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 r98264 = 1.0;
        double r98265 = x;
        double r98266 = r98265 * r98265;
        double r98267 = r98264 - r98266;
        double r98268 = sqrt(r98267);
        return r98268;
}
↓
double f(double x) {
        double r98269 = 1.0;
        double r98270 = x;
        double r98271 = r98270 * r98270;
        double r98272 = r98269 - r98271;
        double r98273 = sqrt(r98272);
        return r98273;
}

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 2019326 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))