Average Error: 0.0 → 0.0
Time: 1.2s
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 r176912 = 1.0;
        double r176913 = x;
        double r176914 = r176913 * r176913;
        double r176915 = r176912 - r176914;
        double r176916 = sqrt(r176915);
        return r176916;
}
↓
double f(double x) {
        double r176917 = 1.0;
        double r176918 = x;
        double r176919 = r176918 * r176918;
        double r176920 = r176917 - r176919;
        double r176921 = sqrt(r176920);
        return r176921;
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

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 2019298 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))