = x_im;
        double r53137 = y_im;
        double r53138 = r53136 * r53137;
        double r53139 = r53135 - r53138;
        return r53139;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r53140 = x_re;
        double r53141 = y_re;
        double r53142 = r53140 * r53141;
        double r53143 = x_im;
        double r53144 = y_im;
        double r53145 = r53143 * r53144;
        double r53146 = r53142 - r53145;
        return r53146;
}

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 2020046 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))