Average Error: 0.0 → 0.0
Time: 544.0ms
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 r178480 = 1.0;
        double r178481 = x;
        double r178482 = r178481 * r178481;
        double r178483 = r178480 - r178482;
        double r178484 = sqrt(r178483);
        return r178484;
}
↓
double f(double x) {
        double r178485 = 1.0;
        double r178486 = x;
        double r178487 = r178486 * r178486;
        double r178488 = r178485 - r178487;
        double r178489 = sqrt(r178488);
        return r178489;
}

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 2020025 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))