Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt[3]{{\left(\sqrt{1 - x \cdot x}\right)}^{3}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt[3]{{\left(\sqrt{1 - x \cdot x}\right)}^{3}}
double f(double x) {
        double r175090 = 1.0;
        double r175091 = x;
        double r175092 = r175091 * r175091;
        double r175093 = r175090 - r175092;
        double r175094 = sqrt(r175093);
        return r175094;
}
↓
double f(double x) {
        double r175095 = 1.0;
        double r175096 = x;
        double r175097 = r175096 * r175096;
        double r175098 = r175095 - r175097;
        double r175099 = sqrt(r175098);
        double r175100 = 3.0;
        double r175101 = pow(r175099, r175100);
        double r175102 = cbrt(r175101);
        return r175102;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))