Average Error: 0.0 → 0.0
Time: 1.3m
Precision: 64
Internal Precision: 576
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\left(\sqrt{\frac{1}{x}} + 1\right) \cdot \left(\sqrt{\frac{1}{x}} - 1\right)\right)\]

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 difference-of-sqr-10.0

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))