Average Error: 31.0 → 17.4
Time: 3.6s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -2.222006465724332039862348815623896484961 \cdot 10^{103}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 4.856770854610730383064334389991702440912 \cdot 10^{140}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -2.222006465724332039862348815623896484961 \cdot 10^{103}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 4.856770854610730383064334389991702440912 \cdot 10^{140}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r2658324 = re;
        double r2658325 = r2658324 * r2658324;
        double r2658326 = im;
        double r2658327 = r2658326 * r2658326;
        double r2658328 = r2658325 + r2658327;
        double r2658329 = sqrt(r2658328);
        return r2658329;
}
↓
double f(double re, double im) {
        double r2658330 = re;
        double r2658331 = -2.222006465724332e+103;
        bool r2658332 = r2658330 <= r2658331;
        double r2658333 = -r2658330;
        double r2658334 = 4.85677085461073e+140;
        bool r2658335 = r2658330 <= r2658334;
        double r2658336 = im;
        double r2658337 = r2658336 * r2658336;
        double r2658338 = r2658330 * r2658330;
        double r2658339 = r2658337 + r2658338;
        double r2658340 = sqrt(r2658339);
        double r2658341 = r2658335 ? r2658340 : r2658330;
        double r2658342 = r2658332 ? r2658333 : r2658341;
        return r2658342;
}

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 < -2.222006465724332e+103

    1. Initial program 52.0

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

    2. Taylor expanded around -inf 10.0

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

    3. Simplified10.0

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

    if -2.222006465724332e+103 < re < 4.85677085461073e+140

    1. Initial program 20.7

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

    if 4.85677085461073e+140 < re

    1. Initial program 59.6

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

    2. Taylor expanded around inf 8.9

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

  4. Final simplification17.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.222006465724332039862348815623896484961 \cdot 10^{103}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 4.856770854610730383064334389991702440912 \cdot 10^{140}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))