Average Error: 0.0 → 0.0
Time: 3.6s
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 r185754 = 1.0;
        double r185755 = x;
        double r185756 = r185755 * r185755;
        double r185757 = r185754 - r185756;
        double r185758 = sqrt(r185757);
        return r185758;
}
↓
double f(double x) {
        double r185759 = 1.0;
        double r185760 = x;
        double r185761 = r185760 * r185760;
        double r185762 = r185759 - r185761;
        double r185763 = sqrt(r185762);
        return r185763;
}

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 2019179 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))