Average Error: 1.6 → 0
Time: 4.3s
Precision: 64
$\sqrt{x + 2} - \sqrt{x + 1}$
$\frac{\left(-1\right) + 2}{\sqrt{x + 2} + \sqrt{x + 1}}$
\sqrt{x + 2} - \sqrt{x + 1}
\frac{\left(-1\right) + 2}{\sqrt{x + 2} + \sqrt{x + 1}}
double f(double x) {
double r43671 = x;
double r43672 = 2.0;
double r43673 = r43671 + r43672;
double r43674 = sqrt(r43673);
double r43675 = 1.0;
double r43676 = r43671 + r43675;
double r43677 = sqrt(r43676);
double r43678 = r43674 - r43677;
return r43678;
}


double f(double x) {
double r43679 = 1.0;
double r43680 = -r43679;
double r43681 = 2.0;
double r43682 = r43680 + r43681;
double r43683 = x;
double r43684 = r43683 + r43681;
double r43685 = sqrt(r43684);
double r43686 = r43683 + r43679;
double r43687 = sqrt(r43686);
double r43688 = r43685 + r43687;
double r43689 = r43682 / r43688;
return r43689;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 1.6

$\sqrt{x + 2} - \sqrt{x + 1}$
2. Using strategy rm
3. Applied flip--1.6

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

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

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

# Reproduce

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