Average Error: 30.0 → 1.8
Time: 39.8s
Precision: 64
Internal Precision: 1600
\[\log x - \log \left(\sinh x\right)\]
\[\frac{1}{180} \cdot {x}^{4} - \left(\frac{1}{6} \cdot {x}^{2} + e^{\log \left(\frac{1}{2835} \cdot {x}^{6}\right)}\right)\]

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.0

    \[\log x - \log \left(\sinh x\right)\]
  2. Taylor expanded around 0 1.8

    \[\leadsto \color{blue}{\frac{1}{180} \cdot {x}^{4} - \left(\frac{1}{6} \cdot {x}^{2} + \frac{1}{2835} \cdot {x}^{6}\right)}\]
  3. Using strategy rm
  4. Applied add-exp-log1.8

    \[\leadsto \frac{1}{180} \cdot {x}^{4} - \left(\frac{1}{6} \cdot {x}^{2} + \color{blue}{e^{\log \left(\frac{1}{2835} \cdot {x}^{6}\right)}}\right)\]

Runtime

Time bar (total: 39.8s)Debug log

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