Average Error: 0.0 → 0.0
Time: 951.0ms
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 r965 = 1.0;
        double r966 = x;
        double r967 = r966 * r966;
        double r968 = r965 - r967;
        double r969 = sqrt(r968);
        return r969;
}
↓
double f(double x) {
        double r970 = 1.0;
        double r971 = x;
        double r972 = r971 * r971;
        double r973 = r970 - r972;
        double r974 = sqrt(r973);
        return r974;
}

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 2020025 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))