Average Error: 30.3 → 30.0
Time: 19.1s
Precision: 64
Internal Precision: 1344
$\frac{1}{\sqrt{x + 2} - \sqrt{x}}$
$\frac{1}{\sqrt{x + 2} \cdot \sqrt{x + 2} - \sqrt{x} \cdot \sqrt{x}} \cdot \left(\sqrt{x + 2} + \sqrt{x}\right)$

# Try it out

Results

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# Derivation

1. Initial program 30.3

$\frac{1}{\sqrt{x + 2} - \sqrt{x}}$
2. Initial simplification30.3

$\leadsto \frac{1}{\sqrt{x + 2} - \sqrt{x}}$
3. Using strategy rm
4. Applied flip--30.3

$\leadsto \frac{1}{\color{blue}{\frac{\sqrt{x + 2} \cdot \sqrt{x + 2} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 2} + \sqrt{x}}}}$
5. Applied associate-/r/30.0

$\leadsto \color{blue}{\frac{1}{\sqrt{x + 2} \cdot \sqrt{x + 2} - \sqrt{x} \cdot \sqrt{x}} \cdot \left(\sqrt{x + 2} + \sqrt{x}\right)}$
6. Final simplification30.0

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

# Runtime

Time bar (total: 19.1s)Debug log

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