Average Error: 0.1 → 0.2
Time: 13.9s
Precision: 64
Internal Precision: 320
\[\sqrt{x} - \frac{1.0}{\sqrt{x}}\]
\[\frac{\sqrt{x} \cdot \sqrt{x} - \frac{1.0}{\sqrt{x}} \cdot \frac{1.0}{\sqrt{x}}}{\sqrt{x} + \frac{1.0}{\sqrt{x}}}\]

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.1

    \[\sqrt{x} - \frac{1.0}{\sqrt{x}}\]
  2. Initial simplification0.1

    \[\leadsto \sqrt{x} - \frac{1.0}{\sqrt{x}}\]
  3. Using strategy rm
  4. Applied flip--0.2

    \[\leadsto \color{blue}{\frac{\sqrt{x} \cdot \sqrt{x} - \frac{1.0}{\sqrt{x}} \cdot \frac{1.0}{\sqrt{x}}}{\sqrt{x} + \frac{1.0}{\sqrt{x}}}}\]
  5. Final simplification0.2

    \[\leadsto \frac{\sqrt{x} \cdot \sqrt{x} - \frac{1.0}{\sqrt{x}} \cdot \frac{1.0}{\sqrt{x}}}{\sqrt{x} + \frac{1.0}{\sqrt{x}}}\]

Runtime

Time bar (total: 13.9s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sqrt(x) - 1. / sqrt(x)"
  (- (sqrt x) (/ 1.0 (sqrt x))))