Average Error: 32.6 → 32.6
Time: 29.4s
Precision: 64
$\frac{-1}{\tan \left(\frac{x \cdot pi}{360}\right)}$
$\frac{-1}{\frac{\sin \left(\frac{x \cdot pi}{360}\right)}{\cos \left(\frac{x \cdot pi}{360}\right)}}$
\frac{-1}{\tan \left(\frac{x \cdot pi}{360}\right)}
\frac{-1}{\frac{\sin \left(\frac{x \cdot pi}{360}\right)}{\cos \left(\frac{x \cdot pi}{360}\right)}}
double f(double x, double pi) {
double r15434061 = 1.0;
double r15434062 = -r15434061;
double r15434063 = x;
double r15434064 = pi;
double r15434065 = r15434063 * r15434064;
double r15434066 = 360.0;
double r15434067 = r15434065 / r15434066;
double r15434068 = tan(r15434067);
double r15434069 = r15434062 / r15434068;
return r15434069;
}


double f(double x, double pi) {
double r15434070 = -1.0;
double r15434071 = x;
double r15434072 = pi;
double r15434073 = r15434071 * r15434072;
double r15434074 = 360.0;
double r15434075 = r15434073 / r15434074;
double r15434076 = sin(r15434075);
double r15434077 = cos(r15434075);
double r15434078 = r15434076 / r15434077;
double r15434079 = r15434070 / r15434078;
return r15434079;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 32.6

$\frac{-1}{\tan \left(\frac{x \cdot pi}{360}\right)}$
2. Using strategy rm

$\leadsto \frac{-1}{\tan \left(\frac{x \cdot pi}{\color{blue}{\sqrt{360} \cdot \sqrt{360}}}\right)}$
4. Applied times-frac32.6

$\leadsto \frac{-1}{\tan \color{blue}{\left(\frac{x}{\sqrt{360}} \cdot \frac{pi}{\sqrt{360}}\right)}}$
5. Taylor expanded around -inf 32.6

$\leadsto \frac{-1}{\color{blue}{\frac{\sin \left(\frac{x \cdot pi}{{\left(\sqrt{360}\right)}^{2}}\right)}{\cos \left(\frac{x \cdot pi}{{\left(\sqrt{360}\right)}^{2}}\right)}}}$
6. Simplified32.6

$\leadsto \frac{-1}{\color{blue}{\frac{\sin \left(\frac{x \cdot pi}{360}\right)}{\cos \left(\frac{x \cdot pi}{360}\right)}}}$
7. Final simplification32.6

$\leadsto \frac{-1}{\frac{\sin \left(\frac{x \cdot pi}{360}\right)}{\cos \left(\frac{x \cdot pi}{360}\right)}}$

# Reproduce

herbie shell --seed 1
(FPCore (x pi)
:name "-1/tan(x * pi / 360)"
(/ (- 1) (tan (/ (* x pi) 360))))