Average Error: 0.0 → 0.0
Time: 1.1s
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 r130765 = 1.0;
        double r130766 = x;
        double r130767 = r130766 * r130766;
        double r130768 = r130765 - r130767;
        double r130769 = sqrt(r130768);
        return r130769;
}
↓
double f(double x) {
        double r130770 = 1.0;
        double r130771 = x;
        double r130772 = r130771 * r130771;
        double r130773 = r130770 - r130772;
        double r130774 = sqrt(r130773);
        return r130774;
}

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 2019303 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))