Average Error: 11.1 → 3.4
Time: 18.2s
Precision: 64
$\left(\frac{1}{{pR}^{2}} \cdot \left(\cos \left(p0 - pR \cdot t\right) - \cos p0\right)\right) \cdot a$
$0 \cdot a$
\left(\frac{1}{{pR}^{2}} \cdot \left(\cos \left(p0 - pR \cdot t\right) - \cos p0\right)\right) \cdot a
0 \cdot a
double f(double pR, double p0, double t, double a) {
double r534803 = 1.0;
double r534804 = pR;
double r534805 = 2.0;
double r534806 = pow(r534804, r534805);
double r534807 = r534803 / r534806;
double r534808 = p0;
double r534809 = t;
double r534810 = r534804 * r534809;
double r534811 = r534808 - r534810;
double r534812 = cos(r534811);
double r534813 = cos(r534808);
double r534814 = r534812 - r534813;
double r534815 = r534807 * r534814;
double r534816 = a;
double r534817 = r534815 * r534816;
return r534817;
}


double f(double __attribute__((unused)) pR, double __attribute__((unused)) p0, double __attribute__((unused)) t, double a) {
double r534818 = 0.0;
double r534819 = a;
double r534820 = r534818 * r534819;
return r534820;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 11.1

$\left(\frac{1}{{pR}^{2}} \cdot \left(\cos \left(p0 - pR \cdot t\right) - \cos p0\right)\right) \cdot a$
2. Taylor expanded around 0 3.4

$\leadsto \color{blue}{0} \cdot a$
3. Final simplification3.4

$\leadsto 0 \cdot a$

# Reproduce

herbie shell --seed 1
(FPCore (pR p0 t a)
:name "1 / pR^2 * (cos(p0 - pR*t) - cos(p0)) * a"
:precision binary32
(* (* (/ 1 (pow pR 2)) (- (cos (- p0 (* pR t))) (cos p0))) a))