Average Error: 0.0 → 0.0
Time: 570.0ms
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 r160970 = 1.0;
        double r160971 = x;
        double r160972 = r160971 * r160971;
        double r160973 = r160970 - r160972;
        double r160974 = sqrt(r160973);
        return r160974;
}
↓
double f(double x) {
        double r160975 = 1.0;
        double r160976 = x;
        double r160977 = r160976 * r160976;
        double r160978 = r160975 - r160977;
        double r160979 = sqrt(r160978);
        return r160979;
}

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 2020036 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))