Average Error: 29.1 → 16.6
Time: 3.7s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -1.3623275024248427 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 3.3803793863833235 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -1.3623275024248427 \cdot 10^{+154}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 3.3803793863833235 \cdot 10^{+93}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r3560843 = re;
        double r3560844 = r3560843 * r3560843;
        double r3560845 = im;
        double r3560846 = r3560845 * r3560845;
        double r3560847 = r3560844 + r3560846;
        double r3560848 = sqrt(r3560847);
        return r3560848;
}
↓
double f(double re, double im) {
        double r3560849 = re;
        double r3560850 = -1.3623275024248427e+154;
        bool r3560851 = r3560849 <= r3560850;
        double r3560852 = -r3560849;
        double r3560853 = 3.3803793863833235e+93;
        bool r3560854 = r3560849 <= r3560853;
        double r3560855 = im;
        double r3560856 = r3560855 * r3560855;
        double r3560857 = r3560849 * r3560849;
        double r3560858 = r3560856 + r3560857;
        double r3560859 = sqrt(r3560858);
        double r3560860 = r3560854 ? r3560859 : r3560849;
        double r3560861 = r3560851 ? r3560852 : r3560860;
        return r3560861;
}

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 < -1.3623275024248427e+154

    1. Initial program 59.4

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

    2. Taylor expanded around -inf 7.0

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

    3. Simplified7.0

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

    if -1.3623275024248427e+154 < re < 3.3803793863833235e+93

    1. Initial program 19.6

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

    if 3.3803793863833235e+93 < re

    1. Initial program 46.6

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

    2. Taylor expanded around inf 11.2

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

  4. Final simplification16.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.3623275024248427 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 3.3803793863833235 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))