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 r172427 = 1.0;
        double r172428 = x;
        double r172429 = r172428 * r172428;
        double r172430 = r172427 - r172429;
        double r172431 = sqrt(r172430);
        return r172431;
}
↓
double f(double x) {
        double r172432 = 1.0;
        double r172433 = x;
        double r172434 = r172433 * r172433;
        double r172435 = r172432 - r172434;
        double r172436 = sqrt(r172435);
        return r172436;
}

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