Average Error: 0.0 → 0.0
Time: 5.0s
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 r138035 = 1.0;
        double r138036 = x;
        double r138037 = r138036 * r138036;
        double r138038 = r138035 - r138037;
        double r138039 = sqrt(r138038);
        return r138039;
}
↓
double f(double x) {
        double r138040 = 1.0;
        double r138041 = x;
        double r138042 = r138041 * r138041;
        double r138043 = r138040 - r138042;
        double r138044 = sqrt(r138043);
        return r138044;
}

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 2019194 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))