Average Error: 0.0 → 0.5
Time: 17.5s
Precision: 64
Internal Precision: 320
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[\left(x + \log x\right) + \left(x \cdot \frac{1}{2}\right) \cdot x\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.5

    \[\leadsto -\color{blue}{\left(-\left(\frac{1}{2} \cdot {x}^{2} + \left(\log x + x\right)\right)\right)}\]

  3. Applied simplify0.5

    \[\leadsto \color{blue}{\left(x + \log x\right) + \left(x \cdot \frac{1}{2}\right) \cdot x}\]

Runtime

Time bar (total: 17.5s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))