Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\frac{1 \cdot \left(1 \cdot 1\right) - \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + \left(x \cdot x\right) \cdot 1\right) + 1 \cdot 1}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\frac{1 \cdot \left(1 \cdot 1\right) - \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + \left(x \cdot x\right) \cdot 1\right) + 1 \cdot 1}}
double f(double x) {
        double r8826754 = 1.0;
        double r8826755 = x;
        double r8826756 = r8826755 * r8826755;
        double r8826757 = r8826754 - r8826756;
        double r8826758 = sqrt(r8826757);
        return r8826758;
}
↓
double f(double x) {
        double r8826759 = 1.0;
        double r8826760 = r8826759 * r8826759;
        double r8826761 = r8826759 * r8826760;
        double r8826762 = x;
        double r8826763 = r8826762 * r8826762;
        double r8826764 = r8826763 * r8826763;
        double r8826765 = r8826763 * r8826764;
        double r8826766 = r8826761 - r8826765;
        double r8826767 = r8826763 * r8826759;
        double r8826768 = r8826764 + r8826767;
        double r8826769 = r8826768 + r8826760;
        double r8826770 = r8826766 / r8826769;
        double r8826771 = sqrt(r8826770);
        return r8826771;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))