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 r113297 = x_re;
        double r113298 = y_re;
        double r113299 = r113297 * r113298;
        double r113300 = x_im;
        double r113301 = y_im;
        double r113302 = r113300 * r113301;
        double r113303 = r113299 - r113302;
        return r113303;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r113304 = x_re;
        double r113305 = y_re;
        double r113306 = r113304 * r113305;
        double r113307 = x_im;
        double r113308 = y_im;
        double r113309 = r113307 * r113308;
        double r113310 = r113306 - r113309;
        return r113310;
}

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 2019323 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))