Average Error: 0.0 → 0.0
Time: 1.5s
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 r181012 = 1.0;
        double r181013 = x;
        double r181014 = r181013 * r181013;
        double r181015 = r181012 - r181014;
        double r181016 = sqrt(r181015);
        return r181016;
}
↓
double f(double x) {
        double r181017 = 1.0;
        double r181018 = x;
        double r181019 = r181018 * r181018;
        double r181020 = r181017 - r181019;
        double r181021 = sqrt(r181020);
        return r181021;
}

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 2019209 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))