Average Error: 0.0 → 0.0
Time: 4.2s
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 r164971 = 1.0;
        double r164972 = x;
        double r164973 = r164972 * r164972;
        double r164974 = r164971 - r164973;
        double r164975 = sqrt(r164974);
        return r164975;
}
↓
double f(double x) {
        double r164976 = 1.0;
        double r164977 = x;
        double r164978 = r164977 * r164977;
        double r164979 = r164976 - r164978;
        double r164980 = sqrt(r164979);
        return r164980;
}

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 2019212 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))