Average Error: 31.3 → 17.8
Time: 1.4s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -6.39388144865274 \cdot 10^{+123}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2.2949124501890465 \cdot 10^{-243}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \leq 1.0223475346325806 \cdot 10^{-246}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.597914161920686 \cdot 10^{+74}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -6.39388144865274 \cdot 10^{+123}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \leq -2.2949124501890465 \cdot 10^{-243}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \leq 1.0223475346325806 \cdot 10^{-246}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \leq 2.597914161920686 \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 <= -6.39388144865274e+123)) {
		VAR = ((double) -(x));
	} else {
		double VAR_1;
		if ((x <= -2.2949124501890465e-243)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			double VAR_2;
			if ((x <= 1.0223475346325806e-246)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 2.597914161920686e+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

Original31.3
Target17.4
Herbie17.8
\[\begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -6.39388144865274029e123

    1. Initial program 56.7

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

    2. Taylor expanded around -inf 8.5

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

    3. Simplified8.5

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

    if -6.39388144865274029e123 < x < -2.2949124501890465e-243 or 1.02234753463258063e-246 < x < 2.59791416192068604e74

    1. Initial program 19.7

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

    if -2.2949124501890465e-243 < x < 1.02234753463258063e-246

    1. Initial program 30.1

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

    2. Taylor expanded around 0 33.1

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

    if 2.59791416192068604e74 < x

    1. Initial program 47.0

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

    2. Taylor expanded around inf 10.9

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

  4. Final simplification17.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.39388144865274 \cdot 10^{+123}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2.2949124501890465 \cdot 10^{-243}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \leq 1.0223475346325806 \cdot 10^{-246}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 2.597914161920686 \cdot 10^{+74}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))))