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 r1721013 = re;
        double r1721014 = r1721013 * r1721013;
        double r1721015 = im;
        double r1721016 = r1721015 * r1721015;
        double r1721017 = r1721014 + r1721016;
        double r1721018 = sqrt(r1721017);
        return r1721018;
}
↓
double f(double re, double im) {
        double r1721019 = re;
        double r1721020 = -6.15241991167455e+150;
        bool r1721021 = r1721019 <= r1721020;
        double r1721022 = -r1721019;
        double r1721023 = 1.8791426213625292e+66;
        bool r1721024 = r1721019 <= r1721023;
        double r1721025 = im;
        double r1721026 = r1721025 * r1721025;
        double r1721027 = r1721019 * r1721019;
        double r1721028 = r1721026 + r1721027;
        double r1721029 = sqrt(r1721028);
        double r1721030 = r1721024 ? r1721029 : r1721019;
        double r1721031 = r1721021 ? r1721022 : r1721030;
        return r1721031;
}

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))))