Average Error: 32.1 → 17.7
Time: 2.0s
Precision: binary64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \leq -1.6030379465267134 \cdot 10^{+91}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \leq 1.1847833684373557 \cdot 10^{+118}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \leq -1.6030379465267134 \cdot 10^{+91}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \leq 1.1847833684373557 \cdot 10^{+118}:\\
\;\;\;\;\sqrt{re \cdot re + im \cdot im}\\

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

\end{array}
double code(double re, double im) {
	return ((double) sqrt(((double) (((double) (re * re)) + ((double) (im * im))))));
}
↓
double code(double re, double im) {
	double VAR;
	if ((re <= -1.6030379465267134e+91)) {
		VAR = ((double) -(re));
	} else {
		double VAR_1;
		if ((re <= 1.1847833684373557e+118)) {
			VAR_1 = ((double) sqrt(((double) (((double) (re * re)) + ((double) (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 < -1.6030379465267134e91

    1. Initial program 51.6

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

    2. Taylor expanded around -inf 11.2

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

    3. Simplified11.2

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

    if -1.6030379465267134e91 < re < 1.18478336843735573e118

    1. Initial program 21.5

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

    if 1.18478336843735573e118 < re

    1. Initial program 55.2

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

    2. Taylor expanded around inf 9.2

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

  4. Final simplification17.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \leq -1.6030379465267134 \cdot 10^{+91}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \leq 1.1847833684373557 \cdot 10^{+118}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))