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 r188423 = 1.0;
        double r188424 = x;
        double r188425 = r188424 * r188424;
        double r188426 = r188423 - r188425;
        double r188427 = sqrt(r188426);
        return r188427;
}
↓
double f(double x) {
        double r188428 = 1.0;
        double r188429 = x;
        double r188430 = r188429 * r188429;
        double r188431 = r188428 - r188430;
        double r188432 = sqrt(r188431);
        return r188432;
}

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