Average Error: 17.4 → 0.4
Time: 39.8s
Precision: 64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(\left(\ell \cdot 2 + \left(\left(\ell \cdot \ell\right) \cdot \ell\right) \cdot \frac{1}{3}\right) + \frac{1}{60} \cdot \left(\left(\ell \cdot \ell\right) \cdot \left(\left(\ell \cdot \ell\right) \cdot \ell\right)\right)\right)\right) + U\]
\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(\left(\ell \cdot 2 + \left(\left(\ell \cdot \ell\right) \cdot \ell\right) \cdot \frac{1}{3}\right) + \frac{1}{60} \cdot \left(\left(\ell \cdot \ell\right) \cdot \left(\left(\ell \cdot \ell\right) \cdot \ell\right)\right)\right)\right) + U
double f(double J, double l, double K, double U) {
        double r4239262 = J;
        double r4239263 = l;
        double r4239264 = exp(r4239263);
        double r4239265 = -r4239263;
        double r4239266 = exp(r4239265);
        double r4239267 = r4239264 - r4239266;
        double r4239268 = r4239262 * r4239267;
        double r4239269 = K;
        double r4239270 = 2.0;
        double r4239271 = r4239269 / r4239270;
        double r4239272 = cos(r4239271);
        double r4239273 = r4239268 * r4239272;
        double r4239274 = U;
        double r4239275 = r4239273 + r4239274;
        return r4239275;
}
↓
double f(double J, double l, double K, double U) {
        double r4239276 = J;
        double r4239277 = K;
        double r4239278 = 2.0;
        double r4239279 = r4239277 / r4239278;
        double r4239280 = cos(r4239279);
        double r4239281 = l;
        double r4239282 = r4239281 * r4239278;
        double r4239283 = r4239281 * r4239281;
        double r4239284 = r4239283 * r4239281;
        double r4239285 = 0.3333333333333333;
        double r4239286 = r4239284 * r4239285;
        double r4239287 = r4239282 + r4239286;
        double r4239288 = 0.016666666666666666;
        double r4239289 = r4239283 * r4239284;
        double r4239290 = r4239288 * r4239289;
        double r4239291 = r4239287 + r4239290;
        double r4239292 = r4239280 * r4239291;
        double r4239293 = r4239276 * r4239292;
        double r4239294 = U;
        double r4239295 = r4239293 + r4239294;
        return r4239295;
}

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 17.4

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

  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

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

  5. Applied associate-*l*0.4

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019144 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U))