Average Error: 0.0 → 0.0
Time: 23.9s
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 r9907762 = 1.0;
        double r9907763 = x;
        double r9907764 = r9907763 * r9907763;
        double r9907765 = r9907762 - r9907764;
        double r9907766 = sqrt(r9907765);
        return r9907766;
}
↓
double f(double x) {
        double r9907767 = 1.0;
        double r9907768 = x;
        double r9907769 = r9907768 * r9907768;
        double r9907770 = r9907767 - r9907769;
        double r9907771 = sqrt(r9907770);
        return r9907771;
}

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 2019200 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))