Average Error: 18.1 → 13.3
Time: 8.9s
Precision: 64
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} = -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \le 3.823360998351127193476059713026580272921 \cdot 10^{304}\right):\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\left|\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right| \cdot \sqrt{\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}}\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\\ \end{array}\]
\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}}
↓
\begin{array}{l}
\mathbf{if}\;\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}} = -\infty \lor \neg \left(\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}} \le 3.823360998351127193476059713026580272921 \cdot 10^{304}\right):\\
\;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\left|\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right| \cdot \sqrt{\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}}\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\\

\end{array}
double f(double J, double K, double U) {
        double r178063 = -2.0;
        double r178064 = J;
        double r178065 = r178063 * r178064;
        double r178066 = K;
        double r178067 = 2.0;
        double r178068 = r178066 / r178067;
        double r178069 = cos(r178068);
        double r178070 = r178065 * r178069;
        double r178071 = 1.0;
        double r178072 = U;
        double r178073 = r178067 * r178064;
        double r178074 = r178073 * r178069;
        double r178075 = r178072 / r178074;
        double r178076 = pow(r178075, r178067);
        double r178077 = r178071 + r178076;
        double r178078 = sqrt(r178077);
        double r178079 = r178070 * r178078;
        return r178079;
}
↓
double f(double J, double K, double U) {
        double r178080 = -2.0;
        double r178081 = J;
        double r178082 = r178080 * r178081;
        double r178083 = K;
        double r178084 = 2.0;
        double r178085 = r178083 / r178084;
        double r178086 = cos(r178085);
        double r178087 = r178082 * r178086;
        double r178088 = 1.0;
        double r178089 = U;
        double r178090 = r178084 * r178081;
        double r178091 = r178090 * r178086;
        double r178092 = r178089 / r178091;
        double r178093 = pow(r178092, r178084);
        double r178094 = r178088 + r178093;
        double r178095 = sqrt(r178094);
        double r178096 = r178087 * r178095;
        double r178097 = -inf.0;
        bool r178098 = r178096 <= r178097;
        double r178099 = 3.823360998351127e+304;
        bool r178100 = r178096 <= r178099;
        double r178101 = !r178100;
        bool r178102 = r178098 || r178101;
        double r178103 = 0.25;
        double r178104 = sqrt(r178103);
        double r178105 = r178104 * r178089;
        double r178106 = 0.5;
        double r178107 = r178106 * r178083;
        double r178108 = cos(r178107);
        double r178109 = r178081 * r178108;
        double r178110 = r178105 / r178109;
        double r178111 = r178087 * r178110;
        double r178112 = cbrt(r178094);
        double r178113 = fabs(r178112);
        double r178114 = sqrt(r178112);
        double r178115 = r178113 * r178114;
        double r178116 = sqrt(r178115);
        double r178117 = r178087 * r178116;
        double r178118 = sqrt(r178095);
        double r178119 = r178117 * r178118;
        double r178120 = r178102 ? r178111 : r178119;
        return r178120;
}

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. Split input into 2 regimes

  2. if (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < -inf.0 or 3.823360998351127e+304 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

    1. Initial program 63.1

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

    2. Taylor expanded around inf 46.0

      \[\leadsto \left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \color{blue}{\frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}}\]

    if -inf.0 < (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) < 3.823360998351127e+304

    1. Initial program 0.1

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

    3. Applied add-sqr-sqrt0.1

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

    4. Applied sqrt-prod0.3

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

    5. Applied associate-*r*0.3

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

    7. Applied add-cube-cbrt0.3

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

    8. Applied sqrt-prod0.3

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

    9. Simplified0.3

      \[\leadsto \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\color{blue}{\left|\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right|} \cdot \sqrt{\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}}\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification13.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} = -\infty \lor \neg \left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}} \le 3.823360998351127193476059713026580272921 \cdot 10^{304}\right):\\ \;\;\;\;\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \frac{\sqrt{0.25} \cdot U}{J \cdot \cos \left(0.5 \cdot K\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{\left|\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\right| \cdot \sqrt{\sqrt[3]{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}}\right) \cdot \sqrt{\sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019352 
(FPCore (J K U)
  :name "Maksimov and Kolovsky, Equation (3)"
  :precision binary64
  (* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))