Average Error: 17.3 → 0.4
Time: 27.9s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left({\ell}^{3} \cdot \left(\frac{1}{3} \cdot J\right) + J \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left({\ell}^{3} \cdot \left(\frac{1}{3} \cdot J\right) + J \cdot \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
double f(double J, double l, double K, double U) {
        double r238346 = J;
        double r238347 = l;
        double r238348 = exp(r238347);
        double r238349 = -r238347;
        double r238350 = exp(r238349);
        double r238351 = r238348 - r238350;
        double r238352 = r238346 * r238351;
        double r238353 = K;
        double r238354 = 2.0;
        double r238355 = r238353 / r238354;
        double r238356 = cos(r238355);
        double r238357 = r238352 * r238356;
        double r238358 = U;
        double r238359 = r238357 + r238358;
        return r238359;
}
↓
double f(double J, double l, double K, double U) {
        double r238360 = l;
        double r238361 = 3.0;
        double r238362 = pow(r238360, r238361);
        double r238363 = 0.3333333333333333;
        double r238364 = J;
        double r238365 = r238363 * r238364;
        double r238366 = r238362 * r238365;
        double r238367 = 0.016666666666666666;
        double r238368 = 5.0;
        double r238369 = pow(r238360, r238368);
        double r238370 = r238367 * r238369;
        double r238371 = 2.0;
        double r238372 = r238371 * r238360;
        double r238373 = r238370 + r238372;
        double r238374 = r238364 * r238373;
        double r238375 = r238366 + r238374;
        double r238376 = K;
        double r238377 = 2.0;
        double r238378 = r238376 / r238377;
        double r238379 = cos(r238378);
        double r238380 = r238375 * r238379;
        double r238381 = U;
        double r238382 = r238380 + r238381;
        return r238382;
}

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

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

  4. Applied distribute-lft-in0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020043 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))