Average Error: 0.0 → 0.0
Time: 3.8s
Precision: binary64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + 1 \cdot \left(1 + x \cdot x\right)}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + 1 \cdot \left(1 + x \cdot x\right)}}
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
↓
(FPCore (x)
 :precision binary64
 (sqrt
  (/ (- (pow 1.0 3.0) (pow x 6.0)) (+ (pow x 4.0) (* 1.0 (+ 1.0 (* x x)))))))
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (x * x))))));
}
↓
double code(double x) {
	return ((double) sqrt((((double) (((double) pow(1.0, 3.0)) - ((double) pow(x, 6.0)))) / ((double) (((double) pow(x, 4.0)) + ((double) (1.0 * ((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 Error: 0.0 bits

    \[\sqrt{1 - x \cdot x}\]
  2. Using strategy rm

  3. Applied flip3--Error: 0.0 bits

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

  4. SimplifiedError: 0.0 bits

    \[\leadsto \sqrt{\frac{\color{blue}{{1}^{3} - {x}^{6}}}{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}\]

  5. SimplifiedError: 0.0 bits

    \[\leadsto \sqrt{\frac{{1}^{3} - {x}^{6}}{\color{blue}{{x}^{4} + 1 \cdot \left(1 + x \cdot x\right)}}}\]

  6. Final simplificationError: 0.0 bits

    \[\leadsto \sqrt{\frac{{1}^{3} - {x}^{6}}{{x}^{4} + 1 \cdot \left(1 + x \cdot x\right)}}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))