Average Error: 16.2 → 15.8
Time: 55.6s
Precision: 64
Internal Precision: 1344
\[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
↓
\[\frac{\frac{1}{\left(\sqrt[3]{\frac{\left(\alpha + \beta\right) + 2.0}{\beta}} \cdot \sqrt[3]{\frac{\left(\alpha + \beta\right) + 2.0}{\beta}}\right) \cdot \sqrt[3]{\frac{\left(\alpha + \beta\right) + 2.0}{\beta}}} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}{2.0}\]

Error

Bits error versus alpha

Bits error versus beta

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.2

    \[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
  2. Using strategy rm

  3. Applied div-sub16.2

    \[\leadsto \frac{\color{blue}{\left(\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \frac{\alpha}{\left(\alpha + \beta\right) + 2.0}\right)} + 1.0}{2.0}\]

  4. Applied associate-+l-15.7

    \[\leadsto \frac{\color{blue}{\frac{\beta}{\left(\alpha + \beta\right) + 2.0} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}}{2.0}\]
  5. Using strategy rm

  6. Applied clear-num15.7

    \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\left(\alpha + \beta\right) + 2.0}{\beta}}} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}{2.0}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt15.8

    \[\leadsto \frac{\frac{1}{\color{blue}{\left(\sqrt[3]{\frac{\left(\alpha + \beta\right) + 2.0}{\beta}} \cdot \sqrt[3]{\frac{\left(\alpha + \beta\right) + 2.0}{\beta}}\right) \cdot \sqrt[3]{\frac{\left(\alpha + \beta\right) + 2.0}{\beta}}}} - \left(\frac{\alpha}{\left(\alpha + \beta\right) + 2.0} - 1.0\right)}{2.0}\]

Runtime

Time bar (total: 55.6s)Debug logProfile

herbie shell --seed 2018195 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/1"
  :pre (and (> alpha -1) (> beta -1))
  (/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0))