Average Error: 17.2 → 0.4
Time: 24.8s
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 r123293 = J;
        double r123294 = l;
        double r123295 = exp(r123294);
        double r123296 = -r123294;
        double r123297 = exp(r123296);
        double r123298 = r123295 - r123297;
        double r123299 = r123293 * r123298;
        double r123300 = K;
        double r123301 = 2.0;
        double r123302 = r123300 / r123301;
        double r123303 = cos(r123302);
        double r123304 = r123299 * r123303;
        double r123305 = U;
        double r123306 = r123304 + r123305;
        return r123306;
}
↓
double f(double J, double l, double K, double U) {
        double r123307 = J;
        double r123308 = 0.3333333333333333;
        double r123309 = l;
        double r123310 = 3.0;
        double r123311 = pow(r123309, r123310);
        double r123312 = r123308 * r123311;
        double r123313 = 0.016666666666666666;
        double r123314 = 5.0;
        double r123315 = pow(r123309, r123314);
        double r123316 = r123313 * r123315;
        double r123317 = 2.0;
        double r123318 = r123317 * r123309;
        double r123319 = r123316 + r123318;
        double r123320 = r123312 + r123319;
        double r123321 = K;
        double r123322 = 2.0;
        double r123323 = r123321 / r123322;
        double r123324 = cos(r123323);
        double r123325 = r123320 * r123324;
        double r123326 = r123307 * r123325;
        double r123327 = U;
        double r123328 = r123326 + r123327;
        return r123328;
}

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

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

  4. Applied associate-*l*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019351 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))