Average Error: 39.1 → 0.2
Time: 29.0s
Precision: 64
Internal Precision: 1344
$\frac{\left(-1\right) + \sqrt{1 + x}}{1 + \sqrt{1 + x}}$
$\frac{-x}{\left(\left(-1\right) - \sqrt{x + 1}\right) \cdot \left(1 + \sqrt{x + 1}\right)}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 39.1

$\frac{\left(-1\right) + \sqrt{1 + x}}{1 + \sqrt{1 + x}}$
2. Using strategy rm
3. Applied flip-+39.1

$\leadsto \frac{\color{blue}{\frac{\left(-1\right) \cdot \left(-1\right) - \sqrt{1 + x} \cdot \sqrt{1 + x}}{\left(-1\right) - \sqrt{1 + x}}}}{1 + \sqrt{1 + x}}$
4. Applied associate-/l/39.1

$\leadsto \color{blue}{\frac{\left(-1\right) \cdot \left(-1\right) - \sqrt{1 + x} \cdot \sqrt{1 + x}}{\left(1 + \sqrt{1 + x}\right) \cdot \left(\left(-1\right) - \sqrt{1 + x}\right)}}$
5. Simplified0.2

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

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

# Runtime

Time bar (total: 29.0s)Debug log

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