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 r114801 = 1.0;
        double r114802 = x;
        double r114803 = r114802 * r114802;
        double r114804 = r114801 - r114803;
        double r114805 = sqrt(r114804);
        return r114805;
}
↓
double f(double x) {
        double r114806 = 1.0;
        double r114807 = x;
        double r114808 = r114807 * r114807;
        double r114809 = r114806 - r114808;
        double r114810 = sqrt(r114809);
        return r114810;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

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 2019235 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))