Average Error: 0.0 → 0.0
Time: 5.4s
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 r10665073 = 1.0;
        double r10665074 = x;
        double r10665075 = r10665074 * r10665074;
        double r10665076 = r10665073 - r10665075;
        double r10665077 = sqrt(r10665076);
        return r10665077;
}
↓
double f(double x) {
        double r10665078 = 1.0;
        double r10665079 = x;
        double r10665080 = r10665079 * r10665079;
        double r10665081 = r10665078 - r10665080;
        double r10665082 = sqrt(r10665081);
        return r10665082;
}

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 2019179 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))