Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}
double f(double x) {
        double r151440 = 1.0;
        double r151441 = x;
        double r151442 = r151441 * r151441;
        double r151443 = r151440 - r151442;
        double r151444 = sqrt(r151443);
        return r151444;
}
↓
double f(double x) {
        double r151445 = 1.0;
        double r151446 = sqrt(r151445);
        double r151447 = x;
        double r151448 = r151446 + r151447;
        double r151449 = r151446 - r151447;
        double r151450 = r151448 * r151449;
        double r151451 = sqrt(r151450);
        return r151451;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \sqrt{\color{blue}{\sqrt{1} \cdot \sqrt{1}} - x \cdot x}\]

  4. Applied difference-of-squares0.0

    \[\leadsto \sqrt{\color{blue}{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))