Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\sqrt{1.0 - x \cdot x}\]
↓
\[\sqrt{1.0 - x \cdot x}\]
\sqrt{1.0 - x \cdot x}
↓
\sqrt{1.0 - x \cdot x}
double f(double x) {
        double r9024464 = 1.0;
        double r9024465 = x;
        double r9024466 = r9024465 * r9024465;
        double r9024467 = r9024464 - r9024466;
        double r9024468 = sqrt(r9024467);
        return r9024468;
}
↓
double f(double x) {
        double r9024469 = 1.0;
        double r9024470 = x;
        double r9024471 = r9024470 * r9024470;
        double r9024472 = r9024469 - r9024471;
        double r9024473 = sqrt(r9024472);
        return r9024473;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

    \[\sqrt{1.0 - x \cdot x}\]

  2. Final simplification0.0

    \[\leadsto \sqrt{1.0 - x \cdot x}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))