Average Error: 0.0 → 0.0
Time: 1.5s
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 r107183 = 1.0;
        double r107184 = x;
        double r107185 = r107184 * r107184;
        double r107186 = r107183 - r107185;
        double r107187 = sqrt(r107186);
        return r107187;
}
↓
double f(double x) {
        double r107188 = 1.0;
        double r107189 = x;
        double r107190 = r107189 * r107189;
        double r107191 = r107188 - r107190;
        double r107192 = sqrt(r107191);
        return r107192;
}

Error

Bits error versus x

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Results

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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 2019199 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))