Error

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Target

Derivation

1. Initial program 32.1

   \[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}\]

2. Simplified30.7

   \[\leadsto \color{blue}{(\left(\frac{-1}{x}\right) \cdot \left(\left|x\right|\right) + 1)_*}\]

3. Taylor expanded around inf 0

   \[\leadsto \color{blue}{1 - \frac{\left|x\right|}{x}}\]

4. Final simplification0

   \[\leadsto 1 - \frac{\left|x\right|}{x}\]

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (x)
  :name "sqrt sqr"

  :herbie-target
  (if (< x 0) 2 0)

  (- (/ x x) (* (/ 1 x) (sqrt (* x x)))))

Details

Time bar (total: 3.9s)Debug log