Average Error: 0.0 → 0.0
Time: 2.0s
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 r122084 = 1.0;
        double r122085 = x;
        double r122086 = r122085 * r122085;
        double r122087 = r122084 - r122086;
        double r122088 = sqrt(r122087);
        return r122088;
}
↓
double f(double x) {
        double r122089 = 1.0;
        double r122090 = x;
        double r122091 = r122090 * r122090;
        double r122092 = r122089 - r122091;
        double r122093 = sqrt(r122092);
        return r122093;
}

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 2019308 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))