Average Error: 60.7 → 53.7
Time: 20.6s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{\left(\left(\log \left(e^{\sqrt[3]{\sqrt[3]{n + f}}}\right) \cdot \left(-\sqrt[3]{\sqrt[3]{n + f}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{n + f}}\right) \cdot \sqrt[3]{n + f}}{\frac{f - n}{\sqrt[3]{n + f}}}\]

Error

Bits error versus f

Bits error versus n

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 60.7

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt60.7

    \[\leadsto \frac{-\color{blue}{\left(\sqrt[3]{f + n} \cdot \sqrt[3]{f + n}\right) \cdot \sqrt[3]{f + n}}}{f - n}\]

  4. Applied distribute-lft-neg-in60.7

    \[\leadsto \frac{\color{blue}{\left(-\sqrt[3]{f + n} \cdot \sqrt[3]{f + n}\right) \cdot \sqrt[3]{f + n}}}{f - n}\]

  5. Applied associate-/l*60.7

    \[\leadsto \color{blue}{\frac{-\sqrt[3]{f + n} \cdot \sqrt[3]{f + n}}{\frac{f - n}{\sqrt[3]{f + n}}}}\]
  6. Using strategy rm

  7. Applied add-log-exp53.8

    \[\leadsto \frac{-\color{blue}{\log \left(e^{\sqrt[3]{f + n}}\right)} \cdot \sqrt[3]{f + n}}{\frac{f - n}{\sqrt[3]{f + n}}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt53.8

    \[\leadsto \frac{-\log \left(e^{\color{blue}{\left(\sqrt[3]{\sqrt[3]{f + n}} \cdot \sqrt[3]{\sqrt[3]{f + n}}\right) \cdot \sqrt[3]{\sqrt[3]{f + n}}}}\right) \cdot \sqrt[3]{f + n}}{\frac{f - n}{\sqrt[3]{f + n}}}\]

  10. Applied exp-prod53.8

    \[\leadsto \frac{-\log \color{blue}{\left({\left(e^{\sqrt[3]{\sqrt[3]{f + n}} \cdot \sqrt[3]{\sqrt[3]{f + n}}}\right)}^{\left(\sqrt[3]{\sqrt[3]{f + n}}\right)}\right)} \cdot \sqrt[3]{f + n}}{\frac{f - n}{\sqrt[3]{f + n}}}\]

  11. Applied log-pow53.7

    \[\leadsto \frac{-\color{blue}{\left(\sqrt[3]{\sqrt[3]{f + n}} \cdot \log \left(e^{\sqrt[3]{\sqrt[3]{f + n}} \cdot \sqrt[3]{\sqrt[3]{f + n}}}\right)\right)} \cdot \sqrt[3]{f + n}}{\frac{f - n}{\sqrt[3]{f + n}}}\]
  12. Using strategy rm

  13. Applied exp-prod53.7

    \[\leadsto \frac{-\left(\sqrt[3]{\sqrt[3]{f + n}} \cdot \log \color{blue}{\left({\left(e^{\sqrt[3]{\sqrt[3]{f + n}}}\right)}^{\left(\sqrt[3]{\sqrt[3]{f + n}}\right)}\right)}\right) \cdot \sqrt[3]{f + n}}{\frac{f - n}{\sqrt[3]{f + n}}}\]

  14. Applied log-pow53.7

    \[\leadsto \frac{-\left(\sqrt[3]{\sqrt[3]{f + n}} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{f + n}} \cdot \log \left(e^{\sqrt[3]{\sqrt[3]{f + n}}}\right)\right)}\right) \cdot \sqrt[3]{f + n}}{\frac{f - n}{\sqrt[3]{f + n}}}\]

  15. Final simplification53.7

    \[\leadsto \frac{\left(\left(\log \left(e^{\sqrt[3]{\sqrt[3]{n + f}}}\right) \cdot \left(-\sqrt[3]{\sqrt[3]{n + f}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{n + f}}\right) \cdot \sqrt[3]{n + f}}{\frac{f - n}{\sqrt[3]{n + f}}}\]

Runtime

Time bar (total: 20.6s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))