Average Error: 17.1 → 0.3
Time: 28.7s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right) \cdot \ell\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \frac{1}{3} \cdot \left(\ell \cdot \ell\right)\right) \cdot \ell\right) \cdot \left(\cos \left(\frac{K}{2}\right) \cdot J\right)
double f(double J, double l, double K, double U) {
        double r1484224 = J;
        double r1484225 = l;
        double r1484226 = exp(r1484225);
        double r1484227 = -r1484225;
        double r1484228 = exp(r1484227);
        double r1484229 = r1484226 - r1484228;
        double r1484230 = r1484224 * r1484229;
        double r1484231 = K;
        double r1484232 = 2.0;
        double r1484233 = r1484231 / r1484232;
        double r1484234 = cos(r1484233);
        double r1484235 = r1484230 * r1484234;
        double r1484236 = U;
        double r1484237 = r1484235 + r1484236;
        return r1484237;
}
↓
double f(double J, double l, double K, double U) {
        double r1484238 = U;
        double r1484239 = l;
        double r1484240 = 5.0;
        double r1484241 = pow(r1484239, r1484240);
        double r1484242 = 0.016666666666666666;
        double r1484243 = r1484241 * r1484242;
        double r1484244 = 2.0;
        double r1484245 = 0.3333333333333333;
        double r1484246 = r1484239 * r1484239;
        double r1484247 = r1484245 * r1484246;
        double r1484248 = r1484244 + r1484247;
        double r1484249 = r1484248 * r1484239;
        double r1484250 = r1484243 + r1484249;
        double r1484251 = K;
        double r1484252 = r1484251 / r1484244;
        double r1484253 = cos(r1484252);
        double r1484254 = J;
        double r1484255 = r1484253 * r1484254;
        double r1484256 = r1484250 * r1484255;
        double r1484257 = r1484238 + r1484256;
        return r1484257;
}

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

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

  5. Applied pow10.3

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

  6. Applied pow10.3

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

  7. Applied pow-prod-down0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

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))