Average Error: 0.0 → 0.0
Time: 5.1s
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 r7338439 = 1.0;
        double r7338440 = x;
        double r7338441 = r7338440 * r7338440;
        double r7338442 = r7338439 - r7338441;
        double r7338443 = sqrt(r7338442);
        return r7338443;
}
↓
double f(double x) {
        double r7338444 = 1.0;
        double r7338445 = x;
        double r7338446 = r7338445 * r7338445;
        double r7338447 = r7338444 - r7338446;
        double r7338448 = sqrt(r7338447);
        return r7338448;
}

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 2019168 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))