Average Error: 17.2 → 0.4
Time: 23.0s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\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 r84359 = J;
        double r84360 = l;
        double r84361 = exp(r84360);
        double r84362 = -r84360;
        double r84363 = exp(r84362);
        double r84364 = r84361 - r84363;
        double r84365 = r84359 * r84364;
        double r84366 = K;
        double r84367 = 2.0;
        double r84368 = r84366 / r84367;
        double r84369 = cos(r84368);
        double r84370 = r84365 * r84369;
        double r84371 = U;
        double r84372 = r84370 + r84371;
        return r84372;
}
↓
double f(double J, double l, double K, double U) {
        double r84373 = J;
        double r84374 = 0.3333333333333333;
        double r84375 = l;
        double r84376 = 3.0;
        double r84377 = pow(r84375, r84376);
        double r84378 = r84374 * r84377;
        double r84379 = 0.016666666666666666;
        double r84380 = 5.0;
        double r84381 = pow(r84375, r84380);
        double r84382 = r84379 * r84381;
        double r84383 = 2.0;
        double r84384 = r84383 * r84375;
        double r84385 = r84382 + r84384;
        double r84386 = r84378 + r84385;
        double r84387 = K;
        double r84388 = 2.0;
        double r84389 = r84387 / r84388;
        double r84390 = cos(r84389);
        double r84391 = r84386 * r84390;
        double r84392 = r84373 * r84391;
        double r84393 = U;
        double r84394 = r84392 + r84393;
        return r84394;
}

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 2019298 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))