Average Error: 0.0 → 0.0
Time: 974.0ms
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 r7569628 = 1.0;
        double r7569629 = x;
        double r7569630 = r7569629 * r7569629;
        double r7569631 = r7569628 - r7569630;
        double r7569632 = sqrt(r7569631);
        return r7569632;
}
↓
double f(double x) {
        double r7569633 = 1.0;
        double r7569634 = x;
        double r7569635 = r7569634 * r7569634;
        double r7569636 = r7569633 - r7569635;
        double r7569637 = sqrt(r7569636);
        return r7569637;
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

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 2019164 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))