Average Error: 0.0 → 0.0
Time: 896.0ms
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 r212117 = 1.0;
        double r212118 = x;
        double r212119 = r212118 * r212118;
        double r212120 = r212117 - r212119;
        double r212121 = sqrt(r212120);
        return r212121;
}
↓
double f(double x) {
        double r212122 = 1.0;
        double r212123 = x;
        double r212124 = r212123 * r212123;
        double r212125 = r212122 - r212124;
        double r212126 = sqrt(r212125);
        return r212126;
}

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 2020035 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))