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

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Results

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Derivation

1. Initial program 0.0

$\left(\sqrt{x} + {x}^{2}\right) - {2}^{x}$
2. Using strategy rm

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

$\leadsto \color{blue}{\sqrt{\sqrt{x} + {x}^{2}} \cdot \sqrt{\sqrt{x} + {x}^{2}}} - \sqrt{{2}^{x}} \cdot \sqrt{{2}^{x}}$
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)))