Average Error: 29.5 → 17.3
Time: 9.7s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -9.047687227227441 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.8891330792293805 \cdot 10^{+160}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -9.047687227227441 \cdot 10^{+152}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 2.8891330792293805 \cdot 10^{+160}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r1063633 = re;
        double r1063634 = r1063633 * r1063633;
        double r1063635 = im;
        double r1063636 = r1063635 * r1063635;
        double r1063637 = r1063634 + r1063636;
        double r1063638 = sqrt(r1063637);
        return r1063638;
}
↓
double f(double re, double im) {
        double r1063639 = re;
        double r1063640 = -9.047687227227441e+152;
        bool r1063641 = r1063639 <= r1063640;
        double r1063642 = -r1063639;
        double r1063643 = 2.8891330792293805e+160;
        bool r1063644 = r1063639 <= r1063643;
        double r1063645 = im;
        double r1063646 = r1063645 * r1063645;
        double r1063647 = r1063639 * r1063639;
        double r1063648 = r1063646 + r1063647;
        double r1063649 = sqrt(r1063648);
        double r1063650 = r1063644 ? r1063649 : r1063639;
        double r1063651 = r1063641 ? r1063642 : r1063650;
        return r1063651;
}

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 < -9.047687227227441e+152

    1. Initial program 59.2

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

    2. Taylor expanded around -inf 8.3

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

    3. Simplified8.3

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

    if -9.047687227227441e+152 < re < 2.8891330792293805e+160

    1. Initial program 20.1

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

    if 2.8891330792293805e+160 < re

    1. Initial program 59.3

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

    2. Taylor expanded around inf 8.4

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

  4. Final simplification17.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -9.047687227227441 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.8891330792293805 \cdot 10^{+160}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))