Average Error: 0.4 → 0.4
Time: 42.8s
Precision: 64
\[\frac{\cos \left({e}^{\left(-x\right)}\right)}{\sin \left({e}^{x}\right)}\]
\[\cos \left({e}^{\left(-x\right)}\right) \cdot \frac{1}{\sin \left(e^{\left(\sqrt[3]{\log e \cdot x} \cdot \sqrt[3]{\log e \cdot x}\right) \cdot \sqrt[3]{\log e \cdot x}}\right)}\]
\frac{\cos \left({e}^{\left(-x\right)}\right)}{\sin \left({e}^{x}\right)}
\cos \left({e}^{\left(-x\right)}\right) \cdot \frac{1}{\sin \left(e^{\left(\sqrt[3]{\log e \cdot x} \cdot \sqrt[3]{\log e \cdot x}\right) \cdot \sqrt[3]{\log e \cdot x}}\right)}
double f(double e, double x) {
        double r18797480 = e;
        double r18797481 = x;
        double r18797482 = -r18797481;
        double r18797483 = pow(r18797480, r18797482);
        double r18797484 = cos(r18797483);
        double r18797485 = pow(r18797480, r18797481);
        double r18797486 = sin(r18797485);
        double r18797487 = r18797484 / r18797486;
        return r18797487;
}

double f(double e, double x) {
        double r18797488 = e;
        double r18797489 = x;
        double r18797490 = -r18797489;
        double r18797491 = pow(r18797488, r18797490);
        double r18797492 = cos(r18797491);
        double r18797493 = 1.0;
        double r18797494 = log(r18797488);
        double r18797495 = r18797494 * r18797489;
        double r18797496 = cbrt(r18797495);
        double r18797497 = r18797496 * r18797496;
        double r18797498 = r18797497 * r18797496;
        double r18797499 = exp(r18797498);
        double r18797500 = sin(r18797499);
        double r18797501 = r18797493 / r18797500;
        double r18797502 = r18797492 * r18797501;
        return r18797502;
}

Error

Bits error versus e

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{\cos \left({e}^{\left(-x\right)}\right)}{\sin \left({e}^{x}\right)}\]
  2. Using strategy rm
  3. Applied div-inv0.4

    \[\leadsto \color{blue}{\cos \left({e}^{\left(-x\right)}\right) \cdot \frac{1}{\sin \left({e}^{x}\right)}}\]
  4. Simplified0.4

    \[\leadsto \cos \left({e}^{\left(-x\right)}\right) \cdot \color{blue}{\frac{1}{\sin \left(e^{x \cdot \log e}\right)}}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.4

    \[\leadsto \cos \left({e}^{\left(-x\right)}\right) \cdot \frac{1}{\sin \left(e^{\color{blue}{\left(\sqrt[3]{x \cdot \log e} \cdot \sqrt[3]{x \cdot \log e}\right) \cdot \sqrt[3]{x \cdot \log e}}}\right)}\]
  7. Final simplification0.4

    \[\leadsto \cos \left({e}^{\left(-x\right)}\right) \cdot \frac{1}{\sin \left(e^{\left(\sqrt[3]{\log e \cdot x} \cdot \sqrt[3]{\log e \cdot x}\right) \cdot \sqrt[3]{\log e \cdot x}}\right)}\]

Reproduce

herbie shell --seed 1 
(FPCore (e x)
  :name "cos(e^-x)/sin(e^x)"
  (/ (cos (pow e (- x))) (sin (pow e x))))