Average Error: 0.0 → 0.0
Time: 509.0ms
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 r163901 = 1.0;
        double r163902 = x;
        double r163903 = r163902 * r163902;
        double r163904 = r163901 - r163903;
        double r163905 = sqrt(r163904);
        return r163905;
}
↓
double f(double x) {
        double r163906 = 1.0;
        double r163907 = x;
        double r163908 = r163907 * r163907;
        double r163909 = r163906 - r163908;
        double r163910 = sqrt(r163909);
        return r163910;
}

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 2020065 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))