Average Error: 29.4 → 16.3
Time: 4.5s
Precision: 64
\[\sqrt{x \cdot x + y \cdot y}\]
\[\begin{array}{l} \mathbf{if}\;x \le -5.325979075963888 \cdot 10^{+153}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le 1.6722096998730964 \cdot 10^{+129}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]
\sqrt{x \cdot x + y \cdot y}
\begin{array}{l}
\mathbf{if}\;x \le -5.325979075963888 \cdot 10^{+153}:\\
\;\;\;\;-x\\

\mathbf{elif}\;x \le 1.6722096998730964 \cdot 10^{+129}:\\
\;\;\;\;\sqrt{y \cdot y + x \cdot x}\\

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

\end{array}
double f(double x, double y) {
        double r43414176 = x;
        double r43414177 = r43414176 * r43414176;
        double r43414178 = y;
        double r43414179 = r43414178 * r43414178;
        double r43414180 = r43414177 + r43414179;
        double r43414181 = sqrt(r43414180);
        return r43414181;
}

double f(double x, double y) {
        double r43414182 = x;
        double r43414183 = -5.325979075963888e+153;
        bool r43414184 = r43414182 <= r43414183;
        double r43414185 = -r43414182;
        double r43414186 = 1.6722096998730964e+129;
        bool r43414187 = r43414182 <= r43414186;
        double r43414188 = y;
        double r43414189 = r43414188 * r43414188;
        double r43414190 = r43414182 * r43414182;
        double r43414191 = r43414189 + r43414190;
        double r43414192 = sqrt(r43414191);
        double r43414193 = r43414187 ? r43414192 : r43414182;
        double r43414194 = r43414184 ? r43414185 : r43414193;
        return r43414194;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes
  2. if x < -5.325979075963888e+153

    1. Initial program 59.2

      \[\sqrt{x \cdot x + y \cdot y}\]
    2. Taylor expanded around -inf 7.8

      \[\leadsto \color{blue}{-1 \cdot x}\]
    3. Simplified7.8

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

    if -5.325979075963888e+153 < x < 1.6722096998730964e+129

    1. Initial program 19.4

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

    if 1.6722096998730964e+129 < x

    1. Initial program 53.3

      \[\sqrt{x \cdot x + y \cdot y}\]
    2. Taylor expanded around inf 8.1

      \[\leadsto \color{blue}{x}\]
  3. Recombined 3 regimes into one program.
  4. Final simplification16.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.325979075963888 \cdot 10^{+153}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \le 1.6722096998730964 \cdot 10^{+129}:\\ \;\;\;\;\sqrt{y \cdot y + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array}\]

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "sqrt(x*x + y*y)"
  (sqrt (+ (* x x) (* y y))))