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;
}



Try it out

Results

 In Out
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

$\leadsto \frac{\sin \left(x \cdot x\right)}{\color{blue}{\log \left(e^{\cos \left(x \cdot x\right)}\right)}}$
4. Using strategy rm

$\leadsto \frac{\sin \left(x \cdot x\right)}{\log \color{blue}{\left(\sqrt{e^{\cos \left(x \cdot x\right)}} \cdot \sqrt{e^{\cos \left(x \cdot x\right)}}\right)}}$
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))))