Average Error: 0.0 → 0.0
Time: 4.9s
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 r153430 = 1.0;
        double r153431 = x;
        double r153432 = r153431 * r153431;
        double r153433 = r153430 - r153432;
        double r153434 = sqrt(r153433);
        return r153434;
}
↓
double f(double x) {
        double r153435 = 1.0;
        double r153436 = x;
        double r153437 = r153436 * r153436;
        double r153438 = r153435 - r153437;
        double r153439 = sqrt(r153438);
        return r153439;
}

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 2019208 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))