Error

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

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Enter valid numbers for all inputs

Target

Original	60.9
Target	0.4
Herbie	0.0

\[-\left(\left(\left(1 + x\right) + \frac{x \cdot x}{2}\right) + \frac{5}{12} \cdot {x}^{3}\right)\]

Derivation

Initial program 60.9
\[\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}\]
Initial simplification59.9
\[\leadsto \frac{\log \left(1 - x\right)}{\log_* (1 + x)}\]
Using strategy rm
Applied sub-neg59.9
\[\leadsto \frac{\log \color{blue}{\left(1 + \left(-x\right)\right)}}{\log_* (1 + x)}\]
Applied log1p-def0.0
\[\leadsto \frac{\color{blue}{\log_* (1 + \left(-x\right))}}{\log_* (1 + x)}\]
Final simplification0.0
\[\leadsto \frac{\log_* (1 + \left(-x\right))}{\log_* (1 + x)}\]

Runtime

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

herbie shell --seed 2018286 +o rules:numerics
(FPCore (x)
  :name "qlog (example 3.10)"
  :pre (and (< -1 x) (< x 1))

  :herbie-target
  (- (+ (+ (+ 1 x) (/ (* x x) 2)) (* 5/12 (pow x 3))))

  (/ (log (- 1 x)) (log (+ 1 x))))