Average Error: 31.8 → 18.5
Time: 2.7s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.25443431135417537 \cdot 10^{129}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.40477998933113187 \cdot 10^{-158}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -1.02637373854441201 \cdot 10^{-303}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 2.032966617252637 \cdot 10^{102}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -6.25443431135417537 \cdot 10^{129}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le -1.40477998933113187 \cdot 10^{-158}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le -1.02637373854441201 \cdot 10^{-303}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 2.032966617252637 \cdot 10^{102}:\\
\;\;\;\;\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 <= -6.254434311354175e+129)) {
		VAR = (-1.0 * x);
	} else {
		double VAR_1;
		if ((x <= -1.4047799893311319e-158)) {
			VAR_1 = sqrt(((x * x) + (y * y)));
		} else {
			double VAR_2;
			if ((x <= -1.026373738544412e-303)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 2.032966617252637e+102)) {
					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

Original31.8
Target17.9
Herbie18.5
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -6.254434311354175e+129

    1. Initial program 58.3

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

    2. Taylor expanded around -inf 9.4

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

    if -6.254434311354175e+129 < x < -1.4047799893311319e-158 or -1.026373738544412e-303 < x < 2.032966617252637e+102

    1. Initial program 19.4

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

    if -1.4047799893311319e-158 < x < -1.026373738544412e-303

    1. Initial program 30.5

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

    2. Taylor expanded around 0 35.2

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

    if 2.032966617252637e+102 < x

    1. Initial program 52.3

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

    2. Taylor expanded around inf 10.5

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

  4. Final simplification18.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.25443431135417537 \cdot 10^{129}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -1.40477998933113187 \cdot 10^{-158}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le -1.02637373854441201 \cdot 10^{-303}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 2.032966617252637 \cdot 10^{102}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 
(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))))