Average Error: 29.7 → 17.4
Time: 2.9s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.3377295553932065 \cdot 10^{+154}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -3.6726164932126896 \cdot 10^{-218}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le 1.590629195950438 \cdot 10^{-228}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 2.882396363471933 \cdot 10^{+117}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.3377295553932065 \cdot 10^{+154}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \le -3.6726164932126896 \cdot 10^{-218}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

\mathbf{elif}\;x \le 1.590629195950438 \cdot 10^{-228}:\\
\;\;\;\;y\\

\mathbf{elif}\;x \le 2.882396363471933 \cdot 10^{+117}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

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

\end{array}
double f(double x, double y) {
        double r15442421 = x;
        double r15442422 = r15442421 * r15442421;
        double r15442423 = y;
        double r15442424 = r15442423 * r15442423;
        double r15442425 = r15442422 + r15442424;
        double r15442426 = sqrt(r15442425);
        return r15442426;
}
↓
double f(double x, double y) {
        double r15442427 = x;
        double r15442428 = -1.3377295553932065e+154;
        bool r15442429 = r15442427 <= r15442428;
        double r15442430 = -r15442427;
        double r15442431 = -3.6726164932126896e-218;
        bool r15442432 = r15442427 <= r15442431;
        double r15442433 = y;
        double r15442434 = r15442433 * r15442433;
        double r15442435 = r15442427 * r15442427;
        double r15442436 = r15442434 + r15442435;
        double r15442437 = sqrt(r15442436);
        double r15442438 = 1.590629195950438e-228;
        bool r15442439 = r15442427 <= r15442438;
        double r15442440 = 2.882396363471933e+117;
        bool r15442441 = r15442427 <= r15442440;
        double r15442442 = r15442441 ? r15442437 : r15442427;
        double r15442443 = r15442439 ? r15442433 : r15442442;
        double r15442444 = r15442432 ? r15442437 : r15442443;
        double r15442445 = r15442429 ? r15442430 : r15442444;
        return r15442445;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.7
Target16.9
Herbie17.4
\[\begin{array}{l} \mathbf{if}\;x \lt -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \lt 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if x < -1.3377295553932065e+154

    1. Initial program 59.4

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

    2. Taylor expanded around -inf 7.6

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

    3. Simplified7.6

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

    if -1.3377295553932065e+154 < x < -3.6726164932126896e-218 or 1.590629195950438e-228 < x < 2.882396363471933e+117

    1. Initial program 17.7

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

    if -3.6726164932126896e-218 < x < 1.590629195950438e-228

    1. Initial program 29.3

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

    2. Taylor expanded around 0 33.6

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

    if 2.882396363471933e+117 < x

    1. Initial program 50.9

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

    2. Taylor expanded around inf 9.4

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

  4. Final simplification17.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.3377295553932065 \cdot 10^{+154}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le -3.6726164932126896 \cdot 10^{-218}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{elif}\;x \le 1.590629195950438 \cdot 10^{-228}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \le 2.882396363471933 \cdot 10^{+117}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(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))))