Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[\sqrt{1 - x \cdot x}\]
↓
\[\frac{\sqrt{1 - {x}^{6}}}{\sqrt{1 + \left(x \cdot x + {x}^{4}\right)}}\]
\sqrt{1 - x \cdot x}
↓
\frac{\sqrt{1 - {x}^{6}}}{\sqrt{1 + \left(x \cdot x + {x}^{4}\right)}}
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
↓
(FPCore (x)
 :precision binary64
 (/ (sqrt (- 1.0 (pow x 6.0))) (sqrt (+ 1.0 (+ (* x x) (pow x 4.0))))))
double code(double x) {
	return sqrt(1.0 - (x * x));
}
↓
double code(double x) {
	return sqrt(1.0 - pow(x, 6.0)) / sqrt(1.0 + ((x * x) + pow(x, 4.0)));
}

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 flip3--_binary64_48560.0

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

  4. Applied sqrt-div_binary64_48690.0

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

  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{\sqrt{1 - {x}^{6}}}}{\sqrt{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}\]

  6. Simplified0.0

    \[\leadsto \frac{\sqrt{1 - {x}^{6}}}{\color{blue}{\sqrt{1 + \left(x \cdot x + {x}^{4}\right)}}}\]

  7. Final simplification0.0

    \[\leadsto \frac{\sqrt{1 - {x}^{6}}}{\sqrt{1 + \left(x \cdot x + {x}^{4}\right)}}\]

Reproduce

herbie shell --seed 2021007 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))