Average Error: 29.8 → 16.7
Time: 6.3s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -1.1130849794491008 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.5581431714237065 \cdot 10^{+141}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -1.1130849794491008 \cdot 10^{+154}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \le 2.5581431714237065 \cdot 10^{+141}:\\
\;\;\;\;\sqrt{im \cdot im + re \cdot re}\\

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

\end{array}
double f(double re, double im) {
        double r2841401 = re;
        double r2841402 = r2841401 * r2841401;
        double r2841403 = im;
        double r2841404 = r2841403 * r2841403;
        double r2841405 = r2841402 + r2841404;
        double r2841406 = sqrt(r2841405);
        return r2841406;
}
↓
double f(double re, double im) {
        double r2841407 = re;
        double r2841408 = -1.1130849794491008e+154;
        bool r2841409 = r2841407 <= r2841408;
        double r2841410 = -r2841407;
        double r2841411 = 2.5581431714237065e+141;
        bool r2841412 = r2841407 <= r2841411;
        double r2841413 = im;
        double r2841414 = r2841413 * r2841413;
        double r2841415 = r2841407 * r2841407;
        double r2841416 = r2841414 + r2841415;
        double r2841417 = sqrt(r2841416);
        double r2841418 = r2841412 ? r2841417 : r2841407;
        double r2841419 = r2841409 ? r2841410 : r2841418;
        return r2841419;
}

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 < -1.1130849794491008e+154

    1. Initial program 59.3

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

    2. Taylor expanded around -inf 7.8

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

    3. Simplified7.8

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

    if -1.1130849794491008e+154 < re < 2.5581431714237065e+141

    1. Initial program 19.8

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

    if 2.5581431714237065e+141 < re

    1. Initial program 55.8

      \[\sqrt{re \cdot re + im \cdot im}\]
    2. Using strategy rm

    3. Applied add-exp-log56.2

      \[\leadsto \color{blue}{e^{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}}\]

    4. Taylor expanded around inf 8.9

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

  4. Final simplification16.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.1130849794491008 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.5581431714237065 \cdot 10^{+141}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))