Average Error: 29.6 → 16.9
Time: 2.7s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -1.1749852319542656 \cdot 10^{+99}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 6.852760898293699 \cdot 10^{+140}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -1.1749852319542656 \cdot 10^{+99}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 6.852760898293699 \cdot 10^{+140}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r1128589 = re;
        double r1128590 = r1128589 * r1128589;
        double r1128591 = im;
        double r1128592 = r1128591 * r1128591;
        double r1128593 = r1128590 + r1128592;
        double r1128594 = sqrt(r1128593);
        return r1128594;
}
↓
double f(double re, double im) {
        double r1128595 = re;
        double r1128596 = -1.1749852319542656e+99;
        bool r1128597 = r1128595 <= r1128596;
        double r1128598 = -r1128595;
        double r1128599 = 6.852760898293699e+140;
        bool r1128600 = r1128595 <= r1128599;
        double r1128601 = im;
        double r1128602 = r1128601 * r1128601;
        double r1128603 = r1128595 * r1128595;
        double r1128604 = r1128602 + r1128603;
        double r1128605 = sqrt(r1128604);
        double r1128606 = r1128600 ? r1128605 : r1128595;
        double r1128607 = r1128597 ? r1128598 : r1128606;
        return r1128607;
}

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 < -1.1749852319542656e+99

    1. Initial program 46.9

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

    2. Taylor expanded around -inf 10.4

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

    3. Simplified10.4

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

    if -1.1749852319542656e+99 < re < 6.852760898293699e+140

    1. Initial program 20.3

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

    if 6.852760898293699e+140 < re

    1. Initial program 55.8

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

    2. Taylor expanded around inf 7.9

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

  4. Final simplification16.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.1749852319542656 \cdot 10^{+99}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 6.852760898293699 \cdot 10^{+140}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019107 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))