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 r140867 = 1.0;
        double r140868 = x;
        double r140869 = r140868 * r140868;
        double r140870 = r140867 - r140869;
        double r140871 = sqrt(r140870);
        return r140871;
}
↓
double f(double x) {
        double r140872 = 1.0;
        double r140873 = x;
        double r140874 = r140873 * r140873;
        double r140875 = r140872 - r140874;
        double r140876 = sqrt(r140875);
        return r140876;
}

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 2019325 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))