Average Error: 0.0 → 0.0
Time: 1.6s
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 r91379 = 1.0;
        double r91380 = x;
        double r91381 = r91380 * r91380;
        double r91382 = r91379 - r91381;
        double r91383 = sqrt(r91382);
        return r91383;
}
↓
double f(double x) {
        double r91384 = 1.0;
        double r91385 = x;
        double r91386 = r91385 * r91385;
        double r91387 = r91384 - r91386;
        double r91388 = sqrt(r91387);
        return r91388;
}

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 2019303 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))