Average Error: 0.0 → 0.0
Time: 4.5s
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 r143450 = 1.0;
        double r143451 = x;
        double r143452 = r143451 * r143451;
        double r143453 = r143450 - r143452;
        double r143454 = sqrt(r143453);
        return r143454;
}
↓
double f(double x) {
        double r143455 = 1.0;
        double r143456 = x;
        double r143457 = r143456 * r143456;
        double r143458 = r143455 - r143457;
        double r143459 = sqrt(r143458);
        return r143459;
}

Error

Bits error versus x

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Results

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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 2019194 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))