Average Error: 17.7 → 0.4
Time: 25.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(\left(2 \cdot \ell + \frac{1}{3} \cdot {\ell}^{3}\right) + {\ell}^{5} \cdot \frac{1}{60}\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(\left(2 \cdot \ell + \frac{1}{3} \cdot {\ell}^{3}\right) + {\ell}^{5} \cdot \frac{1}{60}\right)
double f(double J, double l, double K, double U) {
        double r72918 = J;
        double r72919 = l;
        double r72920 = exp(r72919);
        double r72921 = -r72919;
        double r72922 = exp(r72921);
        double r72923 = r72920 - r72922;
        double r72924 = r72918 * r72923;
        double r72925 = K;
        double r72926 = 2.0;
        double r72927 = r72925 / r72926;
        double r72928 = cos(r72927);
        double r72929 = r72924 * r72928;
        double r72930 = U;
        double r72931 = r72929 + r72930;
        return r72931;
}
↓
double f(double J, double l, double K, double U) {
        double r72932 = U;
        double r72933 = K;
        double r72934 = 2.0;
        double r72935 = r72933 / r72934;
        double r72936 = cos(r72935);
        double r72937 = J;
        double r72938 = r72936 * r72937;
        double r72939 = 2.0;
        double r72940 = l;
        double r72941 = r72939 * r72940;
        double r72942 = 0.3333333333333333;
        double r72943 = 3.0;
        double r72944 = pow(r72940, r72943);
        double r72945 = r72942 * r72944;
        double r72946 = r72941 + r72945;
        double r72947 = 5.0;
        double r72948 = pow(r72940, r72947);
        double r72949 = 0.016666666666666666;
        double r72950 = r72948 * r72949;
        double r72951 = r72946 + r72950;
        double r72952 = r72938 * r72951;
        double r72953 = r72932 + r72952;
        return r72953;
}

Error

Bits error versus J

Bits error versus l

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

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

  2. Taylor expanded around 0 0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  3. Simplified0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(\frac{1}{60} \cdot {\ell}^{5} + \left(\frac{1}{3} \cdot {\ell}^{3} + 2 \cdot \ell\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
  4. Using strategy rm

  5. Applied pow10.4

    \[\leadsto \left(J \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + \left(\frac{1}{3} \cdot {\ell}^{3} + 2 \cdot \ell\right)\right)\right) \cdot \color{blue}{{\left(\cos \left(\frac{K}{2}\right)\right)}^{1}} + U\]

  6. Applied pow10.4

    \[\leadsto \left(J \cdot \color{blue}{{\left(\frac{1}{60} \cdot {\ell}^{5} + \left(\frac{1}{3} \cdot {\ell}^{3} + 2 \cdot \ell\right)\right)}^{1}}\right) \cdot {\left(\cos \left(\frac{K}{2}\right)\right)}^{1} + U\]

  7. Applied pow10.4

    \[\leadsto \left(\color{blue}{{J}^{1}} \cdot {\left(\frac{1}{60} \cdot {\ell}^{5} + \left(\frac{1}{3} \cdot {\ell}^{3} + 2 \cdot \ell\right)\right)}^{1}\right) \cdot {\left(\cos \left(\frac{K}{2}\right)\right)}^{1} + U\]

  8. Applied pow-prod-down0.4

    \[\leadsto \color{blue}{{\left(J \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + \left(\frac{1}{3} \cdot {\ell}^{3} + 2 \cdot \ell\right)\right)\right)}^{1}} \cdot {\left(\cos \left(\frac{K}{2}\right)\right)}^{1} + U\]

  9. Applied pow-prod-down0.4

    \[\leadsto \color{blue}{{\left(\left(J \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + \left(\frac{1}{3} \cdot {\ell}^{3} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right)}^{1}} + U\]

  10. Simplified0.4

    \[\leadsto {\color{blue}{\left(\left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + \left({\ell}^{3} \cdot \frac{1}{3} + \ell \cdot 2\right)\right)\right)}}^{1} + U\]

  11. Final simplification0.4

    \[\leadsto U + \left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(\left(2 \cdot \ell + \frac{1}{3} \cdot {\ell}^{3}\right) + {\ell}^{5} \cdot \frac{1}{60}\right)\]

Reproduce

herbie shell --seed 2019196 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))