Average Error: 25.6 → 25.6
Time: 12.7s
Precision: 64
\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
↓
\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}
↓
\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1202186 = x_im;
        double r1202187 = y_re;
        double r1202188 = r1202186 * r1202187;
        double r1202189 = x_re;
        double r1202190 = y_im;
        double r1202191 = r1202189 * r1202190;
        double r1202192 = r1202188 - r1202191;
        double r1202193 = r1202187 * r1202187;
        double r1202194 = r1202190 * r1202190;
        double r1202195 = r1202193 + r1202194;
        double r1202196 = r1202192 / r1202195;
        return r1202196;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1202197 = x_im;
        double r1202198 = y_re;
        double r1202199 = r1202197 * r1202198;
        double r1202200 = x_re;
        double r1202201 = y_im;
        double r1202202 = r1202200 * r1202201;
        double r1202203 = r1202199 - r1202202;
        double r1202204 = r1202198 * r1202198;
        double r1202205 = r1202201 * r1202201;
        double r1202206 = r1202204 + r1202205;
        double r1202207 = r1202203 / r1202206;
        return r1202207;
}

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 25.6

    \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt25.6

    \[\leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{\color{blue}{\sqrt{y.re \cdot y.re + y.im \cdot y.im} \cdot \sqrt{y.re \cdot y.re + y.im \cdot y.im}}}\]

  4. Applied associate-/r*25.6

    \[\leadsto \color{blue}{\frac{\frac{x.im \cdot y.re - x.re \cdot y.im}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}}}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}}}\]
  5. Using strategy rm

  6. Applied div-inv25.6

    \[\leadsto \frac{\color{blue}{\left(x.im \cdot y.re - x.re \cdot y.im\right) \cdot \frac{1}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}}}}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}}\]

  7. Applied associate-/l*25.7

    \[\leadsto \color{blue}{\frac{x.im \cdot y.re - x.re \cdot y.im}{\frac{\sqrt{y.re \cdot y.re + y.im \cdot y.im}}{\frac{1}{\sqrt{y.re \cdot y.re + y.im \cdot y.im}}}}}\]

  8. Simplified25.6

    \[\leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{\color{blue}{y.re \cdot y.re + y.im \cdot y.im}}\]

  9. Final simplification25.6

    \[\leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))