Average Error: 31.4 → 18.5
Time: 24.8s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.5847343597756595 \cdot 10^{+152}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -2.35268515513709 \cdot 10^{-257}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le 1.6972939667011593 \cdot 10^{-158}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 3.161818111636812 \cdot 10^{+106}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.5847343597756595 \cdot 10^{+152}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \le -2.35268515513709 \cdot 10^{-257}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

\mathbf{elif}\;x \le 1.6972939667011593 \cdot 10^{-158}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 3.161818111636812 \cdot 10^{+106}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

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

\end{array}
double f(double x, double y) {
        double r36781160 = x;
        double r36781161 = r36781160 * r36781160;
        double r36781162 = y;
        double r36781163 = r36781162 * r36781162;
        double r36781164 = r36781161 + r36781163;
        double r36781165 = sqrt(r36781164);
        return r36781165;
}
↓
double f(double x, double y) {
        double r36781166 = x;
        double r36781167 = -2.5847343597756595e+152;
        bool r36781168 = r36781166 <= r36781167;
        double r36781169 = -r36781166;
        double r36781170 = -2.35268515513709e-257;
        bool r36781171 = r36781166 <= r36781170;
        double r36781172 = y;
        double r36781173 = r36781172 * r36781172;
        double r36781174 = r36781166 * r36781166;
        double r36781175 = r36781173 + r36781174;
        double r36781176 = sqrt(r36781175);
        double r36781177 = 1.6972939667011593e-158;
        bool r36781178 = r36781166 <= r36781177;
        double r36781179 = 3.161818111636812e+106;
        bool r36781180 = r36781166 <= r36781179;
        double r36781181 = r36781180 ? r36781176 : r36781166;
        double r36781182 = r36781178 ? r36781172 : r36781181;
        double r36781183 = r36781171 ? r36781176 : r36781182;
        double r36781184 = r36781168 ? r36781169 : r36781183;
        return r36781184;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original31.4
Target17.7
Herbie18.5
\[\begin{array}{l} \mathbf{if}\;x \lt -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -2.5847343597756595e+152

    1. Initial program 63.4

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

    2. Taylor expanded around -inf 8.7

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

    3. Simplified8.7

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

    if -2.5847343597756595e+152 < x < -2.35268515513709e-257 or 1.6972939667011593e-158 < x < 3.161818111636812e+106

    1. Initial program 18.0

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

    if -2.35268515513709e-257 < x < 1.6972939667011593e-158

    1. Initial program 30.0

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

    2. Taylor expanded around 0 35.1

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

    if 3.161818111636812e+106 < x

    1. Initial program 52.7

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

    2. Taylor expanded around inf 10.6

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

  4. Final simplification18.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.5847343597756595 \cdot 10^{+152}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -2.35268515513709 \cdot 10^{-257}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le 1.6972939667011593 \cdot 10^{-158}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 3.161818111636812 \cdot 10^{+106}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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))))