Average Error: 17.6 → 0.4
Time: 8.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \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
double f(double J, double l, double K, double U) {
        double r161183 = J;
        double r161184 = l;
        double r161185 = exp(r161184);
        double r161186 = -r161184;
        double r161187 = exp(r161186);
        double r161188 = r161185 - r161187;
        double r161189 = r161183 * r161188;
        double r161190 = K;
        double r161191 = 2.0;
        double r161192 = r161190 / r161191;
        double r161193 = cos(r161192);
        double r161194 = r161189 * r161193;
        double r161195 = U;
        double r161196 = r161194 + r161195;
        return r161196;
}
↓
double f(double J, double l, double K, double U) {
        double r161197 = J;
        double r161198 = 0.3333333333333333;
        double r161199 = l;
        double r161200 = 3.0;
        double r161201 = pow(r161199, r161200);
        double r161202 = r161198 * r161201;
        double r161203 = 0.016666666666666666;
        double r161204 = 5.0;
        double r161205 = pow(r161199, r161204);
        double r161206 = r161203 * r161205;
        double r161207 = 2.0;
        double r161208 = r161207 * r161199;
        double r161209 = r161206 + r161208;
        double r161210 = r161202 + r161209;
        double r161211 = r161197 * r161210;
        double r161212 = K;
        double r161213 = 2.0;
        double r161214 = r161212 / r161213;
        double r161215 = cos(r161214);
        double r161216 = r161211 * r161215;
        double r161217 = U;
        double r161218 = r161216 + r161217;
        return r161218;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019346 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))