Average Error: 0.0 → 0.0
Time: 3.0s
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 r1913169 = x_re;
        double r1913170 = y_re;
        double r1913171 = r1913169 * r1913170;
        double r1913172 = x_im;
        double r1913173 = y_im;
        double r1913174 = r1913172 * r1913173;
        double r1913175 = r1913171 - r1913174;
        return r1913175;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1913176 = x_re;
        double r1913177 = y_re;
        double r1913178 = r1913176 * r1913177;
        double r1913179 = x_im;
        double r1913180 = y_im;
        double r1913181 = r1913179 * r1913180;
        double r1913182 = r1913178 - r1913181;
        return r1913182;
}

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 2019163 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))