Average Error: 0.0 → 0.7
Time: 19.9s
Precision: 64
Internal Precision: 128
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(\sqrt{2 - \frac{2}{1 + t}} \cdot \sqrt{2 - \frac{2}{1 + t}}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

  2. Initial simplification0.0

    \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.7

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

  5. Final simplification0.7

    \[\leadsto 1 - \frac{1}{2 + \left(\sqrt{2 - \frac{2}{1 + t}} \cdot \sqrt{2 - \frac{2}{1 + t}}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

Runtime

Time bar (total: 19.9s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.70.70.70.0100%
herbie shell --seed 2018353 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))