Average Error: 0.0 → 0.0
Time: 16.2s
Precision: 64
Internal Precision: 320
$\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\sqrt{x + 1} - \sqrt{x}}{2}$
$\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{2}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\sqrt{x + 1} - \sqrt{x}}{2}$
2. Using strategy rm
3. Applied flip--0.0

$\leadsto \frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}}}{2}$
4. Applied simplify0.0

$\leadsto \frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}}{2}$

# Runtime

Time bar (total: 16.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "(sqrt(x+1)+sqrt(x))/2+(sqrt(x+1)-sqrt(x))/2"
(+ (/ (+ (sqrt (+ x 1)) (sqrt x)) 2) (/ (- (sqrt (+ x 1)) (sqrt x)) 2)))