Average Error: 0.0 → 0.0
Time: 19.4s
Precision: 64
Internal Precision: 128
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[-\log \left((e^{\log_* (1 + e^{\sqrt[3]{\frac{f + n}{f - n} \cdot \left(\frac{f + n}{f - n} \cdot \frac{f + n}{f - n}\right)}})} - 1)^*\right)\]

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-log-exp0.0

    \[\leadsto -\color{blue}{\log \left(e^{\frac{n + f}{f - n}}\right)}\]
  5. Using strategy rm

  6. Applied expm1-log1p-u0.0

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

  8. Applied add-cbrt-cube0.0

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

  9. Final simplification0.0

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

Runtime

Time bar (total: 19.4s)Debug logProfile

herbie shell --seed 2018348 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))