Average Error: 17.7 → 0.4
Time: 23.0s
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 r81076 = J;
        double r81077 = l;
        double r81078 = exp(r81077);
        double r81079 = -r81077;
        double r81080 = exp(r81079);
        double r81081 = r81078 - r81080;
        double r81082 = r81076 * r81081;
        double r81083 = K;
        double r81084 = 2.0;
        double r81085 = r81083 / r81084;
        double r81086 = cos(r81085);
        double r81087 = r81082 * r81086;
        double r81088 = U;
        double r81089 = r81087 + r81088;
        return r81089;
}
↓
double f(double J, double l, double K, double U) {
        double r81090 = J;
        double r81091 = 0.3333333333333333;
        double r81092 = l;
        double r81093 = 3.0;
        double r81094 = pow(r81092, r81093);
        double r81095 = r81091 * r81094;
        double r81096 = 0.016666666666666666;
        double r81097 = 5.0;
        double r81098 = pow(r81092, r81097);
        double r81099 = r81096 * r81098;
        double r81100 = 2.0;
        double r81101 = r81100 * r81092;
        double r81102 = r81099 + r81101;
        double r81103 = r81095 + r81102;
        double r81104 = r81090 * r81103;
        double r81105 = K;
        double r81106 = 2.0;
        double r81107 = r81105 / r81106;
        double r81108 = cos(r81107);
        double r81109 = r81104 * r81108;
        double r81110 = U;
        double r81111 = r81109 + r81110;
        return r81111;
}

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

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

  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 2019297 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))