Average Error: 29.6 → 18.2
Time: 4.4s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.2918446586536957 \cdot 10^{+154}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -2.6219396713989246 \cdot 10^{+28}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le -3.209519593925633 \cdot 10^{-28}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le -8.056228658328031 \cdot 10^{-199}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le -3.759150523562943 \cdot 10^{-268}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.4301923552016937 \cdot 10^{+155}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.2918446586536957 \cdot 10^{+154}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \le -2.6219396713989246 \cdot 10^{+28}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

\mathbf{elif}\;x \le -3.209519593925633 \cdot 10^{-28}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le -8.056228658328031 \cdot 10^{-199}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

\mathbf{elif}\;x \le -3.759150523562943 \cdot 10^{-268}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 1.4301923552016937 \cdot 10^{+155}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

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

\end{array}
double f(double x, double y) {
        double r35268591 = x;
        double r35268592 = r35268591 * r35268591;
        double r35268593 = y;
        double r35268594 = r35268593 * r35268593;
        double r35268595 = r35268592 + r35268594;
        double r35268596 = sqrt(r35268595);
        return r35268596;
}
↓
double f(double x, double y) {
        double r35268597 = x;
        double r35268598 = -1.2918446586536957e+154;
        bool r35268599 = r35268597 <= r35268598;
        double r35268600 = -r35268597;
        double r35268601 = -2.6219396713989246e+28;
        bool r35268602 = r35268597 <= r35268601;
        double r35268603 = y;
        double r35268604 = r35268603 * r35268603;
        double r35268605 = r35268597 * r35268597;
        double r35268606 = r35268604 + r35268605;
        double r35268607 = sqrt(r35268606);
        double r35268608 = -3.209519593925633e-28;
        bool r35268609 = r35268597 <= r35268608;
        double r35268610 = -8.056228658328031e-199;
        bool r35268611 = r35268597 <= r35268610;
        double r35268612 = -3.759150523562943e-268;
        bool r35268613 = r35268597 <= r35268612;
        double r35268614 = 1.4301923552016937e+155;
        bool r35268615 = r35268597 <= r35268614;
        double r35268616 = r35268615 ? r35268607 : r35268597;
        double r35268617 = r35268613 ? r35268603 : r35268616;
        double r35268618 = r35268611 ? r35268607 : r35268617;
        double r35268619 = r35268609 ? r35268603 : r35268618;
        double r35268620 = r35268602 ? r35268607 : r35268619;
        double r35268621 = r35268599 ? r35268600 : r35268620;
        return r35268621;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.6
Target16.7
Herbie18.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -1.2918446586536957e+154

    1. Initial program 59.4

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

    2. Taylor expanded around -inf 7.0

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

    3. Simplified7.0

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

    if -1.2918446586536957e+154 < x < -2.6219396713989246e+28 or -3.209519593925633e-28 < x < -8.056228658328031e-199 or -3.759150523562943e-268 < x < 1.4301923552016937e+155

    1. Initial program 19.1

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

    if -2.6219396713989246e+28 < x < -3.209519593925633e-28 or -8.056228658328031e-199 < x < -3.759150523562943e-268

    1. Initial program 23.9

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

    2. Taylor expanded around 0 40.8

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

    if 1.4301923552016937e+155 < x

    1. Initial program 59.5

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

    2. Taylor expanded around inf 7.0

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

  4. Final simplification18.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.2918446586536957 \cdot 10^{+154}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -2.6219396713989246 \cdot 10^{+28}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le -3.209519593925633 \cdot 10^{-28}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le -8.056228658328031 \cdot 10^{-199}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le -3.759150523562943 \cdot 10^{-268}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 1.4301923552016937 \cdot 10^{+155}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"

  :herbie-target
  (if (< x -1.1236950826599826e+145) (- x) (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x))

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