Average Error: 0.0 → 0.0
Time: 5.8s
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 r71972 = x_re;
        double r71973 = y_re;
        double r71974 = r71972 * r71973;
        double r71975 = x_im;
        double r71976 = y_im;
        double r71977 = r71975 * r71976;
        double r71978 = r71974 - r71977;
        return r71978;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r71979 = x_re;
        double r71980 = y_re;
        double r71981 = r71979 * r71980;
        double r71982 = x_im;
        double r71983 = y_im;
        double r71984 = r71982 * r71983;
        double r71985 = r71981 - r71984;
        return r71985;
}

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 2020042 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))