Average Error: 59.7 → 0.4
Time: 12.0s
Precision: 64
$\sqrt{x - 12} - \sqrt{x}$
$\frac{1}{\sqrt{x - 12} + \sqrt{x}} \cdot \left(-12 + \left(x - x\right)\right)$
\sqrt{x - 12} - \sqrt{x}
\frac{1}{\sqrt{x - 12} + \sqrt{x}} \cdot \left(-12 + \left(x - x\right)\right)
double f(double x) {
double r40278047 = x;
double r40278048 = 12.0;
double r40278049 = r40278047 - r40278048;
double r40278050 = sqrt(r40278049);
double r40278051 = sqrt(r40278047);
double r40278052 = r40278050 - r40278051;
return r40278052;
}


double f(double x) {
double r40278053 = 1.0;
double r40278054 = x;
double r40278055 = 12.0;
double r40278056 = r40278054 - r40278055;
double r40278057 = sqrt(r40278056);
double r40278058 = sqrt(r40278054);
double r40278059 = r40278057 + r40278058;
double r40278060 = r40278053 / r40278059;
double r40278061 = -12.0;
double r40278062 = r40278054 - r40278054;
double r40278063 = r40278061 + r40278062;
double r40278064 = r40278060 * r40278063;
return r40278064;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 59.7

$\sqrt{x - 12} - \sqrt{x}$
2. Using strategy rm
3. Applied flip--59.2

$\leadsto \color{blue}{\frac{\sqrt{x - 12} \cdot \sqrt{x - 12} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x - 12} + \sqrt{x}}}$
4. Simplified0.3

$\leadsto \frac{\color{blue}{-12 + \left(x - x\right)}}{\sqrt{x - 12} + \sqrt{x}}$
5. Using strategy rm
6. Applied div-inv0.4

$\leadsto \color{blue}{\left(-12 + \left(x - x\right)\right) \cdot \frac{1}{\sqrt{x - 12} + \sqrt{x}}}$
7. Final simplification0.4

$\leadsto \frac{1}{\sqrt{x - 12} + \sqrt{x}} \cdot \left(-12 + \left(x - x\right)\right)$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sqrt(x-12) - sqrt(x)"
(- (sqrt (- x 12)) (sqrt x)))