Average Error: 0.0 → 0.0
Time: 517.0ms
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 r199237 = 1.0;
        double r199238 = x;
        double r199239 = r199238 * r199238;
        double r199240 = r199237 - r199239;
        double r199241 = sqrt(r199240);
        return r199241;
}
↓
double f(double x) {
        double r199242 = 1.0;
        double r199243 = x;
        double r199244 = r199243 * r199243;
        double r199245 = r199242 - r199244;
        double r199246 = sqrt(r199245);
        return r199246;
}

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))))