Average Error: 17.6 → 0.4
Time: 42.2s
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 r79925 = J;
        double r79926 = l;
        double r79927 = exp(r79926);
        double r79928 = -r79926;
        double r79929 = exp(r79928);
        double r79930 = r79927 - r79929;
        double r79931 = r79925 * r79930;
        double r79932 = K;
        double r79933 = 2.0;
        double r79934 = r79932 / r79933;
        double r79935 = cos(r79934);
        double r79936 = r79931 * r79935;
        double r79937 = U;
        double r79938 = r79936 + r79937;
        return r79938;
}
↓
double f(double J, double l, double K, double U) {
        double r79939 = J;
        double r79940 = 0.3333333333333333;
        double r79941 = l;
        double r79942 = 3.0;
        double r79943 = pow(r79941, r79942);
        double r79944 = r79940 * r79943;
        double r79945 = 0.016666666666666666;
        double r79946 = 5.0;
        double r79947 = pow(r79941, r79946);
        double r79948 = r79945 * r79947;
        double r79949 = 2.0;
        double r79950 = r79949 * r79941;
        double r79951 = r79948 + r79950;
        double r79952 = r79944 + r79951;
        double r79953 = K;
        double r79954 = 2.0;
        double r79955 = r79953 / r79954;
        double r79956 = cos(r79955);
        double r79957 = r79952 * r79956;
        double r79958 = r79939 * r79957;
        double r79959 = U;
        double r79960 = r79958 + r79959;
        return r79960;
}

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 17.6

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

  2. Taylor expanded around 0 0.4

    \[\leadsto \left(J \cdot \color{blue}{\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
  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 2019303 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))