Average Error: 17.2 → 0.3
Time: 8.6s
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 r109091 = J;
        double r109092 = l;
        double r109093 = exp(r109092);
        double r109094 = -r109092;
        double r109095 = exp(r109094);
        double r109096 = r109093 - r109095;
        double r109097 = r109091 * r109096;
        double r109098 = K;
        double r109099 = 2.0;
        double r109100 = r109098 / r109099;
        double r109101 = cos(r109100);
        double r109102 = r109097 * r109101;
        double r109103 = U;
        double r109104 = r109102 + r109103;
        return r109104;
}
↓
double f(double J, double l, double K, double U) {
        double r109105 = J;
        double r109106 = 0.3333333333333333;
        double r109107 = l;
        double r109108 = 3.0;
        double r109109 = pow(r109107, r109108);
        double r109110 = r109106 * r109109;
        double r109111 = 0.016666666666666666;
        double r109112 = 5.0;
        double r109113 = pow(r109107, r109112);
        double r109114 = r109111 * r109113;
        double r109115 = 2.0;
        double r109116 = r109115 * r109107;
        double r109117 = r109114 + r109116;
        double r109118 = r109110 + r109117;
        double r109119 = K;
        double r109120 = 2.0;
        double r109121 = r109119 / r109120;
        double r109122 = cos(r109121);
        double r109123 = r109118 * r109122;
        double r109124 = r109105 * r109123;
        double r109125 = U;
        double r109126 = r109124 + r109125;
        return r109126;
}

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 0.3

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

  4. Applied associate-*l*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020027 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))