Average Error: 29.9 → 16.7
Time: 3.3s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -3.233858830546266 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 3.4644478033583236 \cdot 10^{+152}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -3.233858830546266 \cdot 10^{+153}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 3.4644478033583236 \cdot 10^{+152}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r2020533 = re;
        double r2020534 = r2020533 * r2020533;
        double r2020535 = im;
        double r2020536 = r2020535 * r2020535;
        double r2020537 = r2020534 + r2020536;
        double r2020538 = sqrt(r2020537);
        return r2020538;
}
↓
double f(double re, double im) {
        double r2020539 = re;
        double r2020540 = -3.233858830546266e+153;
        bool r2020541 = r2020539 <= r2020540;
        double r2020542 = -r2020539;
        double r2020543 = 3.4644478033583236e+152;
        bool r2020544 = r2020539 <= r2020543;
        double r2020545 = im;
        double r2020546 = r2020545 * r2020545;
        double r2020547 = r2020539 * r2020539;
        double r2020548 = r2020546 + r2020547;
        double r2020549 = sqrt(r2020548);
        double r2020550 = r2020544 ? r2020549 : r2020539;
        double r2020551 = r2020541 ? r2020542 : r2020550;
        return r2020551;
}

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 < -3.233858830546266e+153

    1. Initial program 59.2

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

    2. Taylor expanded around -inf 7.8

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

    3. Simplified7.8

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

    if -3.233858830546266e+153 < re < 3.4644478033583236e+152

    1. Initial program 19.9

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

    if 3.4644478033583236e+152 < re

    1. Initial program 58.5

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

    2. Taylor expanded around inf 7.6

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

  4. Final simplification16.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -3.233858830546266 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 3.4644478033583236 \cdot 10^{+152}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019135 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))