Average Error: 30.3 → 30.3
Time: 18.7s
Precision: 64
\[\frac{\sin \left(x \cdot x\right)}{\cos \left(x \cdot x\right)}\]
\[\frac{\sin \left(x \cdot x\right)}{\log \left(\sqrt{e^{\cos \left(x \cdot x\right)}}\right) + \log \left(\sqrt{e^{\cos \left(x \cdot x\right)}}\right)}\]
\frac{\sin \left(x \cdot x\right)}{\cos \left(x \cdot x\right)}
\frac{\sin \left(x \cdot x\right)}{\log \left(\sqrt{e^{\cos \left(x \cdot x\right)}}\right) + \log \left(\sqrt{e^{\cos \left(x \cdot x\right)}}\right)}
double f(double x) {
        double r848279 = x;
        double r848280 = r848279 * r848279;
        double r848281 = sin(r848280);
        double r848282 = cos(r848280);
        double r848283 = r848281 / r848282;
        return r848283;
}

double f(double x) {
        double r848284 = x;
        double r848285 = r848284 * r848284;
        double r848286 = sin(r848285);
        double r848287 = cos(r848285);
        double r848288 = exp(r848287);
        double r848289 = sqrt(r848288);
        double r848290 = log(r848289);
        double r848291 = r848290 + r848290;
        double r848292 = r848286 / r848291;
        return r848292;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.3

    \[\frac{\sin \left(x \cdot x\right)}{\cos \left(x \cdot x\right)}\]
  2. Using strategy rm
  3. Applied add-log-exp30.3

    \[\leadsto \frac{\sin \left(x \cdot x\right)}{\color{blue}{\log \left(e^{\cos \left(x \cdot x\right)}\right)}}\]
  4. Using strategy rm
  5. Applied add-sqr-sqrt30.3

    \[\leadsto \frac{\sin \left(x \cdot x\right)}{\log \color{blue}{\left(\sqrt{e^{\cos \left(x \cdot x\right)}} \cdot \sqrt{e^{\cos \left(x \cdot x\right)}}\right)}}\]
  6. Applied log-prod30.3

    \[\leadsto \frac{\sin \left(x \cdot x\right)}{\color{blue}{\log \left(\sqrt{e^{\cos \left(x \cdot x\right)}}\right) + \log \left(\sqrt{e^{\cos \left(x \cdot x\right)}}\right)}}\]
  7. Final simplification30.3

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

Reproduce

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