Average Error: 17.3 → 0.6
Time: 22.1s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot \ell\right) \cdot 2\right)\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
U + \cos \left(\frac{K}{2}\right) \cdot \left(\left(J \cdot \ell\right) \cdot 2\right)
double f(double J, double l, double K, double U) {
        double r1385467 = J;
        double r1385468 = l;
        double r1385469 = exp(r1385468);
        double r1385470 = -r1385468;
        double r1385471 = exp(r1385470);
        double r1385472 = r1385469 - r1385471;
        double r1385473 = r1385467 * r1385472;
        double r1385474 = K;
        double r1385475 = 2.0;
        double r1385476 = r1385474 / r1385475;
        double r1385477 = cos(r1385476);
        double r1385478 = r1385473 * r1385477;
        double r1385479 = U;
        double r1385480 = r1385478 + r1385479;
        return r1385480;
}
↓
double f(double J, double l, double K, double U) {
        double r1385481 = U;
        double r1385482 = K;
        double r1385483 = 2.0;
        double r1385484 = r1385482 / r1385483;
        double r1385485 = cos(r1385484);
        double r1385486 = J;
        double r1385487 = l;
        double r1385488 = r1385486 * r1385487;
        double r1385489 = r1385488 * r1385483;
        double r1385490 = r1385485 * r1385489;
        double r1385491 = r1385481 + r1385490;
        return r1385491;
}

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. Simplified17.3

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

  3. Taylor expanded around 0 0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019153 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))