Average Error: 31.5 → 18.0
Time: 945.0ms
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.88499570758548 \cdot 10^{124}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -8.0386532336525431 \cdot 10^{-303}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.8902523850390375 \cdot 10^{-167}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.30263506617115279 \cdot 10^{154}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.88499570758548 \cdot 10^{124}:\\
\;\;\;\;-1 \cdot x\\

\mathbf{elif}\;x \le -8.0386532336525431 \cdot 10^{-303}:\\
\;\;\;\;\sqrt{x \cdot x + y \cdot y}\\

\mathbf{elif}\;x \le 1.8902523850390375 \cdot 10^{-167}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.30263506617115279 \cdot 10^{154}:\\
\;\;\;\;\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 <= -2.88499570758548e+124)) {
		VAR = (-1.0 * x);
	} else {
		double VAR_1;
		if ((x <= -8.038653233652543e-303)) {
			VAR_1 = sqrt(((x * x) + (y * y)));
		} else {
			double VAR_2;
			if ((x <= 1.8902523850390375e-167)) {
				VAR_2 = y;
			} else {
				double VAR_3;
				if ((x <= 1.3026350661711528e+154)) {
					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

Original31.5
Target17.7
Herbie18.0
\[\begin{array}{l} \mathbf{if}\;x \lt -1.123695082659983 \cdot 10^{145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.11655762118336204 \cdot 10^{93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -2.88499570758548e+124

    1. Initial program 57.0

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

    2. Taylor expanded around -inf 9.6

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

    if -2.88499570758548e+124 < x < -8.038653233652543e-303 or 1.8902523850390375e-167 < x < 1.3026350661711528e+154

    1. Initial program 18.8

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

    if -8.038653233652543e-303 < x < 1.8902523850390375e-167

    1. Initial program 31.0

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

    2. Taylor expanded around 0 34.5

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

    if 1.3026350661711528e+154 < x

    1. Initial program 64.0

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

    2. Taylor expanded around inf 8.4

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

  4. Final simplification18.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.88499570758548 \cdot 10^{124}:\\ \;\;\;\;-1 \cdot x\\ \mathbf{elif}\;x \le -8.0386532336525431 \cdot 10^{-303}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{elif}\;x \le 1.8902523850390375 \cdot 10^{-167}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.30263506617115279 \cdot 10^{154}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 
(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))))