Average Error: 17.4 → 0.4
Time: 10.1s
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 r118961 = J;
        double r118962 = l;
        double r118963 = exp(r118962);
        double r118964 = -r118962;
        double r118965 = exp(r118964);
        double r118966 = r118963 - r118965;
        double r118967 = r118961 * r118966;
        double r118968 = K;
        double r118969 = 2.0;
        double r118970 = r118968 / r118969;
        double r118971 = cos(r118970);
        double r118972 = r118967 * r118971;
        double r118973 = U;
        double r118974 = r118972 + r118973;
        return r118974;
}
↓
double f(double J, double l, double K, double U) {
        double r118975 = J;
        double r118976 = 0.3333333333333333;
        double r118977 = l;
        double r118978 = 3.0;
        double r118979 = pow(r118977, r118978);
        double r118980 = r118976 * r118979;
        double r118981 = 0.016666666666666666;
        double r118982 = 5.0;
        double r118983 = pow(r118977, r118982);
        double r118984 = r118981 * r118983;
        double r118985 = 2.0;
        double r118986 = r118985 * r118977;
        double r118987 = r118984 + r118986;
        double r118988 = r118980 + r118987;
        double r118989 = K;
        double r118990 = 2.0;
        double r118991 = r118989 / r118990;
        double r118992 = cos(r118991);
        double r118993 = r118988 * r118992;
        double r118994 = r118975 * r118993;
        double r118995 = U;
        double r118996 = r118994 + r118995;
        return r118996;
}

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 17.4

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

  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 2020036 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))