Average Error: 17.5 → 0.4
Time: 39.3s
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 r85579 = J;
        double r85580 = l;
        double r85581 = exp(r85580);
        double r85582 = -r85580;
        double r85583 = exp(r85582);
        double r85584 = r85581 - r85583;
        double r85585 = r85579 * r85584;
        double r85586 = K;
        double r85587 = 2.0;
        double r85588 = r85586 / r85587;
        double r85589 = cos(r85588);
        double r85590 = r85585 * r85589;
        double r85591 = U;
        double r85592 = r85590 + r85591;
        return r85592;
}
↓
double f(double J, double l, double K, double U) {
        double r85593 = J;
        double r85594 = 0.3333333333333333;
        double r85595 = l;
        double r85596 = 3.0;
        double r85597 = pow(r85595, r85596);
        double r85598 = r85594 * r85597;
        double r85599 = 0.016666666666666666;
        double r85600 = 5.0;
        double r85601 = pow(r85595, r85600);
        double r85602 = r85599 * r85601;
        double r85603 = 2.0;
        double r85604 = r85603 * r85595;
        double r85605 = r85602 + r85604;
        double r85606 = r85598 + r85605;
        double r85607 = K;
        double r85608 = 2.0;
        double r85609 = r85607 / r85608;
        double r85610 = cos(r85609);
        double r85611 = r85606 * r85610;
        double r85612 = r85593 * r85611;
        double r85613 = U;
        double r85614 = r85612 + r85613;
        return r85614;
}

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. 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 2019347 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))