Average Error: 0.0 → 0.1
Time: 18.4s
Precision: 64
Internal Precision: 320
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\left(-\sqrt[3]{\frac{f + n}{f - n}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\frac{f + n}{f - n}} \cdot \left(\sqrt[3]{\frac{f + n}{f - n}} \cdot \sqrt[3]{\frac{f + n}{f - n}}\right)} \cdot \sqrt[3]{\frac{f + n}{f - n}}\right)\]

Error

Bits error versus f

Bits error versus n

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Your Program's Arguments

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-cube-cbrt0.1

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

  6. Applied add-cube-cbrt0.1

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

  7. Final simplification0.1

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

Runtime

Time bar (total: 18.4s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.10.10.00.00%
herbie shell --seed 2018295 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))