Average Error: 0.0 → 0.0
Time: 6.6s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}
double f(double x) {
        double r7207854 = 1.0;
        double r7207855 = x;
        double r7207856 = r7207855 * r7207855;
        double r7207857 = r7207854 - r7207856;
        double r7207858 = sqrt(r7207857);
        return r7207858;
}
↓
double f(double x) {
        double r7207859 = 1.0;
        double r7207860 = x;
        double r7207861 = r7207860 * r7207860;
        double r7207862 = r7207859 - r7207861;
        double r7207863 = sqrt(r7207862);
        double r7207864 = r7207862 * r7207863;
        double r7207865 = cbrt(r7207864);
        return r7207865;
}

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 add-cbrt-cube0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto \sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))