Average Error: 29.6 → 17.3
Time: 2.6s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -1.4662125478442153 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 6.855762661566607 \cdot 10^{+153}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -1.4662125478442153 \cdot 10^{+153}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 6.855762661566607 \cdot 10^{+153}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r1211852 = re;
        double r1211853 = r1211852 * r1211852;
        double r1211854 = im;
        double r1211855 = r1211854 * r1211854;
        double r1211856 = r1211853 + r1211855;
        double r1211857 = sqrt(r1211856);
        return r1211857;
}
↓
double f(double re, double im) {
        double r1211858 = re;
        double r1211859 = -1.4662125478442153e+153;
        bool r1211860 = r1211858 <= r1211859;
        double r1211861 = -r1211858;
        double r1211862 = 6.855762661566607e+153;
        bool r1211863 = r1211858 <= r1211862;
        double r1211864 = im;
        double r1211865 = r1211864 * r1211864;
        double r1211866 = r1211858 * r1211858;
        double r1211867 = r1211865 + r1211866;
        double r1211868 = sqrt(r1211867);
        double r1211869 = r1211863 ? r1211868 : r1211858;
        double r1211870 = r1211860 ? r1211861 : r1211869;
        return r1211870;
}

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 < -1.4662125478442153e+153

    1. Initial program 59.2

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

    2. Taylor expanded around -inf 8.8

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

    3. Simplified8.8

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

    if -1.4662125478442153e+153 < re < 6.855762661566607e+153

    1. Initial program 20.0

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

    if 6.855762661566607e+153 < re

    1. Initial program 59.4

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

    2. Taylor expanded around inf 9.1

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

  4. Final simplification17.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.4662125478442153 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 6.855762661566607 \cdot 10^{+153}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019124 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))