Average Error: 0.0 → 0.0
Time: 1.2s
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}}
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
↓
(FPCore (x) :precision binary64 (cbrt (pow (sqrt (- 1.0 (* x x))) 3.0)))
double code(double x) {
	return sqrt(1.0 - (x * x));
}
↓
double code(double x) {
	return cbrt(pow(sqrt(1.0 - (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-cube_binary64_62520.0

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

  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 2020353 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))