Average Error: 18.4 → 8.1
Time: 30.0s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\mathsf{hypot}\left(\sqrt{1}, {\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\]
\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}
↓
\mathsf{hypot}\left(\sqrt{1}, {\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)
double f(double J, double K, double U) {
        double r6383255 = -2.0;
        double r6383256 = J;
        double r6383257 = r6383255 * r6383256;
        double r6383258 = K;
        double r6383259 = 2.0;
        double r6383260 = r6383258 / r6383259;
        double r6383261 = cos(r6383260);
        double r6383262 = r6383257 * r6383261;
        double r6383263 = 1.0;
        double r6383264 = U;
        double r6383265 = r6383259 * r6383256;
        double r6383266 = r6383265 * r6383261;
        double r6383267 = r6383264 / r6383266;
        double r6383268 = pow(r6383267, r6383259);
        double r6383269 = r6383263 + r6383268;
        double r6383270 = sqrt(r6383269);
        double r6383271 = r6383262 * r6383270;
        return r6383271;
}
↓
double f(double J, double K, double U) {
        double r6383272 = 1.0;
        double r6383273 = sqrt(r6383272);
        double r6383274 = U;
        double r6383275 = J;
        double r6383276 = 2.0;
        double r6383277 = r6383275 * r6383276;
        double r6383278 = K;
        double r6383279 = r6383278 / r6383276;
        double r6383280 = cos(r6383279);
        double r6383281 = r6383277 * r6383280;
        double r6383282 = r6383274 / r6383281;
        double r6383283 = 2.0;
        double r6383284 = r6383276 / r6383283;
        double r6383285 = pow(r6383282, r6383284);
        double r6383286 = hypot(r6383273, r6383285);
        double r6383287 = -2.0;
        double r6383288 = r6383287 * r6383275;
        double r6383289 = r6383280 * r6383288;
        double r6383290 = r6383286 * r6383289;
        return r6383290;
}

Error

Bits error versus J

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.4

    \[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
  2. Using strategy rm

  3. Applied sqr-pow18.4

    \[\leadsto \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + \color{blue}{{\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)} \cdot {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}}}\]

  4. Applied add-sqr-sqrt18.4

    \[\leadsto \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\color{blue}{\sqrt{1} \cdot \sqrt{1}} + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)} \cdot {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}}\]

  5. Applied hypot-def8.1

    \[\leadsto \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\mathsf{hypot}\left(\sqrt{1}, {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right)}\]

  6. Final simplification8.1

    \[\leadsto \mathsf{hypot}\left(\sqrt{1}, {\left(\frac{U}{\left(J \cdot 2\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{\left(\frac{2}{2}\right)}\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))