Average Error: 0.1 → 0.0
Time: 18.4s
Precision: 64
Internal Precision: 320
\[\sqrt{x + 1} - \sqrt{x} \cdot x\]
\[\sqrt{x + 1} - {x}^{\left(\frac{1}{2} + 1\right)}\]

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

    \[\sqrt{x + 1} - \sqrt{x} \cdot x\]
  2. Using strategy rm
  3. Applied pow1/20.1

    \[\leadsto \sqrt{x + 1} - \color{blue}{{x}^{\frac{1}{2}}} \cdot x\]
  4. Applied pow-plus0.0

    \[\leadsto \sqrt{x + 1} - \color{blue}{{x}^{\left(\frac{1}{2} + 1\right)}}\]

Runtime

Time bar (total: 18.4s)Debug log

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