Average Error: 17.7 → 0.4
Time: 26.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3} + 2\right) \cdot \ell\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(\left(\ell \cdot \ell\right) \cdot \frac{1}{3} + 2\right) \cdot \ell\right)\right) + U
double f(double J, double l, double K, double U) {
        double r2520074 = J;
        double r2520075 = l;
        double r2520076 = exp(r2520075);
        double r2520077 = -r2520075;
        double r2520078 = exp(r2520077);
        double r2520079 = r2520076 - r2520078;
        double r2520080 = r2520074 * r2520079;
        double r2520081 = K;
        double r2520082 = 2.0;
        double r2520083 = r2520081 / r2520082;
        double r2520084 = cos(r2520083);
        double r2520085 = r2520080 * r2520084;
        double r2520086 = U;
        double r2520087 = r2520085 + r2520086;
        return r2520087;
}
↓
double f(double J, double l, double K, double U) {
        double r2520088 = J;
        double r2520089 = K;
        double r2520090 = 2.0;
        double r2520091 = r2520089 / r2520090;
        double r2520092 = cos(r2520091);
        double r2520093 = l;
        double r2520094 = 5.0;
        double r2520095 = pow(r2520093, r2520094);
        double r2520096 = 0.016666666666666666;
        double r2520097 = r2520095 * r2520096;
        double r2520098 = r2520093 * r2520093;
        double r2520099 = 0.3333333333333333;
        double r2520100 = r2520098 * r2520099;
        double r2520101 = r2520100 + r2520090;
        double r2520102 = r2520101 * r2520093;
        double r2520103 = r2520097 + r2520102;
        double r2520104 = r2520092 * r2520103;
        double r2520105 = r2520088 * r2520104;
        double r2520106 = U;
        double r2520107 = r2520105 + r2520106;
        return r2520107;
}

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 17.7

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

  2. Taylor expanded around 0 0.4

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

  3. Simplified0.4

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019133 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))