Average Error: 29.6 → 29.6
Time: 3.7s
Precision: 64
Internal Precision: 1344
\[\sqrt{x + 1} - \sqrt{x}\]
↓
\[\sqrt{x + 1} - \sqrt{x}\]

Error

Bits error versus x

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Results

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Target

Original29.6
Target0.2
Herbie29.6
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Derivation

  1. Initial program 29.6

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

  2. Initial simplification29.6

    \[\leadsto \sqrt{1 + x} - \sqrt{x}\]

  3. Final simplification29.6

    \[\leadsto \sqrt{x + 1} - \sqrt{x}\]

Runtime

Time bar (total: 3.7s)Debug logProfile

herbie shell --seed 2018251 
(FPCore (x)
  :name "2sqrt (example 3.1)"

  :herbie-target
  (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

  (- (sqrt (+ x 1)) (sqrt x)))