Average Error: 31.2 → 18.0
Time: 2.7s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -7.520886186082616 \cdot 10^{+119}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -5.274722593747874 \cdot 10^{-207}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \leq 1.259166188322571 \cdot 10^{-253}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.5992908826155528 \cdot 10^{+115}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -7.520886186082616 \cdot 10^{+119}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \leq -5.274722593747874 \cdot 10^{-207}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \leq 1.259166188322571 \cdot 10^{-253}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \leq 1.5992908826155528 \cdot 10^{+115}:\\
\;\;\;\;\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 <= -7.520886186082616e+119)) {
		VAR = ((double) -(x));
	} else {
		double VAR_1;
		if ((x <= -5.274722593747874e-207)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			double VAR_2;
			if ((x <= 1.259166188322571e-253)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.5992908826155528e+115)) {
					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

Original31.2
Target17.5
Herbie18.0
\[\begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -7.5208861860826161e119

    1. Initial program Error: 54.0 bits

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

    2. Taylor expanded around -inf Error: 8.9 bits

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

    3. SimplifiedError: 8.9 bits

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

    if -7.5208861860826161e119 < x < -5.27472259374787428e-207 or 1.25916618832257105e-253 < x < 1.59929088261555279e115

    1. Initial program Error: 19.4 bits

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

    if -5.27472259374787428e-207 < x < 1.25916618832257105e-253

    1. Initial program Error: 29.8 bits

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

    2. Taylor expanded around 0 Error: 33.6 bits

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

    if 1.59929088261555279e115 < x

    1. Initial program Error: 53.9 bits

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

    2. Taylor expanded around inf Error: 9.1 bits

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

  4. Final simplificationError: 18.0 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.520886186082616 \cdot 10^{+119}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -5.274722593747874 \cdot 10^{-207}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \leq 1.259166188322571 \cdot 10^{-253}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.5992908826155528 \cdot 10^{+115}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))))