Average Error: 22.0 → 16.1
Time: 12.4s
Precision: 64
$\frac{{x}^{2}}{2 \cdot {a}^{2}}$
$\frac{{x}^{\left(\frac{2}{2}\right)}}{\frac{2 \cdot {a}^{2}}{{x}^{\left(\frac{2}{2}\right)}}}$
\frac{{x}^{2}}{2 \cdot {a}^{2}}
\frac{{x}^{\left(\frac{2}{2}\right)}}{\frac{2 \cdot {a}^{2}}{{x}^{\left(\frac{2}{2}\right)}}}
double f(double x, double a) {
double r34137 = x;
double r34138 = 2.0;
double r34139 = pow(r34137, r34138);
double r34140 = a;
double r34141 = pow(r34140, r34138);
double r34142 = r34138 * r34141;
double r34143 = r34139 / r34142;
return r34143;
}


double f(double x, double a) {
double r34144 = x;
double r34145 = 2.0;
double r34146 = 2.0;
double r34147 = r34145 / r34146;
double r34148 = pow(r34144, r34147);
double r34149 = a;
double r34150 = pow(r34149, r34145);
double r34151 = r34145 * r34150;
double r34152 = r34151 / r34148;
double r34153 = r34148 / r34152;
return r34153;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 22.0

$\frac{{x}^{2}}{2 \cdot {a}^{2}}$
2. Using strategy rm
3. Applied sqr-pow22.0

$\leadsto \frac{\color{blue}{{x}^{\left(\frac{2}{2}\right)} \cdot {x}^{\left(\frac{2}{2}\right)}}}{2 \cdot {a}^{2}}$
4. Applied associate-/l*16.1

$\leadsto \color{blue}{\frac{{x}^{\left(\frac{2}{2}\right)}}{\frac{2 \cdot {a}^{2}}{{x}^{\left(\frac{2}{2}\right)}}}}$
5. Final simplification16.1

$\leadsto \frac{{x}^{\left(\frac{2}{2}\right)}}{\frac{2 \cdot {a}^{2}}{{x}^{\left(\frac{2}{2}\right)}}}$

# Reproduce

herbie shell --seed 1
(FPCore (x a)
:name "(x^2)/(2*a^2)"
:precision binary64
(/ (pow x 2) (* 2 (pow a 2))))