Average Error: 0.1 → 0.1
Time: 22.4s
Precision: 64
Internal Precision: 320
$\sqrt{x + 1} - \frac{\sqrt{x}}{\left|x\right|}$
$\sqrt{x + 1} - \frac{1}{\sqrt{\left|x\right|}} \cdot \frac{\sqrt{x}}{\sqrt{\left|x\right|}}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.1

$\sqrt{x + 1} - \frac{\sqrt{x}}{\left|x\right|}$
2. Using strategy rm

$\leadsto \sqrt{x + 1} - \frac{\sqrt{x}}{\color{blue}{\sqrt{\left|x\right|} \cdot \sqrt{\left|x\right|}}}$
4. Applied *-un-lft-identity0.2

$\leadsto \sqrt{x + 1} - \frac{\color{blue}{1 \cdot \sqrt{x}}}{\sqrt{\left|x\right|} \cdot \sqrt{\left|x\right|}}$
5. Applied times-frac0.1

$\leadsto \sqrt{x + 1} - \color{blue}{\frac{1}{\sqrt{\left|x\right|}} \cdot \frac{\sqrt{x}}{\sqrt{\left|x\right|}}}$

# Runtime

Time bar (total: 22.4s)Debug log

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