Average Error: 0.0 → 0.0
Time: 28.5s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[-\sqrt[3]{\frac{f + n}{f - n} \cdot (e^{\log_* (1 + \frac{\frac{f + n}{f - n} \cdot \left(f + n\right)}{f - n})} - 1)^*}\]

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-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 expm1-log1p-u0.0

    \[\leadsto -\sqrt[3]{\color{blue}{(e^{\log_* (1 + \frac{n + f}{f - n} \cdot \frac{n + f}{f - n})} - 1)^*} \cdot \frac{n + f}{f - n}}\]
  7. Using strategy rm

  8. Applied associate-*l/0.0

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

  9. Final simplification0.0

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

Runtime

Time bar (total: 28.5s)Debug logProfile

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