Average Error: 17.1 → 0.3
Time: 49.5s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(\left(\left(\left(\ell \cdot \ell\right) \cdot \left(\ell \cdot \ell\right)\right) \cdot \ell\right) \cdot \frac{1}{60} + \left(\left(\ell \cdot \left(\ell \cdot \ell\right)\right) \cdot \frac{1}{3} + \ell \cdot 2\right)\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \left(\cos \left(\frac{K}{2}\right) \cdot J\right) \cdot \left(\left(\left(\left(\ell \cdot \ell\right) \cdot \left(\ell \cdot \ell\right)\right) \cdot \ell\right) \cdot \frac{1}{60} + \left(\left(\ell \cdot \left(\ell \cdot \ell\right)\right) \cdot \frac{1}{3} + \ell \cdot 2\right)\right)
double f(double J, double l, double K, double U) {
        double r4407200 = J;
        double r4407201 = l;
        double r4407202 = exp(r4407201);
        double r4407203 = -r4407201;
        double r4407204 = exp(r4407203);
        double r4407205 = r4407202 - r4407204;
        double r4407206 = r4407200 * r4407205;
        double r4407207 = K;
        double r4407208 = 2.0;
        double r4407209 = r4407207 / r4407208;
        double r4407210 = cos(r4407209);
        double r4407211 = r4407206 * r4407210;
        double r4407212 = U;
        double r4407213 = r4407211 + r4407212;
        return r4407213;
}
↓
double f(double J, double l, double K, double U) {
        double r4407214 = U;
        double r4407215 = K;
        double r4407216 = 2.0;
        double r4407217 = r4407215 / r4407216;
        double r4407218 = cos(r4407217);
        double r4407219 = J;
        double r4407220 = r4407218 * r4407219;
        double r4407221 = l;
        double r4407222 = r4407221 * r4407221;
        double r4407223 = r4407222 * r4407222;
        double r4407224 = r4407223 * r4407221;
        double r4407225 = 0.016666666666666666;
        double r4407226 = r4407224 * r4407225;
        double r4407227 = r4407221 * r4407222;
        double r4407228 = 0.3333333333333333;
        double r4407229 = r4407227 * r4407228;
        double r4407230 = r4407221 * r4407216;
        double r4407231 = r4407229 + r4407230;
        double r4407232 = r4407226 + r4407231;
        double r4407233 = r4407220 * r4407232;
        double r4407234 = r4407214 + r4407233;
        return r4407234;
}

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 0.3

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

  3. Simplified0.3

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

  5. Applied associate-*l*0.3

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

  6. Simplified0.3

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

  8. Applied associate-*r*0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))