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

Error

Bits error versus x

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Your Program's Arguments

Results

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
  3. Applied add-sqr-sqrt0.2

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