Average Error: 17.6 → 12.9
Time: 10.1s
Precision: 64
$\sqrt{a + b \cdot {x}^{2}}$
$\sqrt{a + \left(b \cdot {x}^{\left(\frac{2}{2}\right)}\right) \cdot {x}^{\left(\frac{2}{2}\right)}}$
\sqrt{a + b \cdot {x}^{2}}
\sqrt{a + \left(b \cdot {x}^{\left(\frac{2}{2}\right)}\right) \cdot {x}^{\left(\frac{2}{2}\right)}}
double f(double a, double b, double x) {
double r198123 = a;
double r198124 = b;
double r198125 = x;
double r198126 = 2.0;
double r198127 = pow(r198125, r198126);
double r198128 = r198124 * r198127;
double r198129 = r198123 + r198128;
double r198130 = sqrt(r198129);
return r198130;
}

double f(double a, double b, double x) {
double r198131 = a;
double r198132 = b;
double r198133 = x;
double r198134 = 2.0;
double r198135 = 2.0;
double r198136 = r198134 / r198135;
double r198137 = pow(r198133, r198136);
double r198138 = r198132 * r198137;
double r198139 = r198138 * r198137;
double r198140 = r198131 + r198139;
double r198141 = sqrt(r198140);
return r198141;
}

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 17.6

$\sqrt{a + b \cdot {x}^{2}}$
2. Using strategy rm
3. Applied sqr-pow17.6

$\leadsto \sqrt{a + b \cdot \color{blue}{\left({x}^{\left(\frac{2}{2}\right)} \cdot {x}^{\left(\frac{2}{2}\right)}\right)}}$
4. Applied associate-*r*12.9

$\leadsto \sqrt{a + \color{blue}{\left(b \cdot {x}^{\left(\frac{2}{2}\right)}\right) \cdot {x}^{\left(\frac{2}{2}\right)}}}$
5. Final simplification12.9

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

# Reproduce

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