Average Error: 17.3 → 0.4
Time: 28.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right) \cdot \ell\right)\right) + U\]
\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 + \frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right) \cdot \ell\right)\right) + U
double f(double J, double l, double K, double U) {
        double r3688936 = J;
        double r3688937 = l;
        double r3688938 = exp(r3688937);
        double r3688939 = -r3688937;
        double r3688940 = exp(r3688939);
        double r3688941 = r3688938 - r3688940;
        double r3688942 = r3688936 * r3688941;
        double r3688943 = K;
        double r3688944 = 2.0;
        double r3688945 = r3688943 / r3688944;
        double r3688946 = cos(r3688945);
        double r3688947 = r3688942 * r3688946;
        double r3688948 = U;
        double r3688949 = r3688947 + r3688948;
        return r3688949;
}
↓
double f(double J, double l, double K, double U) {
        double r3688950 = J;
        double r3688951 = K;
        double r3688952 = 2.0;
        double r3688953 = r3688951 / r3688952;
        double r3688954 = cos(r3688953);
        double r3688955 = l;
        double r3688956 = 5.0;
        double r3688957 = pow(r3688955, r3688956);
        double r3688958 = 0.016666666666666666;
        double r3688959 = r3688957 * r3688958;
        double r3688960 = 0.3333333333333333;
        double r3688961 = r3688955 * r3688955;
        double r3688962 = r3688960 * r3688961;
        double r3688963 = r3688952 + r3688962;
        double r3688964 = r3688963 * r3688955;
        double r3688965 = r3688959 + r3688964;
        double r3688966 = r3688954 * r3688965;
        double r3688967 = r3688950 * r3688966;
        double r3688968 = U;
        double r3688969 = r3688967 + r3688968;
        return r3688969;
}

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 17.3

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

  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

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019163 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))