Average Error: 0.6 → 0.6
Time: 12.9s
Precision: 64
\[\frac{\sin x + \tanh x}{\sin x - \cos x}\]
\[\frac{\frac{\sin x + \tanh x}{\sin x - \cos x}}{1}\]
\frac{\sin x + \tanh x}{\sin x - \cos x}
\frac{\frac{\sin x + \tanh x}{\sin x - \cos x}}{1}
double f(double x) {
        double r160765 = x;
        double r160766 = sin(r160765);
        double r160767 = tanh(r160765);
        double r160768 = r160766 + r160767;
        double r160769 = cos(r160765);
        double r160770 = r160766 - r160769;
        double r160771 = r160768 / r160770;
        return r160771;
}

double f(double x) {
        double r160772 = x;
        double r160773 = sin(r160772);
        double r160774 = tanh(r160772);
        double r160775 = r160773 + r160774;
        double r160776 = cos(r160772);
        double r160777 = r160773 - r160776;
        double r160778 = r160775 / r160777;
        double r160779 = 1.0;
        double r160780 = r160778 / r160779;
        return r160780;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[\frac{\sin x + \tanh x}{\sin x - \cos x}\]
  2. Using strategy rm
  3. Applied add-log-exp0.6

    \[\leadsto \frac{\sin x + \tanh x}{\sin x - \color{blue}{\log \left(e^{\cos x}\right)}}\]
  4. Applied add-log-exp0.7

    \[\leadsto \frac{\sin x + \tanh x}{\color{blue}{\log \left(e^{\sin x}\right)} - \log \left(e^{\cos x}\right)}\]
  5. Applied diff-log0.7

    \[\leadsto \frac{\sin x + \tanh x}{\color{blue}{\log \left(\frac{e^{\sin x}}{e^{\cos x}}\right)}}\]
  6. Simplified0.6

    \[\leadsto \frac{\sin x + \tanh x}{\log \color{blue}{\left(e^{\sin x - \cos x}\right)}}\]
  7. Using strategy rm
  8. Applied *-un-lft-identity0.6

    \[\leadsto \frac{\sin x + \tanh x}{\log \left(e^{\color{blue}{1 \cdot \left(\sin x - \cos x\right)}}\right)}\]
  9. Applied exp-prod0.6

    \[\leadsto \frac{\sin x + \tanh x}{\log \color{blue}{\left({\left(e^{1}\right)}^{\left(\sin x - \cos x\right)}\right)}}\]
  10. Applied log-pow0.6

    \[\leadsto \frac{\sin x + \tanh x}{\color{blue}{\left(\sin x - \cos x\right) \cdot \log \left(e^{1}\right)}}\]
  11. Applied associate-/r*0.6

    \[\leadsto \color{blue}{\frac{\frac{\sin x + \tanh x}{\sin x - \cos x}}{\log \left(e^{1}\right)}}\]
  12. Final simplification0.6

    \[\leadsto \frac{\frac{\sin x + \tanh x}{\sin x - \cos x}}{1}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "(sin(x) + tanh(x))/(sin(x) - cos(x))"
  :precision binary64
  (/ (+ (sin x) (tanh x)) (- (sin x) (cos x))))