Average Error: 29.7 → 16.8
Time: 11.8s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -8.994030179969843 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.855885243807385 \cdot 10^{+152}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -8.994030179969843 \cdot 10^{+153}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 2.855885243807385 \cdot 10^{+152}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r1477562 = re;
        double r1477563 = r1477562 * r1477562;
        double r1477564 = im;
        double r1477565 = r1477564 * r1477564;
        double r1477566 = r1477563 + r1477565;
        double r1477567 = sqrt(r1477566);
        return r1477567;
}
↓
double f(double re, double im) {
        double r1477568 = re;
        double r1477569 = -8.994030179969843e+153;
        bool r1477570 = r1477568 <= r1477569;
        double r1477571 = -r1477568;
        double r1477572 = 2.855885243807385e+152;
        bool r1477573 = r1477568 <= r1477572;
        double r1477574 = im;
        double r1477575 = r1477574 * r1477574;
        double r1477576 = r1477568 * r1477568;
        double r1477577 = r1477575 + r1477576;
        double r1477578 = sqrt(r1477577);
        double r1477579 = r1477573 ? r1477578 : r1477568;
        double r1477580 = r1477570 ? r1477571 : r1477579;
        return r1477580;
}

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 < -8.994030179969843e+153

    1. Initial program 59.2

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

    2. Taylor expanded around -inf 7.9

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

    3. Simplified7.9

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

    if -8.994030179969843e+153 < re < 2.855885243807385e+152

    1. Initial program 19.9

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

    if 2.855885243807385e+152 < re

    1. Initial program 59.1

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

    2. Taylor expanded around inf 7.1

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

  4. Final simplification16.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -8.994030179969843 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.855885243807385 \cdot 10^{+152}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019129 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))