Average Error: 0.0 → 0.0
Time: 607.0ms
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 r194973 = 1.0;
        double r194974 = x;
        double r194975 = r194974 * r194974;
        double r194976 = r194973 - r194975;
        double r194977 = sqrt(r194976);
        return r194977;
}
↓
double f(double x) {
        double r194978 = 1.0;
        double r194979 = x;
        double r194980 = r194979 * r194979;
        double r194981 = r194978 - r194980;
        double r194982 = sqrt(r194981);
        return r194982;
}

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 2019354 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))