Average Error: 0.0 → 0.0
Time: 1.3s
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 r154050 = 1.0;
        double r154051 = x;
        double r154052 = r154051 * r154051;
        double r154053 = r154050 - r154052;
        double r154054 = sqrt(r154053);
        return r154054;
}
↓
double f(double x) {
        double r154055 = 1.0;
        double r154056 = x;
        double r154057 = r154056 * r154056;
        double r154058 = r154055 - r154057;
        double r154059 = sqrt(r154058);
        return r154059;
}

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 2019353 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))