Average Error: 18.0 → 8.2
Time: 31.0s
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 r6983682 = -2.0;
        double r6983683 = J;
        double r6983684 = r6983682 * r6983683;
        double r6983685 = K;
        double r6983686 = 2.0;
        double r6983687 = r6983685 / r6983686;
        double r6983688 = cos(r6983687);
        double r6983689 = r6983684 * r6983688;
        double r6983690 = 1.0;
        double r6983691 = U;
        double r6983692 = r6983686 * r6983683;
        double r6983693 = r6983692 * r6983688;
        double r6983694 = r6983691 / r6983693;
        double r6983695 = pow(r6983694, r6983686);
        double r6983696 = r6983690 + r6983695;
        double r6983697 = sqrt(r6983696);
        double r6983698 = r6983689 * r6983697;
        return r6983698;
}
↓
double f(double J, double K, double U) {
        double r6983699 = 1.0;
        double r6983700 = sqrt(r6983699);
        double r6983701 = U;
        double r6983702 = J;
        double r6983703 = 2.0;
        double r6983704 = r6983702 * r6983703;
        double r6983705 = K;
        double r6983706 = r6983705 / r6983703;
        double r6983707 = cos(r6983706);
        double r6983708 = r6983704 * r6983707;
        double r6983709 = r6983701 / r6983708;
        double r6983710 = 2.0;
        double r6983711 = r6983703 / r6983710;
        double r6983712 = pow(r6983709, r6983711);
        double r6983713 = hypot(r6983700, r6983712);
        double r6983714 = -2.0;
        double r6983715 = r6983714 * r6983702;
        double r6983716 = r6983707 * r6983715;
        double r6983717 = r6983713 * r6983716;
        return r6983717;
}

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 18.0

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

  3. Applied sqr-pow18.0

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

  4. Applied add-sqr-sqrt18.0

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

  5. Applied hypot-def8.2

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

  6. Final simplification8.2

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

Reproduce

herbie shell --seed 2019172 +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)))))