Average Error: 20.2 → 20.2
Time: 27.3s
Precision: 64
Ground Truth: 128
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
⬇
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]

Error

Bits error versus x

Target

Original20.2
Comparison0.7
Herbie20.2
\[ \frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}} \]

Derivation

  1. Initial program 20.2

    \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
  2. Removed slow pow expressions

Runtime

Total time: 27.3s Debug log

Please include this information when filing a bug report:

herbie --seed '#(2289295193 1909701276 3030536127 128178340 2082831230 142350768)'
(FPCore (x)
  :name "NMSE example 3.6"

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

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