Average Error: 0.0 → 0.0
Time: 1.9s
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 r173189 = 1.0;
        double r173190 = x;
        double r173191 = r173190 * r173190;
        double r173192 = r173189 - r173191;
        double r173193 = sqrt(r173192);
        return r173193;
}
↓
double f(double x) {
        double r173194 = 1.0;
        double r173195 = x;
        double r173196 = r173195 * r173195;
        double r173197 = r173194 - r173196;
        double r173198 = sqrt(r173197);
        return r173198;
}

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 2019199 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))