Average Error: 0.0 → 0.0
Time: 1.4s
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 r52483 = x_re;
        double r52484 = y_re;
        double r52485 = r52483 * r52484;
        double r52486 = x_im;
        double r52487 = y_im;
        double r52488 = r52486 * r52487;
        double r52489 = r52485 - r52488;
        return r52489;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r52490 = x_re;
        double r52491 = y_re;
        double r52492 = r52490 * r52491;
        double r52493 = x_im;
        double r52494 = y_im;
        double r52495 = r52493 * r52494;
        double r52496 = r52492 - r52495;
        return r52496;
}

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 2020049 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))