Average Error: 10.5 → 2.3
Time: 16.3s
Precision: 64
$-10^{3} \le a \le 10^{3}$
$\frac{a}{{pR}^{2}} \cdot \left(\cos \left(p0 - pR \cdot t\right) - \cos p0\right)$
$0$
\frac{a}{{pR}^{2}} \cdot \left(\cos \left(p0 - pR \cdot t\right) - \cos p0\right)
0
double f(double a, double pR, double p0, double t) {
double r524748 = a;
double r524749 = pR;
double r524750 = 2.0;
double r524751 = pow(r524749, r524750);
double r524752 = r524748 / r524751;
double r524753 = p0;
double r524754 = t;
double r524755 = r524749 * r524754;
double r524756 = r524753 - r524755;
double r524757 = cos(r524756);
double r524758 = cos(r524753);
double r524759 = r524757 - r524758;
double r524760 = r524752 * r524759;
return r524760;
}


double f(double __attribute__((unused)) a, double __attribute__((unused)) pR, double __attribute__((unused)) p0, double __attribute__((unused)) t) {
double r524761 = 0.0;
return r524761;
}



# Try it out

Results

 In Out
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# Derivation

1. Initial program 10.5

$\frac{a}{{pR}^{2}} \cdot \left(\cos \left(p0 - pR \cdot t\right) - \cos p0\right)$
2. Taylor expanded around 0 2.3

$\leadsto \color{blue}{0}$
3. Final simplification2.3

$\leadsto 0$

# Reproduce

herbie shell --seed 1
(FPCore (a pR p0 t)
:name "a / pR^2 * (cos(p0 - pR*t) - cos(p0))"
:precision binary32
:pre (<= (- 1e3) a 1e3)
(* (/ a (pow pR 2)) (- (cos (- p0 (* pR t))) (cos p0))))