Average Error: 17.0 → 0.4
Time: 8.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\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 r161186 = J;
        double r161187 = l;
        double r161188 = exp(r161187);
        double r161189 = -r161187;
        double r161190 = exp(r161189);
        double r161191 = r161188 - r161190;
        double r161192 = r161186 * r161191;
        double r161193 = K;
        double r161194 = 2.0;
        double r161195 = r161193 / r161194;
        double r161196 = cos(r161195);
        double r161197 = r161192 * r161196;
        double r161198 = U;
        double r161199 = r161197 + r161198;
        return r161199;
}
↓
double f(double J, double l, double K, double U) {
        double r161200 = J;
        double r161201 = 0.3333333333333333;
        double r161202 = l;
        double r161203 = 3.0;
        double r161204 = pow(r161202, r161203);
        double r161205 = r161201 * r161204;
        double r161206 = 0.016666666666666666;
        double r161207 = 5.0;
        double r161208 = pow(r161202, r161207);
        double r161209 = r161206 * r161208;
        double r161210 = 2.0;
        double r161211 = r161210 * r161202;
        double r161212 = r161209 + r161211;
        double r161213 = r161205 + r161212;
        double r161214 = K;
        double r161215 = 2.0;
        double r161216 = r161214 / r161215;
        double r161217 = cos(r161216);
        double r161218 = r161213 * r161217;
        double r161219 = r161200 * r161218;
        double r161220 = U;
        double r161221 = r161219 + r161220;
        return r161221;
}

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 17.0

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

  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 2020065 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))