Average Error: 30.5 → 17.3
Time: 1.1s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.79671734719750555 \cdot 10^{106}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 4.55718954958977214 \cdot 10^{-298}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 4.0892765348340891 \cdot 10^{-181}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 7.5785972112476335 \cdot 10^{91}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.79671734719750555 \cdot 10^{106}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le 4.55718954958977214 \cdot 10^{-298}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 4.0892765348340891 \cdot 10^{-181}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 7.5785972112476335 \cdot 10^{91}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

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

\end{array}
double code(double x, double y) {
	return sqrt(((x * x) + (y * y)));
}
↓
double code(double x, double y) {
	double VAR;
	if ((x <= -1.7967173471975055e+106)) {
		VAR = (-1.0 * x);
	} else {
		double VAR_1;
		if ((x <= 4.557189549589772e-298)) {
			VAR_1 = sqrt(((x * x) + (y * y)));
		} else {
			double VAR_2;
			if ((x <= 4.089276534834089e-181)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 7.578597211247633e+91)) {
					VAR_3 = sqrt(((x * x) + (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

Original30.5
Target16.7
Herbie17.3
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -1.7967173471975055e+106

    1. Initial program 52.6

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

    2. Taylor expanded around -inf 10.7

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

    if -1.7967173471975055e+106 < x < 4.557189549589772e-298 or 4.089276534834089e-181 < x < 7.578597211247633e+91

    1. Initial program 18.4

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

    if 4.557189549589772e-298 < x < 4.089276534834089e-181

    1. Initial program 30.1

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

    2. Taylor expanded around 0 35.5

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

    if 7.578597211247633e+91 < x

    1. Initial program 50.0

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

    2. Taylor expanded around inf 9.6

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

  4. Final simplification17.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.79671734719750555 \cdot 10^{106}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le 4.55718954958977214 \cdot 10^{-298}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 4.0892765348340891 \cdot 10^{-181}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 7.5785972112476335 \cdot 10^{91}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020092 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :herbie-target
  (if (< x -1.123695082659983e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

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