Average Error: 31.4 → 18.4
Time: 2.1s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.6998950373020774 \cdot 10^{87}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.1243171280702968 \cdot 10^{-257}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 2.4669184868707975 \cdot 10^{-173}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.127182207522478 \cdot 10^{132}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.6998950373020774 \cdot 10^{87}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le -1.1243171280702968 \cdot 10^{-257}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 2.4669184868707975 \cdot 10^{-173}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.127182207522478 \cdot 10^{132}:\\
\;\;\;\;\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 <= -1.6998950373020774e+87)) {
		VAR = ((double) (-1.0 * x));
	} else {
		double VAR_1;
		if ((x <= -1.1243171280702968e-257)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			double VAR_2;
			if ((x <= 2.4669184868707975e-173)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.127182207522478e+132)) {
					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

Original31.4
Target17.8
Herbie18.4
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -1.6998950373020774e87

    1. Initial program 48.8

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

    2. Taylor expanded around -inf 10.5

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

    if -1.6998950373020774e87 < x < -1.1243171280702968e-257 or 2.4669184868707975e-173 < x < 1.127182207522478e132

    1. Initial program 19.1

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

    if -1.1243171280702968e-257 < x < 2.4669184868707975e-173

    1. Initial program 30.4

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

    2. Taylor expanded around 0 34.0

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

    if 1.127182207522478e132 < x

    1. Initial program 58.0

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

    2. Taylor expanded around inf 8.1

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

  4. Final simplification18.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.6998950373020774 \cdot 10^{87}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.1243171280702968 \cdot 10^{-257}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 2.4669184868707975 \cdot 10^{-173}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.127182207522478 \cdot 10^{132}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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))))