Average Error: 17.6 → 0.5
Time: 21.6s
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 r141464 = J;
        double r141465 = l;
        double r141466 = exp(r141465);
        double r141467 = -r141465;
        double r141468 = exp(r141467);
        double r141469 = r141466 - r141468;
        double r141470 = r141464 * r141469;
        double r141471 = K;
        double r141472 = 2.0;
        double r141473 = r141471 / r141472;
        double r141474 = cos(r141473);
        double r141475 = r141470 * r141474;
        double r141476 = U;
        double r141477 = r141475 + r141476;
        return r141477;
}
↓
double f(double J, double l, double K, double U) {
        double r141478 = J;
        double r141479 = 0.3333333333333333;
        double r141480 = l;
        double r141481 = 3.0;
        double r141482 = pow(r141480, r141481);
        double r141483 = r141479 * r141482;
        double r141484 = 0.016666666666666666;
        double r141485 = 5.0;
        double r141486 = pow(r141480, r141485);
        double r141487 = r141484 * r141486;
        double r141488 = 2.0;
        double r141489 = r141488 * r141480;
        double r141490 = r141487 + r141489;
        double r141491 = r141483 + r141490;
        double r141492 = K;
        double r141493 = 2.0;
        double r141494 = r141492 / r141493;
        double r141495 = cos(r141494);
        double r141496 = r141491 * r141495;
        double r141497 = r141478 * r141496;
        double r141498 = U;
        double r141499 = r141497 + r141498;
        return r141499;
}

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 17.6

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

  2. Taylor expanded around 0 0.5

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

  4. Applied associate-*l*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020047 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))