Average Error: 0.0 → 0.0
Time: 1.5s
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 r58944 = x_re;
        double r58945 = y_re;
        double r58946 = r58944 * r58945;
        double r58947 = x_im;
        double r58948 = y_im;
        double r58949 = r58947 * r58948;
        double r58950 = r58946 - r58949;
        return r58950;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r58951 = x_re;
        double r58952 = y_re;
        double r58953 = r58951 * r58952;
        double r58954 = x_im;
        double r58955 = y_im;
        double r58956 = r58954 * r58955;
        double r58957 = r58953 - r58956;
        return r58957;
}

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 2020002 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))