Average Error: 29.7 → 16.7
Time: 8.3s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -2.0322794285022597 \cdot 10^{+138}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 1.470646602701209 \cdot 10^{+125}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -2.0322794285022597 \cdot 10^{+138}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 1.470646602701209 \cdot 10^{+125}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r3085317 = re;
        double r3085318 = r3085317 * r3085317;
        double r3085319 = im;
        double r3085320 = r3085319 * r3085319;
        double r3085321 = r3085318 + r3085320;
        double r3085322 = sqrt(r3085321);
        return r3085322;
}
↓
double f(double re, double im) {
        double r3085323 = re;
        double r3085324 = -2.0322794285022597e+138;
        bool r3085325 = r3085323 <= r3085324;
        double r3085326 = -r3085323;
        double r3085327 = 1.470646602701209e+125;
        bool r3085328 = r3085323 <= r3085327;
        double r3085329 = im;
        double r3085330 = r3085329 * r3085329;
        double r3085331 = r3085323 * r3085323;
        double r3085332 = r3085330 + r3085331;
        double r3085333 = sqrt(r3085332);
        double r3085334 = r3085328 ? r3085333 : r3085323;
        double r3085335 = r3085325 ? r3085326 : r3085334;
        return r3085335;
}

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 < -2.0322794285022597e+138

    1. Initial program 55.2

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

    2. Taylor expanded around -inf 8.6

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

    3. Simplified8.6

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

    if -2.0322794285022597e+138 < re < 1.470646602701209e+125

    1. Initial program 20.0

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

    if 1.470646602701209e+125 < re

    1. Initial program 52.9

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

    2. Taylor expanded around inf 8.3

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

  4. Final simplification16.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.0322794285022597 \cdot 10^{+138}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 1.470646602701209 \cdot 10^{+125}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019119 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))