Average Error: 19.6 → 5.4
Time: 33.0s
Precision: 64
Internal Precision: 1088
$\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}$
$\frac{\frac{1}{x \cdot \left(x + 1\right)}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}$

# Try it out

Results

 In Out
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# Derivation

1. Initial program 19.6

$\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}$
2. Using strategy rm
3. Applied flip--19.6

$\leadsto \color{blue}{\frac{\frac{1}{\sqrt{x}} \cdot \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \cdot \frac{1}{\sqrt{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}}$
4. Applied simplify19.6

$\leadsto \frac{\color{blue}{\frac{1}{x} - \frac{1}{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}$
5. Using strategy rm
6. Applied frac-sub19.0

$\leadsto \frac{\color{blue}{\frac{1 \cdot \left(x + 1\right) - x \cdot 1}{x \cdot \left(x + 1\right)}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}$
7. Applied simplify5.4

$\leadsto \frac{\frac{\color{blue}{1}}{x \cdot \left(x + 1\right)}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}$

# Runtime

Time bar (total: 33.0s)Debug log

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