Average Error: 29.8 → 29.7
Time: 37.6s
Precision: 64
Internal Precision: 1344
\[\sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sin \left(\sqrt{x}\right) \cdot \cos \left(\sqrt{x + 1}\right)\]
\[\sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sqrt[3]{{\left(\sin \left(\sqrt{x}\right)\right)}^{3}} \cdot \cos \left(\sqrt{x + 1}\right)\]

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

    \[\sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sin \left(\sqrt{x}\right) \cdot \cos \left(\sqrt{x + 1}\right)\]
  2. Using strategy rm
  3. Applied add-cbrt-cube29.7

    \[\leadsto \sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \color{blue}{\sqrt[3]{\left(\sin \left(\sqrt{x}\right) \cdot \sin \left(\sqrt{x}\right)\right) \cdot \sin \left(\sqrt{x}\right)}} \cdot \cos \left(\sqrt{x + 1}\right)\]
  4. Applied simplify29.7

    \[\leadsto \sin \left(\sqrt{x + 1}\right) \cdot \cos \left(\sqrt{x}\right) - \sqrt[3]{\color{blue}{{\left(\sin \left(\sqrt{x}\right)\right)}^{3}}} \cdot \cos \left(\sqrt{x + 1}\right)\]

Runtime

Time bar (total: 37.6s)Debug log

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