Average Error: 0.0 → 0.0
Time: 5.9s
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 r8379276 = 1.0;
        double r8379277 = x;
        double r8379278 = r8379277 * r8379277;
        double r8379279 = r8379276 - r8379278;
        double r8379280 = sqrt(r8379279);
        return r8379280;
}
↓
double f(double x) {
        double r8379281 = 1.0;
        double r8379282 = x;
        double r8379283 = r8379282 * r8379282;
        double r8379284 = r8379281 - r8379283;
        double r8379285 = sqrt(r8379284);
        double r8379286 = r8379284 * r8379285;
        double r8379287 = cbrt(r8379286);
        return r8379287;
}

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

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

  5. Final simplification0.0

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

Reproduce

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