Average Error: 0.0 → 0.0
Time: 2.0s
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 r191698 = 1.0;
        double r191699 = x;
        double r191700 = r191699 * r191699;
        double r191701 = r191698 - r191700;
        double r191702 = sqrt(r191701);
        return r191702;
}
↓
double f(double x) {
        double r191703 = 1.0;
        double r191704 = x;
        double r191705 = r191704 * r191704;
        double r191706 = r191703 - r191705;
        double r191707 = sqrt(r191706);
        return r191707;
}

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 2020062 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))