Average Error: 17.1 → 0.4
Time: 44.2s
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 r85364 = J;
        double r85365 = l;
        double r85366 = exp(r85365);
        double r85367 = -r85365;
        double r85368 = exp(r85367);
        double r85369 = r85366 - r85368;
        double r85370 = r85364 * r85369;
        double r85371 = K;
        double r85372 = 2.0;
        double r85373 = r85371 / r85372;
        double r85374 = cos(r85373);
        double r85375 = r85370 * r85374;
        double r85376 = U;
        double r85377 = r85375 + r85376;
        return r85377;
}
↓
double f(double J, double l, double K, double U) {
        double r85378 = J;
        double r85379 = 0.3333333333333333;
        double r85380 = l;
        double r85381 = 3.0;
        double r85382 = pow(r85380, r85381);
        double r85383 = r85379 * r85382;
        double r85384 = 0.016666666666666666;
        double r85385 = 5.0;
        double r85386 = pow(r85380, r85385);
        double r85387 = r85384 * r85386;
        double r85388 = 2.0;
        double r85389 = r85388 * r85380;
        double r85390 = r85387 + r85389;
        double r85391 = r85383 + r85390;
        double r85392 = K;
        double r85393 = 2.0;
        double r85394 = r85392 / r85393;
        double r85395 = cos(r85394);
        double r85396 = r85391 * r85395;
        double r85397 = r85378 * r85396;
        double r85398 = U;
        double r85399 = r85397 + r85398;
        return r85399;
}

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 17.1

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

  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 2019304 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))