Average Error: 0.0 → 0.0
Time: 2.9s
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 r59413 = x_re;
        double r59414 = y_re;
        double r59415 = r59413 * r59414;
        double r59416 = x_im;
        double r59417 = y_im;
        double r59418 = r59416 * r59417;
        double r59419 = r59415 - r59418;
        return r59419;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r59420 = x_re;
        double r59421 = y_re;
        double r59422 = r59420 * r59421;
        double r59423 = x_im;
        double r59424 = y_im;
        double r59425 = r59423 * r59424;
        double r59426 = r59422 - r59425;
        return r59426;
}

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 2020027 +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)))