Average Error: 0.0 → 0.0
Time: 1.4s
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 r194201 = 1.0;
        double r194202 = x;
        double r194203 = r194202 * r194202;
        double r194204 = r194201 - r194203;
        double r194205 = sqrt(r194204);
        return r194205;
}
↓
double f(double x) {
        double r194206 = 1.0;
        double r194207 = x;
        double r194208 = r194207 * r194207;
        double r194209 = r194206 - r194208;
        double r194210 = sqrt(r194209);
        return r194210;
}

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 2020039 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))