Average Error: 17.6 → 0.4
Time: 28.1s
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 r2355088 = J;
        double r2355089 = l;
        double r2355090 = exp(r2355089);
        double r2355091 = -r2355089;
        double r2355092 = exp(r2355091);
        double r2355093 = r2355090 - r2355092;
        double r2355094 = r2355088 * r2355093;
        double r2355095 = K;
        double r2355096 = 2.0;
        double r2355097 = r2355095 / r2355096;
        double r2355098 = cos(r2355097);
        double r2355099 = r2355094 * r2355098;
        double r2355100 = U;
        double r2355101 = r2355099 + r2355100;
        return r2355101;
}
↓
double f(double J, double l, double K, double U) {
        double r2355102 = J;
        double r2355103 = K;
        double r2355104 = 2.0;
        double r2355105 = r2355103 / r2355104;
        double r2355106 = cos(r2355105);
        double r2355107 = l;
        double r2355108 = 5.0;
        double r2355109 = pow(r2355107, r2355108);
        double r2355110 = 0.016666666666666666;
        double r2355111 = r2355109 * r2355110;
        double r2355112 = r2355107 * r2355107;
        double r2355113 = 0.3333333333333333;
        double r2355114 = r2355112 * r2355113;
        double r2355115 = r2355114 + r2355104;
        double r2355116 = r2355115 * r2355107;
        double r2355117 = r2355111 + r2355116;
        double r2355118 = r2355106 * r2355117;
        double r2355119 = r2355102 * r2355118;
        double r2355120 = U;
        double r2355121 = r2355119 + r2355120;
        return r2355121;
}

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

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

  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 2019130 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))