Average Error: 0.0 → 0.0

Time: 23.3s

Precision: 64

Internal Precision: 320

\[\frac{1}{x - 1} + \frac{x}{x + 1}\]

↓

\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right) + \log \left(e^{\frac{1}{x - 1} \cdot \frac{1}{x - 1}}\right)}\]

Error

The X axis uses an exponential scale — Bits error versus `x`

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Derivation

Initial program 0.0
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
Initial simplification0.0
\[\leadsto \frac{1}{x - 1} + \frac{x}{x + 1}\]
Using strategy rm
Applied flip3-+0.0
\[\leadsto \color{blue}{\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right)}}\]
Using strategy rm
Applied add-log-exp0.0
\[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\color{blue}{\log \left(e^{\frac{1}{x - 1} \cdot \frac{1}{x - 1}}\right)} + \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right)}\]
Final simplification0.0
\[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right) + \log \left(e^{\frac{1}{x - 1} \cdot \frac{1}{x - 1}}\right)}\]

Runtime

	Baseline	Herbie	Oracle	Span	%
Regimes	0.0	0.0	0.0	0.0	0%

herbie shell --seed 2018290 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))