Average Error: 0.0 → 0.0
Time: 8.2s
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 r51472 = x_re;
        double r51473 = y_re;
        double r51474 = r51472 * r51473;
        double r51475 = x_im;
        double r51476 = y_im;
        double r51477 = r51475 * r51476;
        double r51478 = r51474 - r51477;
        return r51478;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r51479 = x_re;
        double r51480 = y_re;
        double r51481 = r51479 * r51480;
        double r51482 = x_im;
        double r51483 = y_im;
        double r51484 = r51482 * r51483;
        double r51485 = r51481 - r51484;
        return r51485;
}

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 2019298 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))