Average Error: 0.0 → 0.0
Time: 1.1s
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 r173695 = 1.0;
        double r173696 = x;
        double r173697 = r173696 * r173696;
        double r173698 = r173695 - r173697;
        double r173699 = sqrt(r173698);
        return r173699;
}
↓
double f(double x) {
        double r173700 = 1.0;
        double r173701 = x;
        double r173702 = r173701 * r173701;
        double r173703 = r173700 - r173702;
        double r173704 = sqrt(r173703);
        return r173704;
}

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 2019303 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))