Average Error: 31.7 → 18.4
Time: 1.4s
Precision: binary64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -7.300218245200566 \cdot 10^{+92}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.2530278799008446 \cdot 10^{+80}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -7.300218245200566 \cdot 10^{+92}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \leq 3.2530278799008446 \cdot 10^{+80}:\\
\;\;\;\;\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 <= -7.300218245200566e+92)) {
		VAR = ((double) -(x));
	} else {
		double VAR_1;
		if ((x <= 3.2530278799008446e+80)) {
			VAR_1 = ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))));
		} else {
			VAR_1 = x;
		}
		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

Original31.7
Target18.3
Herbie18.4
\[\begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -7.30021824520056552e92

    1. Initial program 50.5

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

    2. Taylor expanded around -inf 11.4

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

    3. Simplified11.4

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

    if -7.30021824520056552e92 < x < 3.253027879900845e80

    1. Initial program 22.2

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

    if 3.253027879900845e80 < x

    1. Initial program 47.2

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

    2. Taylor expanded around inf 11.7

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

  4. Final simplification18.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.300218245200566 \cdot 10^{+92}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.2530278799008446 \cdot 10^{+80}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))))