Average Error: 0.0 → 0.0
Time: 1.5s
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 r180443 = 1.0;
        double r180444 = x;
        double r180445 = r180444 * r180444;
        double r180446 = r180443 - r180445;
        double r180447 = sqrt(r180446);
        return r180447;
}
↓
double f(double x) {
        double r180448 = 1.0;
        double r180449 = x;
        double r180450 = r180449 * r180449;
        double r180451 = r180448 - r180450;
        double r180452 = sqrt(r180451);
        return r180452;
}

Error

Bits error versus x

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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 2020064 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))