Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[\sqrt{1.0 - x \cdot x}\]
↓
\[\sqrt{1.0 - x \cdot x}\]
\sqrt{1.0 - x \cdot x}
↓
\sqrt{1.0 - x \cdot x}
double f(double x) {
        double r11749548 = 1.0;
        double r11749549 = x;
        double r11749550 = r11749549 * r11749549;
        double r11749551 = r11749548 - r11749550;
        double r11749552 = sqrt(r11749551);
        return r11749552;
}
↓
double f(double x) {
        double r11749553 = 1.0;
        double r11749554 = x;
        double r11749555 = r11749554 * r11749554;
        double r11749556 = r11749553 - r11749555;
        double r11749557 = sqrt(r11749556);
        return r11749557;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

    \[\sqrt{1.0 - x \cdot x}\]

  2. Final simplification0.0

    \[\leadsto \sqrt{1.0 - x \cdot x}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))