Average Error: 17.3 → 0.4
Time: 28.8s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\left(\frac{1}{3} \cdot \ell\right) \cdot \ell + 2\right)\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + \ell \cdot \left(\left(\frac{1}{3} \cdot \ell\right) \cdot \ell + 2\right)\right)\right) + U
double f(double J, double l, double K, double U) {
        double r3690625 = J;
        double r3690626 = l;
        double r3690627 = exp(r3690626);
        double r3690628 = -r3690626;
        double r3690629 = exp(r3690628);
        double r3690630 = r3690627 - r3690629;
        double r3690631 = r3690625 * r3690630;
        double r3690632 = K;
        double r3690633 = 2.0;
        double r3690634 = r3690632 / r3690633;
        double r3690635 = cos(r3690634);
        double r3690636 = r3690631 * r3690635;
        double r3690637 = U;
        double r3690638 = r3690636 + r3690637;
        return r3690638;
}
↓
double f(double J, double l, double K, double U) {
        double r3690639 = J;
        double r3690640 = K;
        double r3690641 = 2.0;
        double r3690642 = r3690640 / r3690641;
        double r3690643 = cos(r3690642);
        double r3690644 = 0.016666666666666666;
        double r3690645 = l;
        double r3690646 = 5.0;
        double r3690647 = pow(r3690645, r3690646);
        double r3690648 = r3690644 * r3690647;
        double r3690649 = 0.3333333333333333;
        double r3690650 = r3690649 * r3690645;
        double r3690651 = r3690650 * r3690645;
        double r3690652 = r3690651 + r3690641;
        double r3690653 = r3690645 * r3690652;
        double r3690654 = r3690648 + r3690653;
        double r3690655 = r3690643 * r3690654;
        double r3690656 = r3690639 * r3690655;
        double r3690657 = U;
        double r3690658 = r3690656 + r3690657;
        return r3690658;
}

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 17.3

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

  2. Taylor expanded around 0 0.4

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

  3. Simplified0.4

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019164 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))