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

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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)))))