Original	19.8
Comparison	0.6
Herbie	0.5

Derivation

Initial program 19.8
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
Using strategy rm
Applied flip-- 19.9
\[\leadsto \color{blue}{\frac{{\left(\frac{1}{\sqrt{x}}\right)}^2 - {\left(\frac{1}{\sqrt{x + 1}}\right)}^2}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}}\]
Applied simplify 19.9
\[\leadsto \frac{\color{blue}{\frac{1}{x} - \frac{1}{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
Using strategy rm
Applied frac-sub 19.3
\[\leadsto \frac{\color{blue}{\frac{1 \cdot \left(x + 1\right) - x \cdot 1}{x \cdot \left(x + 1\right)}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
Applied simplify 5.3
\[\leadsto \frac{\frac{\color{blue}{1 - 0}}{x \cdot \left(x + 1\right)}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
Using strategy rm
Applied *-un-lft-identity 5.3
\[\leadsto \frac{\frac{\color{blue}{1 \cdot \left(1 - 0\right)}}{x \cdot \left(x + 1\right)}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
Applied times-frac 5.0
\[\leadsto \frac{\color{blue}{\frac{1}{x} \cdot \frac{1 - 0}{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
Applied associate-/l* 0.5
\[\leadsto \color{blue}{\frac{\frac{1}{x}}{\frac{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}{\frac{1 - 0}{x + 1}}}}\]
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie shell --seed '#(1064555532 179913862 452496668 2441903500 287849034 462453547)'
(FPCore (x)
  :name "2isqrt (example 3.6)"

  :target
  (/ 1 (+ (* (+ x 1) (sqrt x)) (* x (sqrt (+ x 1)))))

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

Error

Target

Derivation

Runtime