Average Error: 0.0 → 0.0
Time: 1.2s
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 r169091 = 1.0;
        double r169092 = x;
        double r169093 = r169092 * r169092;
        double r169094 = r169091 - r169093;
        double r169095 = sqrt(r169094);
        return r169095;
}
↓
double f(double x) {
        double r169096 = 1.0;
        double r169097 = x;
        double r169098 = r169097 * r169097;
        double r169099 = r169096 - r169098;
        double r169100 = sqrt(r169099);
        return r169100;
}

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 2019235 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))