Average Error: 17.1 → 0.4
Time: 16.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
double f(double J, double l, double K, double U) {
        double r88922 = J;
        double r88923 = l;
        double r88924 = exp(r88923);
        double r88925 = -r88923;
        double r88926 = exp(r88925);
        double r88927 = r88924 - r88926;
        double r88928 = r88922 * r88927;
        double r88929 = K;
        double r88930 = 2.0;
        double r88931 = r88929 / r88930;
        double r88932 = cos(r88931);
        double r88933 = r88928 * r88932;
        double r88934 = U;
        double r88935 = r88933 + r88934;
        return r88935;
}
↓
double f(double J, double l, double K, double U) {
        double r88936 = J;
        double r88937 = 0.3333333333333333;
        double r88938 = l;
        double r88939 = 3.0;
        double r88940 = pow(r88938, r88939);
        double r88941 = r88937 * r88940;
        double r88942 = 0.016666666666666666;
        double r88943 = 5.0;
        double r88944 = pow(r88938, r88943);
        double r88945 = r88942 * r88944;
        double r88946 = 2.0;
        double r88947 = r88946 * r88938;
        double r88948 = r88945 + r88947;
        double r88949 = r88941 + r88948;
        double r88950 = K;
        double r88951 = 2.0;
        double r88952 = r88950 / r88951;
        double r88953 = cos(r88952);
        double r88954 = r88949 * r88953;
        double r88955 = r88936 * r88954;
        double r88956 = U;
        double r88957 = r88955 + r88956;
        return r88957;
}

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 17.1

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

  2. Taylor expanded around 0 0.4

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019304 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))