Average Error: 0.0 → 0.0
Time: 2.3s
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 r171000 = 1.0;
        double r171001 = x;
        double r171002 = r171001 * r171001;
        double r171003 = r171000 - r171002;
        double r171004 = sqrt(r171003);
        return r171004;
}
↓
double f(double x) {
        double r171005 = 1.0;
        double r171006 = x;
        double r171007 = r171006 * r171006;
        double r171008 = r171005 - r171007;
        double r171009 = sqrt(r171008);
        return r171009;
}

Error

Bits error versus x

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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 2020001 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))