Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt[3]{{\left(\sqrt{1 - x \cdot x}\right)}^{3}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt[3]{{\left(\sqrt{1 - x \cdot x}\right)}^{3}}
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (x * x))))));
}
↓
double code(double x) {
	return ((double) cbrt(((double) pow(((double) sqrt(((double) (1.0 - ((double) (x * x)))))), 3.0))));
}

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 2020147 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))