Average Error: 31.7 → 18.4
Time: 1.3s
Precision: binary64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \leq -7.300218245200566 \cdot 10^{+92}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \leq 3.2530278799008446 \cdot 10^{+80}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]
\sqrt{re \cdot re + im \cdot im}
↓
\begin{array}{l}
\mathbf{if}\;re \leq -7.300218245200566 \cdot 10^{+92}:\\
\;\;\;\;-re\\

\mathbf{elif}\;re \leq 3.2530278799008446 \cdot 10^{+80}:\\
\;\;\;\;\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 <= -7.300218245200566e+92)) {
		VAR = ((double) -(re));
	} else {
		double VAR_1;
		if ((re <= 3.2530278799008446e+80)) {
			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 < -7.30021824520056552e92

    1. Initial program 50.5

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

    2. Taylor expanded around -inf 11.4

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

    3. Simplified11.4

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

    if -7.30021824520056552e92 < re < 3.253027879900845e80

    1. Initial program 22.2

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

    if 3.253027879900845e80 < re

    1. Initial program 47.2

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

    2. Taylor expanded around inf 11.7

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

  4. Final simplification18.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \leq -7.300218245200566 \cdot 10^{+92}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \leq 3.2530278799008446 \cdot 10^{+80}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))