Average Error: 0.0 → 0.0
Time: 579.0ms
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 r167083 = 1.0;
        double r167084 = x;
        double r167085 = r167084 * r167084;
        double r167086 = r167083 - r167085;
        double r167087 = sqrt(r167086);
        return r167087;
}
↓
double f(double x) {
        double r167088 = 1.0;
        double r167089 = x;
        double r167090 = r167089 * r167089;
        double r167091 = r167088 - r167090;
        double r167092 = sqrt(r167091);
        return r167092;
}

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 2019354 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))