Average Error: 0.0 → 0.0
Time: 4.4s
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 r3523991 = 1.0;
        double r3523992 = x;
        double r3523993 = r3523992 * r3523992;
        double r3523994 = r3523991 - r3523993;
        double r3523995 = sqrt(r3523994);
        return r3523995;
}
↓
double f(double x) {
        double r3523996 = 1.0;
        double r3523997 = x;
        double r3523998 = r3523997 * r3523997;
        double r3523999 = r3523996 - r3523998;
        double r3524000 = sqrt(r3523999);
        return r3524000;
}

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 2019156 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))