Average Error: 30.4 → 0.2
Time: 8.5s
Precision: 64
$\sqrt{x + 1} - \sqrt{x}$
$\frac{1}{\sqrt{x + 1} + \sqrt{x}}$
\sqrt{x + 1} - \sqrt{x}
\frac{1}{\sqrt{x + 1} + \sqrt{x}}
double f(double x) {
double r1940897 = x;
double r1940898 = 1.0;
double r1940899 = r1940897 + r1940898;
double r1940900 = sqrt(r1940899);
double r1940901 = sqrt(r1940897);
double r1940902 = r1940900 - r1940901;
return r1940902;
}


double f(double x) {
double r1940903 = 1.0;
double r1940904 = x;
double r1940905 = r1940904 + r1940903;
double r1940906 = sqrt(r1940905);
double r1940907 = sqrt(r1940904);
double r1940908 = r1940906 + r1940907;
double r1940909 = r1940903 / r1940908;
return r1940909;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 30.4

$\sqrt{x + 1} - \sqrt{x}$
2. Using strategy rm
3. Applied flip--30.2

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

$\leadsto \frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}$
5. Final simplification0.2

$\leadsto \frac{1}{\sqrt{x + 1} + \sqrt{x}}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "sqrt(x +1) - sqrt(x)"
:precision binary64
(- (sqrt (+ x 1)) (sqrt x)))