Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + \left(1 + x \cdot x\right) \cdot 1}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + \left(1 + x \cdot x\right) \cdot 1}}
double f(double x) {
        double r217844 = 1.0;
        double r217845 = x;
        double r217846 = r217845 * r217845;
        double r217847 = r217844 - r217846;
        double r217848 = sqrt(r217847);
        return r217848;
}
↓
double f(double x) {
        double r217849 = 1.0;
        double r217850 = 3.0;
        double r217851 = pow(r217849, r217850);
        double r217852 = x;
        double r217853 = 6.0;
        double r217854 = pow(r217852, r217853);
        double r217855 = r217851 - r217854;
        double r217856 = 4.0;
        double r217857 = pow(r217852, r217856);
        double r217858 = r217852 * r217852;
        double r217859 = r217849 + r217858;
        double r217860 = r217859 * r217849;
        double r217861 = r217857 + r217860;
        double r217862 = r217855 / r217861;
        double r217863 = sqrt(r217862);
        return r217863;
}

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

    \[\sqrt{1 - x \cdot x}\]
  2. Using strategy rm

  3. Applied flip3--0.0

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

  4. Applied sqrt-div0.0

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

  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{\sqrt{{1}^{3} - {x}^{6}}}}{\sqrt{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}\]

  6. Simplified0.0

    \[\leadsto \frac{\sqrt{{1}^{3} - {x}^{6}}}{\color{blue}{\sqrt{{x}^{4} + \left(1 + x \cdot x\right) \cdot 1}}}\]
  7. Using strategy rm

  8. Applied sqrt-undiv0.0

    \[\leadsto \color{blue}{\sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + \left(1 + x \cdot x\right) \cdot 1}}}\]

  9. Final simplification0.0

    \[\leadsto \sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + \left(1 + x \cdot x\right) \cdot 1}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))