Average Error: 17.8 → 0.7
Time: 10.2s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[2 \cdot \left(J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \ell\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
2 \cdot \left(J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \ell\right)\right) + U
double f(double J, double l, double K, double U) {
        double r167820 = J;
        double r167821 = l;
        double r167822 = exp(r167821);
        double r167823 = -r167821;
        double r167824 = exp(r167823);
        double r167825 = r167822 - r167824;
        double r167826 = r167820 * r167825;
        double r167827 = K;
        double r167828 = 2.0;
        double r167829 = r167827 / r167828;
        double r167830 = cos(r167829);
        double r167831 = r167826 * r167830;
        double r167832 = U;
        double r167833 = r167831 + r167832;
        return r167833;
}
↓
double f(double J, double l, double K, double U) {
        double r167834 = 2.0;
        double r167835 = J;
        double r167836 = 0.5;
        double r167837 = K;
        double r167838 = r167836 * r167837;
        double r167839 = cos(r167838);
        double r167840 = l;
        double r167841 = r167839 * r167840;
        double r167842 = r167835 * r167841;
        double r167843 = r167834 * r167842;
        double r167844 = U;
        double r167845 = r167843 + r167844;
        return r167845;
}

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 17.8

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

  2. Taylor expanded around 0 0.7

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

  3. Taylor expanded around inf 0.7

    \[\leadsto \color{blue}{2 \cdot \left(J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \ell\right)\right)} + U\]

  4. Final simplification0.7

    \[\leadsto 2 \cdot \left(J \cdot \left(\cos \left(0.5 \cdot K\right) \cdot \ell\right)\right) + U\]

Reproduce

herbie shell --seed 2019322 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))