Average Error: 29.6 → 16.7
Time: 4.2s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -3.628100188584437 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.6796985192192203 \cdot 10^{+137}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -3.628100188584437 \cdot 10^{+152}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 2.6796985192192203 \cdot 10^{+137}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r1974766 = re;
        double r1974767 = r1974766 * r1974766;
        double r1974768 = im;
        double r1974769 = r1974768 * r1974768;
        double r1974770 = r1974767 + r1974769;
        double r1974771 = sqrt(r1974770);
        return r1974771;
}
↓
double f(double re, double im) {
        double r1974772 = re;
        double r1974773 = -3.628100188584437e+152;
        bool r1974774 = r1974772 <= r1974773;
        double r1974775 = -r1974772;
        double r1974776 = 2.6796985192192203e+137;
        bool r1974777 = r1974772 <= r1974776;
        double r1974778 = im;
        double r1974779 = r1974778 * r1974778;
        double r1974780 = r1974772 * r1974772;
        double r1974781 = r1974779 + r1974780;
        double r1974782 = sqrt(r1974781);
        double r1974783 = r1974777 ? r1974782 : r1974772;
        double r1974784 = r1974774 ? r1974775 : r1974783;
        return r1974784;
}

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 < -3.628100188584437e+152

    1. Initial program 58.8

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

    2. Taylor expanded around -inf 7.3

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

    3. Simplified7.3

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

    if -3.628100188584437e+152 < re < 2.6796985192192203e+137

    1. Initial program 19.9

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

    if 2.6796985192192203e+137 < re

    1. Initial program 53.9

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

    2. Taylor expanded around inf 8.6

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

  4. Final simplification16.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -3.628100188584437 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.6796985192192203 \cdot 10^{+137}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))