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 r245991 = 1.0;
        double r245992 = x;
        double r245993 = r245992 * r245992;
        double r245994 = r245991 - r245993;
        double r245995 = sqrt(r245994);
        return r245995;
}
↓
double f(double x) {
        double r245996 = 1.0;
        double r245997 = x;
        double r245998 = r245997 * r245997;
        double r245999 = r245996 - r245998;
        double r246000 = sqrt(r245999);
        return r246000;
}

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 2019353 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))