Average Error: 0.0 → 0.0
Time: 58.7s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\left(\frac{-1}{f - n} \cdot \left(\frac{f + n}{f - n} \cdot \left(f + n\right)\right)\right) \cdot \frac{f + n}{f - n}}\]

Error

Bits error versus f

Bits error versus n

Try it out

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 div-inv0.0

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

  6. Applied associate-*r*0.0

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

  7. Final simplification0.0

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

Runtime

Time bar (total: 58.7s)Debug logProfile

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