Average Error: 17.5 → 0.4
Time: 23.6s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(\left(\frac{1}{3} \cdot {\ell}^{3}\right) \cdot J + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(\left(\frac{1}{3} \cdot {\ell}^{3}\right) \cdot J + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r74404 = J;
        double r74405 = l;
        double r74406 = exp(r74405);
        double r74407 = -r74405;
        double r74408 = exp(r74407);
        double r74409 = r74406 - r74408;
        double r74410 = r74404 * r74409;
        double r74411 = K;
        double r74412 = 2.0;
        double r74413 = r74411 / r74412;
        double r74414 = cos(r74413);
        double r74415 = r74410 * r74414;
        double r74416 = U;
        double r74417 = r74415 + r74416;
        return r74417;
}
↓
double f(double J, double l, double K, double U) {
        double r74418 = 0.3333333333333333;
        double r74419 = l;
        double r74420 = 3.0;
        double r74421 = pow(r74419, r74420);
        double r74422 = r74418 * r74421;
        double r74423 = J;
        double r74424 = r74422 * r74423;
        double r74425 = 0.016666666666666666;
        double r74426 = 5.0;
        double r74427 = pow(r74419, r74426);
        double r74428 = r74425 * r74427;
        double r74429 = 2.0;
        double r74430 = r74429 * r74419;
        double r74431 = r74428 + r74430;
        double r74432 = r74431 * r74423;
        double r74433 = r74424 + r74432;
        double r74434 = K;
        double r74435 = 2.0;
        double r74436 = r74434 / r74435;
        double r74437 = cos(r74436);
        double r74438 = r74433 * r74437;
        double r74439 = U;
        double r74440 = r74438 + r74439;
        return r74440;
}

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 distribute-rgt-in0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019291 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))