Average Error: 0.0 → 0.0
Time: 8.5s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + 1 \cdot \left(1 + x \cdot x\right)}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + 1 \cdot \left(1 + x \cdot x\right)}}
double f(double x) {
        double r161807 = 1.0;
        double r161808 = x;
        double r161809 = r161808 * r161808;
        double r161810 = r161807 - r161809;
        double r161811 = sqrt(r161810);
        return r161811;
}
↓
double f(double x) {
        double r161812 = 1.0;
        double r161813 = 3.0;
        double r161814 = pow(r161812, r161813);
        double r161815 = x;
        double r161816 = 6.0;
        double r161817 = pow(r161815, r161816);
        double r161818 = r161814 - r161817;
        double r161819 = 4.0;
        double r161820 = pow(r161815, r161819);
        double r161821 = r161815 * r161815;
        double r161822 = r161812 + r161821;
        double r161823 = r161812 * r161822;
        double r161824 = r161820 + r161823;
        double r161825 = r161818 / r161824;
        double r161826 = sqrt(r161825);
        return r161826;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))