Average Error: 0.0 → 0.0
Time: 975.0ms
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 r99340 = 1.0;
        double r99341 = x;
        double r99342 = r99341 * r99341;
        double r99343 = r99340 - r99342;
        double r99344 = sqrt(r99343);
        return r99344;
}
↓
double f(double x) {
        double r99345 = 1.0;
        double r99346 = x;
        double r99347 = r99346 * r99346;
        double r99348 = r99345 - r99347;
        double r99349 = sqrt(r99348);
        return r99349;
}

Error

Bits error versus x

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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 2019325 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))