Average Error: 0.0 → 0.0
Time: 936.0ms
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 r936 = 1.0;
        double r937 = x;
        double r938 = r937 * r937;
        double r939 = r936 - r938;
        double r940 = sqrt(r939);
        return r940;
}
↓
double f(double x) {
        double r941 = 1.0;
        double r942 = x;
        double r943 = r942 * r942;
        double r944 = r941 - r943;
        double r945 = sqrt(r944);
        return r945;
}

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 2020025 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))