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 r140136 = 1.0;
        double r140137 = x;
        double r140138 = r140137 * r140137;
        double r140139 = r140136 - r140138;
        double r140140 = sqrt(r140139);
        return r140140;
}
↓
double f(double x) {
        double r140141 = 1.0;
        double r140142 = x;
        double r140143 = r140142 * r140142;
        double r140144 = r140141 - r140143;
        double r140145 = sqrt(r140144);
        return r140145;
}

Error

Bits error versus x

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