Average Error: 23.1 → 23.2
Time: 21.0s
Precision: 64
\[e^{\sin \left({\left(\cos x\right)}^{2}\right)}\]
\[{\left(e^{\sqrt{\sin \left({\left(\cos x\right)}^{2}\right)}}\right)}^{\left(\sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}\right)}\]
e^{\sin \left({\left(\cos x\right)}^{2}\right)}
{\left(e^{\sqrt{\sin \left({\left(\cos x\right)}^{2}\right)}}\right)}^{\left(\sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}\right)}
double f(double x) {
        double r184078 = x;
        double r184079 = cos(r184078);
        double r184080 = 2.0;
        double r184081 = pow(r184079, r184080);
        double r184082 = sin(r184081);
        double r184083 = exp(r184082);
        return r184083;
}

double f(double x) {
        double r184084 = x;
        double r184085 = cos(r184084);
        double r184086 = 2.0;
        double r184087 = pow(r184085, r184086);
        double r184088 = sin(r184087);
        double r184089 = sqrt(r184088);
        double r184090 = exp(r184089);
        double r184091 = exp(r184087);
        double r184092 = log(r184091);
        double r184093 = sin(r184092);
        double r184094 = sqrt(r184093);
        double r184095 = pow(r184090, r184094);
        return r184095;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.1

    \[e^{\sin \left({\left(\cos x\right)}^{2}\right)}\]
  2. Using strategy rm
  3. Applied add-log-exp23.1

    \[\leadsto e^{\sin \color{blue}{\left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}}\]
  4. Using strategy rm
  5. Applied add-sqr-sqrt23.2

    \[\leadsto e^{\color{blue}{\sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)} \cdot \sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}}}\]
  6. Applied exp-prod23.2

    \[\leadsto \color{blue}{{\left(e^{\sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}}\right)}^{\left(\sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}\right)}}\]
  7. Simplified23.2

    \[\leadsto {\color{blue}{\left(e^{\sqrt{\sin \left({\left(\cos x\right)}^{2}\right)}}\right)}}^{\left(\sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}\right)}\]
  8. Final simplification23.2

    \[\leadsto {\left(e^{\sqrt{\sin \left({\left(\cos x\right)}^{2}\right)}}\right)}^{\left(\sqrt{\sin \left(\log \left(e^{{\left(\cos x\right)}^{2}}\right)\right)}\right)}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "exp(sin(cos(x)^2))"
  :precision binary64
  (exp (sin (pow (cos x) 2))))