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 r110082 = 1.0;
        double r110083 = x;
        double r110084 = r110083 * r110083;
        double r110085 = r110082 - r110084;
        double r110086 = sqrt(r110085);
        return r110086;
}
↓
double f(double x) {
        double r110087 = 1.0;
        double r110088 = x;
        double r110089 = r110088 * r110088;
        double r110090 = r110087 - r110089;
        double r110091 = sqrt(r110090);
        return r110091;
}

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 2019326 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))