Average Error: 17.2 → 0.4
Time: 29.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left(\left(\ell \cdot \left(\ell \cdot \frac{1}{3}\right)\right) \cdot \ell\right) \cdot J + \left(\left(J \cdot \frac{1}{60}\right) \cdot {\ell}^{5} + \left(2 \cdot \ell\right) \cdot J\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left(\left(\ell \cdot \left(\ell \cdot \frac{1}{3}\right)\right) \cdot \ell\right) \cdot J + \left(\left(J \cdot \frac{1}{60}\right) \cdot {\ell}^{5} + \left(2 \cdot \ell\right) \cdot J\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r3850096 = J;
        double r3850097 = l;
        double r3850098 = exp(r3850097);
        double r3850099 = -r3850097;
        double r3850100 = exp(r3850099);
        double r3850101 = r3850098 - r3850100;
        double r3850102 = r3850096 * r3850101;
        double r3850103 = K;
        double r3850104 = 2.0;
        double r3850105 = r3850103 / r3850104;
        double r3850106 = cos(r3850105);
        double r3850107 = r3850102 * r3850106;
        double r3850108 = U;
        double r3850109 = r3850107 + r3850108;
        return r3850109;
}
↓
double f(double J, double l, double K, double U) {
        double r3850110 = l;
        double r3850111 = 0.3333333333333333;
        double r3850112 = r3850110 * r3850111;
        double r3850113 = r3850110 * r3850112;
        double r3850114 = r3850113 * r3850110;
        double r3850115 = J;
        double r3850116 = r3850114 * r3850115;
        double r3850117 = 0.016666666666666666;
        double r3850118 = r3850115 * r3850117;
        double r3850119 = 5.0;
        double r3850120 = pow(r3850110, r3850119);
        double r3850121 = r3850118 * r3850120;
        double r3850122 = 2.0;
        double r3850123 = r3850122 * r3850110;
        double r3850124 = r3850123 * r3850115;
        double r3850125 = r3850121 + r3850124;
        double r3850126 = r3850116 + r3850125;
        double r3850127 = K;
        double r3850128 = r3850127 / r3850122;
        double r3850129 = cos(r3850128);
        double r3850130 = r3850126 * r3850129;
        double r3850131 = U;
        double r3850132 = r3850130 + r3850131;
        return r3850132;
}

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 17.2

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

  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

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

  4. Taylor expanded around inf 0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019158 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))