Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
Internal Precision: 320
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left((\left(\sqrt{\frac{1}{x}}\right) \cdot \left(\sqrt{\frac{1}{x}}\right) + -1)_*\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt0.0

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

  4. Applied fma-neg0.0

    \[\leadsto -\log \color{blue}{\left((\left(\sqrt{\frac{1}{x}}\right) \cdot \left(\sqrt{\frac{1}{x}}\right) + \left(-1\right))_*\right)}\]

  5. Final simplification0.0

    \[\leadsto -\log \left((\left(\sqrt{\frac{1}{x}}\right) \cdot \left(\sqrt{\frac{1}{x}}\right) + -1)_*\right)\]

Runtime

Time bar (total: 7.2s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.00%
herbie shell --seed 2018340 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))