Average Error: 16.7 → 7.0
Time: 56.4s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\sqrt{\sqrt{1^2 + \left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot 2\right) \cdot J}\right)^2}^*} \cdot \left(\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\sqrt{1^2 + \left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot 2\right) \cdot J}\right)^2}^*}\right)\]
\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}}
↓
\sqrt{\sqrt{1^2 + \left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot 2\right) \cdot J}\right)^2}^*} \cdot \left(\left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\sqrt{1^2 + \left(\frac{U}{\left(\cos \left(\frac{K}{2}\right) \cdot 2\right) \cdot J}\right)^2}^*}\right)
double f(double J, double K, double U) {
        double r18830239 = -2.0;
        double r18830240 = J;
        double r18830241 = r18830239 * r18830240;
        double r18830242 = K;
        double r18830243 = 2.0;
        double r18830244 = r18830242 / r18830243;
        double r18830245 = cos(r18830244);
        double r18830246 = r18830241 * r18830245;
        double r18830247 = 1.0;
        double r18830248 = U;
        double r18830249 = r18830243 * r18830240;
        double r18830250 = r18830249 * r18830245;
        double r18830251 = r18830248 / r18830250;
        double r18830252 = pow(r18830251, r18830243);
        double r18830253 = r18830247 + r18830252;
        double r18830254 = sqrt(r18830253);
        double r18830255 = r18830246 * r18830254;
        return r18830255;
}
↓
double f(double J, double K, double U) {
        double r18830256 = 1.0;
        double r18830257 = U;
        double r18830258 = K;
        double r18830259 = 2.0;
        double r18830260 = r18830258 / r18830259;
        double r18830261 = cos(r18830260);
        double r18830262 = r18830261 * r18830259;
        double r18830263 = J;
        double r18830264 = r18830262 * r18830263;
        double r18830265 = r18830257 / r18830264;
        double r18830266 = hypot(r18830256, r18830265);
        double r18830267 = sqrt(r18830266);
        double r18830268 = -2.0;
        double r18830269 = r18830263 * r18830268;
        double r18830270 = r18830269 * r18830261;
        double r18830271 = r18830270 * r18830267;
        double r18830272 = r18830267 * r18830271;
        return r18830272;
}

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 16.7

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

  2. Simplified6.9

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

  4. Applied add-sqr-sqrt7.0

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

  5. Applied associate-*l*7.0

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

  6. Final simplification7.0

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))