Average Error: 31.6 → 17.9
Time: 2.8s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.340803523077166 \cdot 10^{+139}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -4.786656859853452 \cdot 10^{-266}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -2.7978321376001454 \cdot 10^{-306}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.2882041961296455 \cdot 10^{+92}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -9.340803523077166 \cdot 10^{+139}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \le -4.786656859853452 \cdot 10^{-266}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le -2.7978321376001454 \cdot 10^{-306}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.2882041961296455 \cdot 10^{+92}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{else}:\\
\;\;\;\;x\\

\end{array}
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
}
↓
double code(double x, double y) {
	double VAR;
	if ((x <= -9.340803523077166e+139)) {
		VAR = ((double) -(x));
	} else {
		double VAR_1;
		if ((x <= -4.786656859853452e-266)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			double VAR_2;
			if ((x <= -2.7978321376001454e-306)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.2882041961296455e+92)) {
					VAR_3 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
				} else {
					VAR_3 = x;
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.6
Target17.8
Herbie17.9
\[\begin{array}{l} \mathbf{if}\;x \lt -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -9.3408035230771657e139

    1. Initial program 60.5

      \[\sqrt{x \cdot x + y \cdot y}\]

    2. Taylor expanded around -inf 8.4

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

    3. Simplified8.4

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

    if -9.3408035230771657e139 < x < -4.7866568598534521e-266 or -2.79783213760014545e-306 < x < 1.28820419612964551e92

    1. Initial program 20.8

      \[\sqrt{x \cdot x + y \cdot y}\]

    if -4.7866568598534521e-266 < x < -2.79783213760014545e-306

    1. Initial program 31.2

      \[\sqrt{x \cdot x + y \cdot y}\]

    2. Taylor expanded around 0 31.5

      \[\leadsto \color{blue}{y}\]

    if 1.28820419612964551e92 < x

    1. Initial program 50.9

      \[\sqrt{x \cdot x + y \cdot y}\]

    2. Taylor expanded around inf 11.5

      \[\leadsto \color{blue}{x}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification17.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.340803523077166 \cdot 10^{+139}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -4.786656859853452 \cdot 10^{-266}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -2.7978321376001454 \cdot 10^{-306}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.2882041961296455 \cdot 10^{+92}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :herbie-target
  (if (< x -1.1236950826599826e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

  (sqrt (+ (* x x) (* y y))))