Average Error: 58.6 → 58.6
Time: 8.8s
Precision: 64
Internal Precision: 1344
\[\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)\]
↓
\[\log \left(\frac{1 + x}{1 - x}\right) \cdot \frac{1}{2}\]

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 58.6

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

  2. Final simplification58.6

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

Runtime

Time bar (total: 8.8s)Debug logProfile

herbie shell --seed 2018214 
(FPCore (x)
  :name "Hyperbolic arc-(co)tangent"
  (* (/ 1 2) (log (/ (+ 1 x) (- 1 x)))))