Average Error: 0.0 → 0.0
Time: 1.5s
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 r232345 = 1.0;
        double r232346 = x;
        double r232347 = r232346 * r232346;
        double r232348 = r232345 - r232347;
        double r232349 = sqrt(r232348);
        return r232349;
}
↓
double f(double x) {
        double r232350 = 1.0;
        double r232351 = x;
        double r232352 = r232351 * r232351;
        double r232353 = r232350 - r232352;
        double r232354 = sqrt(r232353);
        return r232354;
}

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 2020049 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))