Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\frac{\sqrt{1 \cdot 1 - {x}^{4}}}{\sqrt{1 + x \cdot x}}\]
\sqrt{1 - x \cdot x}
↓
\frac{\sqrt{1 \cdot 1 - {x}^{4}}}{\sqrt{1 + x \cdot x}}
double f(double x) {
        double r202805 = 1.0;
        double r202806 = x;
        double r202807 = r202806 * r202806;
        double r202808 = r202805 - r202807;
        double r202809 = sqrt(r202808);
        return r202809;
}
↓
double f(double x) {
        double r202810 = 1.0;
        double r202811 = r202810 * r202810;
        double r202812 = x;
        double r202813 = 4.0;
        double r202814 = pow(r202812, r202813);
        double r202815 = r202811 - r202814;
        double r202816 = sqrt(r202815);
        double r202817 = r202812 * r202812;
        double r202818 = r202810 + r202817;
        double r202819 = sqrt(r202818);
        double r202820 = r202816 / r202819;
        return r202820;
}

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 flip--0.0

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

  4. Applied sqrt-div0.0

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

  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{\sqrt{1 \cdot 1 - {x}^{4}}}}{\sqrt{1 + x \cdot x}}\]

  6. Final simplification0.0

    \[\leadsto \frac{\sqrt{1 \cdot 1 - {x}^{4}}}{\sqrt{1 + x \cdot x}}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))