Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{1 - x \cdot x}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{1 - x \cdot x}
double f(double x) {
        double r146691 = 1.0;
        double r146692 = x;
        double r146693 = r146692 * r146692;
        double r146694 = r146691 - r146693;
        double r146695 = sqrt(r146694);
        return r146695;
}
↓
double f(double x) {
        double r146696 = 1.0;
        double r146697 = x;
        double r146698 = r146697 * r146697;
        double r146699 = r146696 - r146698;
        double r146700 = sqrt(r146699);
        return r146700;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))