Average Error: 0.0 → 0.0
Time: 1.3s
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 r157522 = 1.0;
        double r157523 = x;
        double r157524 = r157523 * r157523;
        double r157525 = r157522 - r157524;
        double r157526 = sqrt(r157525);
        return r157526;
}
↓
double f(double x) {
        double r157527 = 1.0;
        double r157528 = x;
        double r157529 = r157528 * r157528;
        double r157530 = r157527 - r157529;
        double r157531 = sqrt(r157530);
        return r157531;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019353 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))