Average Error: 0.0 → 0.0
Time: 924.0ms
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 r174559 = 1.0;
        double r174560 = x;
        double r174561 = r174560 * r174560;
        double r174562 = r174559 - r174561;
        double r174563 = sqrt(r174562);
        return r174563;
}
↓
double f(double x) {
        double r174564 = 1.0;
        double r174565 = x;
        double r174566 = r174565 * r174565;
        double r174567 = r174564 - r174566;
        double r174568 = sqrt(r174567);
        return r174568;
}

Error

Bits error versus x

Try it out

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