Average Error: 0.0 → 0.0
Time: 1.7s
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 r1376230 = x_re;
        double r1376231 = y_re;
        double r1376232 = r1376230 * r1376231;
        double r1376233 = x_im;
        double r1376234 = y_im;
        double r1376235 = r1376233 * r1376234;
        double r1376236 = r1376232 - r1376235;
        return r1376236;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1376237 = x_re;
        double r1376238 = y_re;
        double r1376239 = r1376237 * r1376238;
        double r1376240 = x_im;
        double r1376241 = y_im;
        double r1376242 = r1376240 * r1376241;
        double r1376243 = r1376239 - r1376242;
        return r1376243;
}

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 2019135 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))