Average Error: 0.0 → 0.0
Time: 11.4s
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 r1436091 = x_re;
        double r1436092 = y_re;
        double r1436093 = r1436091 * r1436092;
        double r1436094 = x_im;
        double r1436095 = y_im;
        double r1436096 = r1436094 * r1436095;
        double r1436097 = r1436093 - r1436096;
        return r1436097;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1436098 = x_re;
        double r1436099 = y_re;
        double r1436100 = r1436098 * r1436099;
        double r1436101 = x_im;
        double r1436102 = y_im;
        double r1436103 = r1436101 * r1436102;
        double r1436104 = r1436100 - r1436103;
        return r1436104;
}

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 2019129 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))