Average Error: 17.6 → 0.4
Time: 27.8s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{{\ell}^{5}}{60} + \left(\left(\frac{{\ell}^{3}}{3} + \ell\right) + \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(\frac{{\ell}^{5}}{60} + \left(\left(\frac{{\ell}^{3}}{3} + \ell\right) + \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r114226 = J;
        double r114227 = l;
        double r114228 = exp(r114227);
        double r114229 = -r114227;
        double r114230 = exp(r114229);
        double r114231 = r114228 - r114230;
        double r114232 = r114226 * r114231;
        double r114233 = K;
        double r114234 = 2.0;
        double r114235 = r114233 / r114234;
        double r114236 = cos(r114235);
        double r114237 = r114232 * r114236;
        double r114238 = U;
        double r114239 = r114237 + r114238;
        return r114239;
}
↓
double f(double J, double l, double K, double U) {
        double r114240 = J;
        double r114241 = l;
        double r114242 = 5.0;
        double r114243 = pow(r114241, r114242);
        double r114244 = 60.0;
        double r114245 = r114243 / r114244;
        double r114246 = 3.0;
        double r114247 = pow(r114241, r114246);
        double r114248 = r114247 / r114246;
        double r114249 = r114248 + r114241;
        double r114250 = r114249 + r114241;
        double r114251 = r114245 + r114250;
        double r114252 = r114240 * r114251;
        double r114253 = K;
        double r114254 = 2.0;
        double r114255 = r114253 / r114254;
        double r114256 = cos(r114255);
        double r114257 = r114252 * r114256;
        double r114258 = U;
        double r114259 = r114257 + r114258;
        return r114259;
}

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. Simplified0.4

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

  4. Final simplification0.4

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

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))