Average Error: 17.5 → 0.4
Time: 26.8s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \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
double f(double J, double l, double K, double U) {
        double r75555 = J;
        double r75556 = l;
        double r75557 = exp(r75556);
        double r75558 = -r75556;
        double r75559 = exp(r75558);
        double r75560 = r75557 - r75559;
        double r75561 = r75555 * r75560;
        double r75562 = K;
        double r75563 = 2.0;
        double r75564 = r75562 / r75563;
        double r75565 = cos(r75564);
        double r75566 = r75561 * r75565;
        double r75567 = U;
        double r75568 = r75566 + r75567;
        return r75568;
}
↓
double f(double J, double l, double K, double U) {
        double r75569 = J;
        double r75570 = 0.3333333333333333;
        double r75571 = l;
        double r75572 = 3.0;
        double r75573 = pow(r75571, r75572);
        double r75574 = r75570 * r75573;
        double r75575 = 0.016666666666666666;
        double r75576 = 5.0;
        double r75577 = pow(r75571, r75576);
        double r75578 = r75575 * r75577;
        double r75579 = 2.0;
        double r75580 = r75579 * r75571;
        double r75581 = r75578 + r75580;
        double r75582 = r75574 + r75581;
        double r75583 = r75569 * r75582;
        double r75584 = K;
        double r75585 = 2.0;
        double r75586 = r75584 / r75585;
        double r75587 = cos(r75586);
        double r75588 = r75583 * r75587;
        double r75589 = U;
        double r75590 = r75588 + r75589;
        return r75590;
}

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 17.5

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

  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))