Average Error: 0.0 → 0.1
Time: 35.6s
Precision: 64
Internal Precision: 320
\[\left(\sqrt{x} + {x}^{2}\right) - {2}^{x}\]
\[\frac{\left(\sqrt{{2}^{x}} + \sqrt{\sqrt{x} + x \cdot x}\right) \cdot \left(\left(\sqrt{x} + x \cdot x\right) - {2}^{x}\right)}{\sqrt{\sqrt{x} + {x}^{2}} + \sqrt{{2}^{x}}}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\sqrt{x} + {x}^{2}\right) - {2}^{x}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\sqrt{x} + {x}^{2}\right) - \color{blue}{\sqrt{{2}^{x}} \cdot \sqrt{{2}^{x}}}\]
  4. Applied add-sqr-sqrt0.1

    \[\leadsto \color{blue}{\sqrt{\sqrt{x} + {x}^{2}} \cdot \sqrt{\sqrt{x} + {x}^{2}}} - \sqrt{{2}^{x}} \cdot \sqrt{{2}^{x}}\]
  5. Applied difference-of-squares0.1

    \[\leadsto \color{blue}{\left(\sqrt{\sqrt{x} + {x}^{2}} + \sqrt{{2}^{x}}\right) \cdot \left(\sqrt{\sqrt{x} + {x}^{2}} - \sqrt{{2}^{x}}\right)}\]
  6. Using strategy rm
  7. Applied flip--0.1

    \[\leadsto \left(\sqrt{\sqrt{x} + {x}^{2}} + \sqrt{{2}^{x}}\right) \cdot \color{blue}{\frac{\sqrt{\sqrt{x} + {x}^{2}} \cdot \sqrt{\sqrt{x} + {x}^{2}} - \sqrt{{2}^{x}} \cdot \sqrt{{2}^{x}}}{\sqrt{\sqrt{x} + {x}^{2}} + \sqrt{{2}^{x}}}}\]
  8. Applied associate-*r/0.1

    \[\leadsto \color{blue}{\frac{\left(\sqrt{\sqrt{x} + {x}^{2}} + \sqrt{{2}^{x}}\right) \cdot \left(\sqrt{\sqrt{x} + {x}^{2}} \cdot \sqrt{\sqrt{x} + {x}^{2}} - \sqrt{{2}^{x}} \cdot \sqrt{{2}^{x}}\right)}{\sqrt{\sqrt{x} + {x}^{2}} + \sqrt{{2}^{x}}}}\]
  9. Applied simplify0.1

    \[\leadsto \frac{\color{blue}{\left(\sqrt{{2}^{x}} + \sqrt{\sqrt{x} + x \cdot x}\right) \cdot \left(\left(\sqrt{x} + x \cdot x\right) - {2}^{x}\right)}}{\sqrt{\sqrt{x} + {x}^{2}} + \sqrt{{2}^{x}}}\]

Runtime

Time bar (total: 35.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sqrt(x) + x^2 - 2^x"
  (- (+ (sqrt x) (pow x 2)) (pow 2 x)))