Average Error: 28.9 → 16.6
Time: 11.0s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -1.2743190345131582 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 5.887500437435469 \cdot 10^{+139}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -1.2743190345131582 \cdot 10^{+154}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 5.887500437435469 \cdot 10^{+139}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

\mathbf{else}:\\
\;\;\;\;re\\

\end{array}
double f(double re, double im) {
        double r2946886 = re;
        double r2946887 = r2946886 * r2946886;
        double r2946888 = im;
        double r2946889 = r2946888 * r2946888;
        double r2946890 = r2946887 + r2946889;
        double r2946891 = sqrt(r2946890);
        return r2946891;
}
↓
double f(double re, double im) {
        double r2946892 = re;
        double r2946893 = -1.2743190345131582e+154;
        bool r2946894 = r2946892 <= r2946893;
        double r2946895 = -r2946892;
        double r2946896 = 5.887500437435469e+139;
        bool r2946897 = r2946892 <= r2946896;
        double r2946898 = im;
        double r2946899 = r2946898 * r2946898;
        double r2946900 = r2946892 * r2946892;
        double r2946901 = r2946899 + r2946900;
        double r2946902 = sqrt(r2946901);
        double r2946903 = r2946897 ? r2946902 : r2946892;
        double r2946904 = r2946894 ? r2946895 : r2946903;
        return r2946904;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if re < -1.2743190345131582e+154

    1. Initial program 59.3

      \[\sqrt{re \cdot re + im \cdot im}\]

    2. Taylor expanded around -inf 7.4

      \[\leadsto \color{blue}{-1 \cdot re}\]

    3. Simplified7.4

      \[\leadsto \color{blue}{-re}\]

    if -1.2743190345131582e+154 < re < 5.887500437435469e+139

    1. Initial program 19.4

      \[\sqrt{re \cdot re + im \cdot im}\]

    if 5.887500437435469e+139 < re

    1. Initial program 56.3

      \[\sqrt{re \cdot re + im \cdot im}\]

    2. Taylor expanded around inf 8.7

      \[\leadsto \color{blue}{re}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification16.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.2743190345131582 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 5.887500437435469 \cdot 10^{+139}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))