Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
Internal Precision: 320
$\sqrt{1 - \frac{1}{{x}^{2}}}$
$\frac{\sqrt{{1}^{3} - {\left(\frac{1}{x \cdot x}\right)}^{3}}}{\sqrt{1 + \left(\frac{1}{x \cdot x} + \frac{1}{x \cdot x} \cdot \frac{1}{x \cdot x}\right)}}$

# Try it out

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# Derivation

1. Initial program 0.0

$\sqrt{1 - \frac{1}{{x}^{2}}}$
2. Initial simplification0.0

$\leadsto \sqrt{1 - \frac{1}{x \cdot x}}$
3. Using strategy rm
4. Applied flip3--0.0

$\leadsto \sqrt{\color{blue}{\frac{{1}^{3} - {\left(\frac{1}{x \cdot x}\right)}^{3}}{1 \cdot 1 + \left(\frac{1}{x \cdot x} \cdot \frac{1}{x \cdot x} + 1 \cdot \frac{1}{x \cdot x}\right)}}}$
5. Applied sqrt-div0.0

$\leadsto \color{blue}{\frac{\sqrt{{1}^{3} - {\left(\frac{1}{x \cdot x}\right)}^{3}}}{\sqrt{1 \cdot 1 + \left(\frac{1}{x \cdot x} \cdot \frac{1}{x \cdot x} + 1 \cdot \frac{1}{x \cdot x}\right)}}}$
6. Final simplification0.0

$\leadsto \frac{\sqrt{{1}^{3} - {\left(\frac{1}{x \cdot x}\right)}^{3}}}{\sqrt{1 + \left(\frac{1}{x \cdot x} + \frac{1}{x \cdot x} \cdot \frac{1}{x \cdot x}\right)}}$

# Runtime

Time bar (total: 13.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "sqrt(1-1/x^2)"
(sqrt (- 1 (/ 1 (pow x 2)))))