Average Error: 60.7 → 0.5
Time: 27.1s
Precision: 64
Internal Precision: 1344
\[\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}\]
\[-\left(x + \left(1 + \frac{1}{2} \cdot {x}^{2}\right)\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 60.7

    \[\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}\]
  2. Taylor expanded around 0 0.5

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

Runtime

Time bar (total: 27.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "log(1-x)/log(1+x)"
  (/ (log (- 1 x)) (log (+ 1 x))))