Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\sqrt[3]{{\left(1 - x \cdot x\right)}^{3}}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\sqrt[3]{{\left(1 - x \cdot x\right)}^{3}}}
double f(double x) {
        double r107905 = 1.0;
        double r107906 = x;
        double r107907 = r107906 * r107906;
        double r107908 = r107905 - r107907;
        double r107909 = sqrt(r107908);
        return r107909;
}
↓
double f(double x) {
        double r107910 = 1.0;
        double r107911 = x;
        double r107912 = r107911 * r107911;
        double r107913 = r107910 - r107912;
        double r107914 = 3.0;
        double r107915 = pow(r107913, r107914);
        double r107916 = cbrt(r107915);
        double r107917 = sqrt(r107916);
        return r107917;
}

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

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))