Average Error: 0.0 → 0.0
Time: 1.7s
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 r210392 = 1.0;
        double r210393 = x;
        double r210394 = r210393 * r210393;
        double r210395 = r210392 - r210394;
        double r210396 = sqrt(r210395);
        return r210396;
}
↓
double f(double x) {
        double r210397 = 1.0;
        double r210398 = x;
        double r210399 = r210398 * r210398;
        double r210400 = r210397 - r210399;
        double r210401 = sqrt(r210400);
        return r210401;
}

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))))