Average Error: 17.7 → 7.8
Time: 26.8s
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 r116080 = -2.0;
        double r116081 = J;
        double r116082 = r116080 * r116081;
        double r116083 = K;
        double r116084 = 2.0;
        double r116085 = r116083 / r116084;
        double r116086 = cos(r116085);
        double r116087 = r116082 * r116086;
        double r116088 = 1.0;
        double r116089 = U;
        double r116090 = r116084 * r116081;
        double r116091 = r116090 * r116086;
        double r116092 = r116089 / r116091;
        double r116093 = pow(r116092, r116084);
        double r116094 = r116088 + r116093;
        double r116095 = sqrt(r116094);
        double r116096 = r116087 * r116095;
        return r116096;
}
↓
double f(double J, double K, double U) {
        double r116097 = 1.0;
        double r116098 = sqrt(r116097);
        double r116099 = U;
        double r116100 = J;
        double r116101 = 2.0;
        double r116102 = r116100 * r116101;
        double r116103 = K;
        double r116104 = r116103 / r116101;
        double r116105 = cos(r116104);
        double r116106 = r116102 * r116105;
        double r116107 = r116099 / r116106;
        double r116108 = 2.0;
        double r116109 = r116101 / r116108;
        double r116110 = pow(r116107, r116109);
        double r116111 = hypot(r116098, r116110);
        double r116112 = -2.0;
        double r116113 = r116112 * r116100;
        double r116114 = r116105 * r116113;
        double r116115 = r116111 * r116114;
        return r116115;
}

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 17.7

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

  3. Applied sqr-pow17.7

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

  4. Applied add-sqr-sqrt17.7

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

  5. Applied hypot-def7.8

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

  6. Final simplification7.8

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

Reproduce

herbie shell --seed 2019194 +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)))))