Average Error: 0.0 → 0.0
Time: 1.4s
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 r145230 = 1.0;
        double r145231 = x;
        double r145232 = r145231 * r145231;
        double r145233 = r145230 - r145232;
        double r145234 = sqrt(r145233);
        return r145234;
}
↓
double f(double x) {
        double r145235 = 1.0;
        double r145236 = x;
        double r145237 = r145236 * r145236;
        double r145238 = r145235 - r145237;
        double r145239 = sqrt(r145238);
        return r145239;
}

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 2019196 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))