Average Error: 0.0 → 0.0
Time: 5.7s
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 r8799849 = 1.0;
        double r8799850 = x;
        double r8799851 = r8799850 * r8799850;
        double r8799852 = r8799849 - r8799851;
        double r8799853 = sqrt(r8799852);
        return r8799853;
}
↓
double f(double x) {
        double r8799854 = 1.0;
        double r8799855 = x;
        double r8799856 = r8799855 * r8799855;
        double r8799857 = r8799854 - r8799856;
        double r8799858 = sqrt(r8799857);
        double r8799859 = r8799857 * r8799858;
        double r8799860 = cbrt(r8799859);
        return r8799860;
}

Error

Bits error versus x

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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))))