Average Error: 29.6 → 17.1
Time: 3.9s
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 r3051321 = re;
        double r3051322 = r3051321 * r3051321;
        double r3051323 = im;
        double r3051324 = r3051323 * r3051323;
        double r3051325 = r3051322 + r3051324;
        double r3051326 = sqrt(r3051325);
        return r3051326;
}
↓
double f(double re, double im) {
        double r3051327 = re;
        double r3051328 = -6.15241991167455e+150;
        bool r3051329 = r3051327 <= r3051328;
        double r3051330 = -r3051327;
        double r3051331 = 1.8791426213625292e+66;
        bool r3051332 = r3051327 <= r3051331;
        double r3051333 = im;
        double r3051334 = r3051333 * r3051333;
        double r3051335 = r3051327 * r3051327;
        double r3051336 = r3051334 + r3051335;
        double r3051337 = sqrt(r3051336);
        double r3051338 = r3051332 ? r3051337 : r3051327;
        double r3051339 = r3051329 ? r3051330 : r3051338;
        return r3051339;
}

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))))