Average Error: 31.7 → 18.7
Time: 2.0s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.02179966160642987 \cdot 10^{145}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.5391970346231962 \cdot 10^{-190}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -3.9573712583367902 \cdot 10^{-295}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.29362631726006162 \cdot 10^{74}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.02179966160642987 \cdot 10^{145}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le -1.5391970346231962 \cdot 10^{-190}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le -3.9573712583367902 \cdot 10^{-295}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.29362631726006162 \cdot 10^{74}:\\
\;\;\;\;\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 <= -5.02179966160643e+145)) {
		VAR = ((double) (-1.0 * x));
	} else {
		double VAR_1;
		if ((x <= -1.5391970346231962e-190)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			double VAR_2;
			if ((x <= -3.95737125833679e-295)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.2936263172600616e+74)) {
					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

Original31.7
Target18.2
Herbie18.7
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -5.02179966160642987e145

    1. Initial program 62.1

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

    2. Taylor expanded around -inf 9.5

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

    if -5.02179966160642987e145 < x < -1.5391970346231962e-190 or -3.9573712583367902e-295 < x < 1.29362631726006162e74

    1. Initial program 20.3

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

    if -1.5391970346231962e-190 < x < -3.9573712583367902e-295

    1. Initial program 31.7

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

    2. Taylor expanded around 0 35.1

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

    if 1.29362631726006162e74 < x

    1. Initial program 47.2

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

    2. Taylor expanded around inf 12.9

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

  4. Final simplification18.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.02179966160642987 \cdot 10^{145}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.5391970346231962 \cdot 10^{-190}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -3.9573712583367902 \cdot 10^{-295}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.29362631726006162 \cdot 10^{74}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020147 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

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

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