Average Error: 0.0 → 0.0
Time: 1.9s
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 r152978 = 1.0;
        double r152979 = x;
        double r152980 = r152979 * r152979;
        double r152981 = r152978 - r152980;
        double r152982 = sqrt(r152981);
        return r152982;
}
↓
double f(double x) {
        double r152983 = 1.0;
        double r152984 = x;
        double r152985 = r152984 * r152984;
        double r152986 = r152983 - r152985;
        double r152987 = sqrt(r152986);
        return r152987;
}

Error

Bits error versus x

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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 2020056 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))