Average Error: 0.0 → 0.0
Time: 4.1s
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 r109533 = 1.0;
        double r109534 = x;
        double r109535 = r109534 * r109534;
        double r109536 = r109533 - r109535;
        double r109537 = sqrt(r109536);
        return r109537;
}
↓
double f(double x) {
        double r109538 = 1.0;
        double r109539 = x;
        double r109540 = r109539 * r109539;
        double r109541 = r109538 - r109540;
        double r109542 = sqrt(r109541);
        return r109542;
}

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 2019208 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))