Average Error: 0.0 → 0.0
Time: 545.0ms
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 r141844 = 1.0;
        double r141845 = x;
        double r141846 = r141845 * r141845;
        double r141847 = r141844 - r141846;
        double r141848 = sqrt(r141847);
        return r141848;
}
↓
double f(double x) {
        double r141849 = 1.0;
        double r141850 = x;
        double r141851 = r141850 * r141850;
        double r141852 = r141849 - r141851;
        double r141853 = sqrt(r141852);
        return r141853;
}

Error

Bits error versus x

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Results

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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 2020020 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))