Average Error: 19.1 → 19.1
Time: 29.9s
Precision: 64
Internal Precision: 832
\[\log_* (1 + x) - x\]
\[\frac{\log_* (1 + x) + x}{\frac{\log_* (1 + x) + x}{\log_* (1 + x) - x}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 19.1

    \[\log_* (1 + x) - x\]
  2. Using strategy rm
  3. Applied flip--28.7

    \[\leadsto \color{blue}{\frac{\log_* (1 + x) \cdot \log_* (1 + x) - x \cdot x}{\log_* (1 + x) + x}}\]
  4. Using strategy rm
  5. Applied difference-of-squares28.7

    \[\leadsto \frac{\color{blue}{\left(\log_* (1 + x) + x\right) \cdot \left(\log_* (1 + x) - x\right)}}{\log_* (1 + x) + x}\]
  6. Applied associate-/l*19.1

    \[\leadsto \color{blue}{\frac{\log_* (1 + x) + x}{\frac{\log_* (1 + x) + x}{\log_* (1 + x) - x}}}\]

Runtime

Time bar (total: 29.9s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "log1p(x)-x"
  (- (log1p x) x))