Average Error: 6.1 → 0
Time: 5.6s
Precision: 64
$x \gt 10$
$\sqrt{x + 1} - \sqrt{x + 2}$
$\frac{\left(-2\right) + 1}{\sqrt{x + 1} + \sqrt{x + 2}}$
\sqrt{x + 1} - \sqrt{x + 2}
\frac{\left(-2\right) + 1}{\sqrt{x + 1} + \sqrt{x + 2}}
double f(double x) {
double r3607836 = x;
double r3607837 = 1.0;
double r3607838 = r3607836 + r3607837;
double r3607839 = sqrt(r3607838);
double r3607840 = 2.0;
double r3607841 = r3607836 + r3607840;
double r3607842 = sqrt(r3607841);
double r3607843 = r3607839 - r3607842;
return r3607843;
}


double f(double x) {
double r3607844 = 2.0;
double r3607845 = -r3607844;
double r3607846 = 1.0;
double r3607847 = r3607845 + r3607846;
double r3607848 = x;
double r3607849 = r3607848 + r3607846;
double r3607850 = sqrt(r3607849);
double r3607851 = r3607848 + r3607844;
double r3607852 = sqrt(r3607851);
double r3607853 = r3607850 + r3607852;
double r3607854 = r3607847 / r3607853;
return r3607854;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 6.1

$\sqrt{x + 1} - \sqrt{x + 2}$
2. Using strategy rm
3. Applied flip--6.0

$\leadsto \color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x + 2} \cdot \sqrt{x + 2}}{\sqrt{x + 1} + \sqrt{x + 2}}}$
4. Simplified0

$\leadsto \frac{\color{blue}{1 + \left(0 - 2\right)}}{\sqrt{x + 1} + \sqrt{x + 2}}$
5. Final simplification0

$\leadsto \frac{\left(-2\right) + 1}{\sqrt{x + 1} + \sqrt{x + 2}}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sqrt(x+1) - sqrt(x+2)"
:precision binary32
:pre (> x 10)
(- (sqrt (+ x 1)) (sqrt (+ x 2))))