Average Error: 0.0 → 0.0
Time: 1.1s
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 r21929 = 1.0;
        double r21930 = x;
        double r21931 = r21930 * r21930;
        double r21932 = r21929 - r21931;
        double r21933 = sqrt(r21932);
        return r21933;
}
↓
double f(double x) {
        double r21934 = 1.0;
        double r21935 = x;
        double r21936 = r21935 * r21935;
        double r21937 = r21934 - r21936;
        double r21938 = sqrt(r21937);
        return r21938;
}

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 2019310 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))