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 r148139 = 1.0;
        double r148140 = x;
        double r148141 = r148140 * r148140;
        double r148142 = r148139 - r148141;
        double r148143 = sqrt(r148142);
        return r148143;
}
↓
double f(double x) {
        double r148144 = 1.0;
        double r148145 = x;
        double r148146 = r148145 * r148145;
        double r148147 = r148144 - r148146;
        double r148148 = sqrt(r148147);
        return r148148;
}

Error

Bits error versus x

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Your Program's Arguments

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 2020056 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))