Average Error: 0.0 → 0.0
Time: 50.2s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\frac{f + n}{f - n} \cdot \left(\frac{-1}{f - n} \cdot \left(\frac{f + n}{f - n} \cdot \left(f + n\right)\right)\right)}\]

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. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  5. Applied flip--30.7

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

  6. Applied associate-/r/30.7

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

  7. Applied associate-*l*30.7

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

  8. Simplified0.0

    \[\leadsto \sqrt[3]{\left(\color{blue}{\frac{-1}{f - n}} \cdot \left(\left(f + n\right) \cdot \frac{-\left(f + n\right)}{f - n}\right)\right) \cdot \frac{-\left(f + n\right)}{f - n}}\]

  9. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{f + n}{f - n} \cdot \left(\frac{-1}{f - n} \cdot \left(\frac{f + n}{f - n} \cdot \left(f + n\right)\right)\right)}\]

Runtime

Time bar (total: 50.2s)Debug logProfile

herbie shell --seed 2018273 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))