Average Error: 0.1 → 0.0
Time: 4.1s
Precision: 64
Internal Precision: 576
\[\frac{1}{\sqrt{x + 1}}\]
\[{\left(1 + x\right)}^{\left(-\frac{1}{2}\right)}\]

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

    \[\frac{1}{\sqrt{x + 1}}\]
  2. Initial simplification0.1

    \[\leadsto \frac{1}{\sqrt{x + 1}}\]
  3. Using strategy rm
  4. Applied pow1/20.1

    \[\leadsto \frac{1}{\color{blue}{{\left(x + 1\right)}^{\frac{1}{2}}}}\]
  5. Applied pow-flip0.0

    \[\leadsto \color{blue}{{\left(x + 1\right)}^{\left(-\frac{1}{2}\right)}}\]
  6. Final simplification0.0

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

Runtime

Time bar (total: 4.1s)Debug log

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