Average Error: 29.4 → 16.8
Time: 7.4s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -2.6806112513558803 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 3.221654116729901 \cdot 10^{+106}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -2.6806112513558803 \cdot 10^{+152}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 3.221654116729901 \cdot 10^{+106}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r2298980 = re;
        double r2298981 = r2298980 * r2298980;
        double r2298982 = im;
        double r2298983 = r2298982 * r2298982;
        double r2298984 = r2298981 + r2298983;
        double r2298985 = sqrt(r2298984);
        return r2298985;
}
↓
double f(double re, double im) {
        double r2298986 = re;
        double r2298987 = -2.6806112513558803e+152;
        bool r2298988 = r2298986 <= r2298987;
        double r2298989 = -r2298986;
        double r2298990 = 3.221654116729901e+106;
        bool r2298991 = r2298986 <= r2298990;
        double r2298992 = im;
        double r2298993 = r2298992 * r2298992;
        double r2298994 = r2298986 * r2298986;
        double r2298995 = r2298993 + r2298994;
        double r2298996 = sqrt(r2298995);
        double r2298997 = r2298991 ? r2298996 : r2298986;
        double r2298998 = r2298988 ? r2298989 : r2298997;
        return r2298998;
}

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 < -2.6806112513558803e+152

    1. Initial program 58.8

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

    2. Taylor expanded around -inf 8.7

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

    3. Simplified8.7

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

    if -2.6806112513558803e+152 < re < 3.221654116729901e+106

    1. Initial program 19.7

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

    if 3.221654116729901e+106 < re

    1. Initial program 48.9

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

    2. Taylor expanded around inf 10.6

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

  4. Final simplification16.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.6806112513558803 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 3.221654116729901 \cdot 10^{+106}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))