Average Error: 16.6 → 0.4
Time: 59.6s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right)\right) + U
double f(double J, double l, double K, double U) {
        double r12153925 = J;
        double r12153926 = l;
        double r12153927 = exp(r12153926);
        double r12153928 = -r12153926;
        double r12153929 = exp(r12153928);
        double r12153930 = r12153927 - r12153929;
        double r12153931 = r12153925 * r12153930;
        double r12153932 = K;
        double r12153933 = 2.0;
        double r12153934 = r12153932 / r12153933;
        double r12153935 = cos(r12153934);
        double r12153936 = r12153931 * r12153935;
        double r12153937 = U;
        double r12153938 = r12153936 + r12153937;
        return r12153938;
}
↓
double f(double J, double l, double K, double U) {
        double r12153939 = J;
        double r12153940 = K;
        double r12153941 = 2.0;
        double r12153942 = r12153940 / r12153941;
        double r12153943 = cos(r12153942);
        double r12153944 = l;
        double r12153945 = 5.0;
        double r12153946 = pow(r12153944, r12153945);
        double r12153947 = 0.016666666666666666;
        double r12153948 = r12153946 * r12153947;
        double r12153949 = 0.3333333333333333;
        double r12153950 = r12153949 * r12153944;
        double r12153951 = r12153950 * r12153944;
        double r12153952 = r12153941 + r12153951;
        double r12153953 = r12153952 * r12153944;
        double r12153954 = r12153948 + r12153953;
        double r12153955 = r12153943 * r12153954;
        double r12153956 = r12153939 * r12153955;
        double r12153957 = U;
        double r12153958 = r12153956 + r12153957;
        return r12153958;
}

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 16.6

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

  2. Taylor expanded around 0 0.3

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

  3. Simplified0.4

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019121 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))