Average Error: 29.6 → 17.1
Time: 4.3s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -6.15241991167455 \cdot 10^{+150}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 1.8791426213625292 \cdot 10^{+66}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -6.15241991167455 \cdot 10^{+150}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 1.8791426213625292 \cdot 10^{+66}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r1964778 = re;
        double r1964779 = r1964778 * r1964778;
        double r1964780 = im;
        double r1964781 = r1964780 * r1964780;
        double r1964782 = r1964779 + r1964781;
        double r1964783 = sqrt(r1964782);
        return r1964783;
}
↓
double f(double re, double im) {
        double r1964784 = re;
        double r1964785 = -6.15241991167455e+150;
        bool r1964786 = r1964784 <= r1964785;
        double r1964787 = -r1964784;
        double r1964788 = 1.8791426213625292e+66;
        bool r1964789 = r1964784 <= r1964788;
        double r1964790 = im;
        double r1964791 = r1964790 * r1964790;
        double r1964792 = r1964784 * r1964784;
        double r1964793 = r1964791 + r1964792;
        double r1964794 = sqrt(r1964793);
        double r1964795 = r1964789 ? r1964794 : r1964784;
        double r1964796 = r1964786 ? r1964787 : r1964795;
        return r1964796;
}

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 < -6.15241991167455e+150

    1. Initial program 58.2

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

    2. Taylor expanded around -inf 7.7

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

    3. Simplified7.7

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

    if -6.15241991167455e+150 < re < 1.8791426213625292e+66

    1. Initial program 20.3

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

    if 1.8791426213625292e+66 < re

    1. Initial program 44.2

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

    2. Taylor expanded around inf 11.7

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

  4. Final simplification17.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -6.15241991167455 \cdot 10^{+150}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 1.8791426213625292 \cdot 10^{+66}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))