Average Error: 0.0 → 0.0
Time: 1.3s
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 r50500 = x_re;
        double r50501 = y_re;
        double r50502 = r50500 * r50501;
        double r50503 = x_im;
        double r50504 = y_im;
        double r50505 = r50503 * r50504;
        double r50506 = r50502 - r50505;
        return r50506;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r50507 = x_re;
        double r50508 = y_re;
        double r50509 = r50507 * r50508;
        double r50510 = x_im;
        double r50511 = y_im;
        double r50512 = r50510 * r50511;
        double r50513 = r50509 - r50512;
        return r50513;
}

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 2020062 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))