Average Error: 17.5 → 0.4
Time: 26.1s
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 r113585 = J;
        double r113586 = l;
        double r113587 = exp(r113586);
        double r113588 = -r113586;
        double r113589 = exp(r113588);
        double r113590 = r113587 - r113589;
        double r113591 = r113585 * r113590;
        double r113592 = K;
        double r113593 = 2.0;
        double r113594 = r113592 / r113593;
        double r113595 = cos(r113594);
        double r113596 = r113591 * r113595;
        double r113597 = U;
        double r113598 = r113596 + r113597;
        return r113598;
}
↓
double f(double J, double l, double K, double U) {
        double r113599 = J;
        double r113600 = 0.3333333333333333;
        double r113601 = l;
        double r113602 = 3.0;
        double r113603 = pow(r113601, r113602);
        double r113604 = r113600 * r113603;
        double r113605 = 0.016666666666666666;
        double r113606 = 5.0;
        double r113607 = pow(r113601, r113606);
        double r113608 = r113605 * r113607;
        double r113609 = 2.0;
        double r113610 = r113609 * r113601;
        double r113611 = r113608 + r113610;
        double r113612 = r113604 + r113611;
        double r113613 = r113599 * r113612;
        double r113614 = K;
        double r113615 = 2.0;
        double r113616 = r113614 / r113615;
        double r113617 = cos(r113616);
        double r113618 = r113613 * r113617;
        double r113619 = U;
        double r113620 = r113618 + r113619;
        return r113620;
}

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 2019350 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))