Average Error: 17.7 → 0.4
Time: 47.0s
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 r90390 = J;
        double r90391 = l;
        double r90392 = exp(r90391);
        double r90393 = -r90391;
        double r90394 = exp(r90393);
        double r90395 = r90392 - r90394;
        double r90396 = r90390 * r90395;
        double r90397 = K;
        double r90398 = 2.0;
        double r90399 = r90397 / r90398;
        double r90400 = cos(r90399);
        double r90401 = r90396 * r90400;
        double r90402 = U;
        double r90403 = r90401 + r90402;
        return r90403;
}
↓
double f(double J, double l, double K, double U) {
        double r90404 = J;
        double r90405 = 0.3333333333333333;
        double r90406 = l;
        double r90407 = 3.0;
        double r90408 = pow(r90406, r90407);
        double r90409 = r90405 * r90408;
        double r90410 = 0.016666666666666666;
        double r90411 = 5.0;
        double r90412 = pow(r90406, r90411);
        double r90413 = r90410 * r90412;
        double r90414 = 2.0;
        double r90415 = r90414 * r90406;
        double r90416 = r90413 + r90415;
        double r90417 = r90409 + r90416;
        double r90418 = K;
        double r90419 = 2.0;
        double r90420 = r90418 / r90419;
        double r90421 = cos(r90420);
        double r90422 = r90417 * r90421;
        double r90423 = r90404 * r90422;
        double r90424 = U;
        double r90425 = r90423 + r90424;
        return r90425;
}

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. 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 2019323 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))