Average Error: 0.0 → 0.0
Time: 24.4s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[-\sqrt[3]{\sqrt[3]{\frac{f + n}{f - n} \cdot \left(\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}\right)} \cdot \left(\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}\right)}\]

Error

Bits error versus f

Bits error versus n

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]

  2. Initial simplification0.0

    \[\leadsto -\frac{n + f}{f - n}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube0.0

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

  6. Applied add-cbrt-cube0.0

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

  7. Final simplification0.0

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

Runtime

Time bar (total: 24.4s)Debug logProfile

herbie shell --seed 2018346 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))