Average Error: 0.0 → 0.0
Time: 1.3s
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 r191729 = 1.0;
        double r191730 = x;
        double r191731 = r191730 * r191730;
        double r191732 = r191729 - r191731;
        double r191733 = sqrt(r191732);
        return r191733;
}
↓
double f(double x) {
        double r191734 = 1.0;
        double r191735 = x;
        double r191736 = r191735 * r191735;
        double r191737 = r191734 - r191736;
        double r191738 = sqrt(r191737);
        return r191738;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019362 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))