Average Error: 0.0 → 0.0
Time: 4.2s
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 r171232 = 1.0;
        double r171233 = x;
        double r171234 = r171233 * r171233;
        double r171235 = r171232 - r171234;
        double r171236 = sqrt(r171235);
        return r171236;
}
↓
double f(double x) {
        double r171237 = 1.0;
        double r171238 = x;
        double r171239 = r171238 * r171238;
        double r171240 = r171237 - r171239;
        double r171241 = sqrt(r171240);
        return r171241;
}

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 2020043 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))