Average Error: 0.0 → 0.0
Time: 3.8m
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 r25011527 = x_re;
        double r25011528 = y_re;
        double r25011529 = r25011527 * r25011528;
        double r25011530 = x_im;
        double r25011531 = y_im;
        double r25011532 = r25011530 * r25011531;
        double r25011533 = r25011529 - r25011532;
        return r25011533;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r25011534 = x_re;
        double r25011535 = y_re;
        double r25011536 = r25011534 * r25011535;
        double r25011537 = x_im;
        double r25011538 = y_im;
        double r25011539 = r25011537 * r25011538;
        double r25011540 = r25011536 - r25011539;
        return r25011540;
}

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 2019121 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))