Average Error: 0.0 → 0.0
Time: 2.0s
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 r146209 = 1.0;
        double r146210 = x;
        double r146211 = r146210 * r146210;
        double r146212 = r146209 - r146211;
        double r146213 = sqrt(r146212);
        return r146213;
}
↓
double f(double x) {
        double r146214 = 1.0;
        double r146215 = x;
        double r146216 = r146215 * r146215;
        double r146217 = r146214 - r146216;
        double r146218 = sqrt(r146217);
        return r146218;
}

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 2020034 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))