Average Error: 50.2 → 40.0
Time: 20.5s
Precision: 64
Internal Precision: 1344
\[\frac{\log_* (1 + x) - x}{x \cdot x}\]
\[\log_* (1 + x) \cdot \frac{1}{x \cdot x} - \frac{1}{x}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 50.2

    \[\frac{\log_* (1 + x) - x}{x \cdot x}\]
  2. Using strategy rm
  3. Applied div-sub49.9

    \[\leadsto \color{blue}{\frac{\log_* (1 + x)}{x \cdot x} - \frac{x}{x \cdot x}}\]
  4. Applied simplify40.0

    \[\leadsto \frac{\log_* (1 + x)}{x \cdot x} - \color{blue}{\frac{1}{x}}\]
  5. Using strategy rm
  6. Applied div-inv40.0

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

Runtime

Time bar (total: 20.5s)Debug log

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