Average Error: 31.5 → 17.7
Time: 942.0ms
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -3.2448676667043955 \cdot 10^{94}:\\ \;\;\;\;-1 \cdot re\\ \mathbf{elif}\;re \le 3.30012455476501778 \cdot 10^{108}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \le -3.2448676667043955 \cdot 10^{94}:\\
\;\;\;\;-1 \cdot re\\

\mathbf{elif}\;re \le 3.30012455476501778 \cdot 10^{108}:\\
\;\;\;\;\sqrt{re \cdot re + im \cdot im}\\

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

\end{array}
double code(double re, double im) {
	return sqrt(((re * re) + (im * im)));
}
↓
double code(double re, double im) {
	double VAR;
	if ((re <= -3.2448676667043955e+94)) {
		VAR = (-1.0 * re);
	} else {
		double VAR_1;
		if ((re <= 3.300124554765018e+108)) {
			VAR_1 = sqrt(((re * re) + (im * im)));
		} else {
			VAR_1 = re;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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 < -3.2448676667043955e+94

    1. Initial program 50.7

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

    2. Taylor expanded around -inf 10.8

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

    if -3.2448676667043955e+94 < re < 3.300124554765018e+108

    1. Initial program 21.3

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

    if 3.300124554765018e+108 < re

    1. Initial program 54.0

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

    2. Taylor expanded around inf 9.8

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

  4. Final simplification17.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -3.2448676667043955 \cdot 10^{94}:\\ \;\;\;\;-1 \cdot re\\ \mathbf{elif}\;re \le 3.30012455476501778 \cdot 10^{108}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))