Average Error: 0.0 → 0.0
Time: 521.0ms
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 r189533 = 1.0;
        double r189534 = x;
        double r189535 = r189534 * r189534;
        double r189536 = r189533 - r189535;
        double r189537 = sqrt(r189536);
        return r189537;
}
↓
double f(double x) {
        double r189538 = 1.0;
        double r189539 = x;
        double r189540 = r189539 * r189539;
        double r189541 = r189538 - r189540;
        double r189542 = sqrt(r189541);
        return r189542;
}

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 2020036 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))