Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[\sqrt{1 - x \cdot x}\]
↓
\[\left|\sqrt[3]{1 - x \cdot x}\right| \cdot \sqrt{\sqrt[3]{1 - x \cdot x}}\]
\sqrt{1 - x \cdot x}
↓
\left|\sqrt[3]{1 - x \cdot x}\right| \cdot \sqrt{\sqrt[3]{1 - x \cdot x}}
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (x * x))))));
}
↓
double code(double x) {
	return ((double) (((double) fabs(((double) cbrt(((double) (1.0 - ((double) (x * x)))))))) * ((double) sqrt(((double) cbrt(((double) (1.0 - ((double) (x * x))))))))));
}

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-cube-cbrt0.0

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

  4. Applied sqrt-prod0.0

    \[\leadsto \color{blue}{\sqrt{\sqrt[3]{1 - x \cdot x} \cdot \sqrt[3]{1 - x \cdot x}} \cdot \sqrt{\sqrt[3]{1 - x \cdot x}}}\]

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020169 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))