Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
Cost: 6720
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{1 - x \cdot x}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{1 - x \cdot x}
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
↓
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
double code(double x) {
	return sqrt(1.0 - (x * x));
}
↓
double code(double x) {
	return sqrt(1.0 - (x * x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.3
Cost448
\[1 - \left(x \cdot x\right) \cdot 0.5\]
Alternative 2
Error0.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\sqrt{1 - x \cdot x}\]

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto \sqrt{1 - x \cdot x}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))