Average Error: 29.8 → 0.1
Time: 18.6s
Precision: 64
Internal Precision: 1344
\[\sin \left(\sqrt{x + 1} - \sqrt{x}\right)\]
\[\sin \left(\frac{1}{\sqrt{x + 1} + \sqrt{x}}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.8

    \[\sin \left(\sqrt{x + 1} - \sqrt{x}\right)\]
  2. Using strategy rm
  3. Applied flip--29.5

    \[\leadsto \sin \color{blue}{\left(\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}\right)}\]
  4. Applied simplify0.1

    \[\leadsto \sin \left(\frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}\right)\]

Runtime

Time bar (total: 18.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sin(sqrt(x + 1) - sqrt(x))"
  (sin (- (sqrt (+ x 1)) (sqrt x))))