Average Error: 29.4 → 16.5
Time: 12.1s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -8.181359696053478 \cdot 10^{+96}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 7.263939058947569 \cdot 10^{+108}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -8.181359696053478 \cdot 10^{+96}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 7.263939058947569 \cdot 10^{+108}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r2822088 = re;
        double r2822089 = r2822088 * r2822088;
        double r2822090 = im;
        double r2822091 = r2822090 * r2822090;
        double r2822092 = r2822089 + r2822091;
        double r2822093 = sqrt(r2822092);
        return r2822093;
}
↓
double f(double re, double im) {
        double r2822094 = re;
        double r2822095 = -8.181359696053478e+96;
        bool r2822096 = r2822094 <= r2822095;
        double r2822097 = -r2822094;
        double r2822098 = 7.263939058947569e+108;
        bool r2822099 = r2822094 <= r2822098;
        double r2822100 = im;
        double r2822101 = r2822100 * r2822100;
        double r2822102 = r2822094 * r2822094;
        double r2822103 = r2822101 + r2822102;
        double r2822104 = sqrt(r2822103);
        double r2822105 = r2822099 ? r2822104 : r2822094;
        double r2822106 = r2822096 ? r2822097 : r2822105;
        return r2822106;
}

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 < -8.181359696053478e+96

    1. Initial program 47.8

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

    2. Taylor expanded around -inf 10.3

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

    3. Simplified10.3

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

    if -8.181359696053478e+96 < re < 7.263939058947569e+108

    1. Initial program 19.9

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

    if 7.263939058947569e+108 < re

    1. Initial program 49.9

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

    2. Taylor expanded around inf 8.8

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

  4. Final simplification16.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -8.181359696053478 \cdot 10^{+96}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 7.263939058947569 \cdot 10^{+108}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))