Average Error: 0.0 → 0.1
Time: 28.9s
Precision: 64
Internal Precision: 128
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left((e^{-\log x} - 1)^*\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[-\log \left(\frac{1}{x} - 1\right)\]

  2. Initial simplification0.0

    \[\leadsto -\log \left(\frac{1}{x} - 1\right)\]
  3. Using strategy rm

  4. Applied add-exp-log0.1

    \[\leadsto -\log \left(\color{blue}{e^{\log \left(\frac{1}{x}\right)}} - 1\right)\]

  5. Applied expm1-def0.1

    \[\leadsto -\log \color{blue}{\left((e^{\log \left(\frac{1}{x}\right)} - 1)^*\right)}\]

  6. Simplified0.1

    \[\leadsto -\log \left((e^{\color{blue}{-\log x}} - 1)^*\right)\]

  7. Final simplification0.1

    \[\leadsto -\log \left((e^{-\log x} - 1)^*\right)\]

Runtime

Time bar (total: 28.9s)Debug logProfile

herbie shell --seed 2018256 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))