Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\sqrt[3]{{\left(1 - x \cdot x\right)}^{3}}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\sqrt[3]{{\left(1 - x \cdot x\right)}^{3}}}
double f(double x) {
        double r100540 = 1.0;
        double r100541 = x;
        double r100542 = r100541 * r100541;
        double r100543 = r100540 - r100542;
        double r100544 = sqrt(r100543);
        return r100544;
}
↓
double f(double x) {
        double r100545 = 1.0;
        double r100546 = x;
        double r100547 = r100546 * r100546;
        double r100548 = r100545 - r100547;
        double r100549 = 3.0;
        double r100550 = pow(r100548, r100549);
        double r100551 = cbrt(r100550);
        double r100552 = sqrt(r100551);
        return r100552;
}

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-cbrt-cube0.0

    \[\leadsto \sqrt{\color{blue}{\sqrt[3]{\left(\left(1 - x \cdot x\right) \cdot \left(1 - x \cdot x\right)\right) \cdot \left(1 - x \cdot x\right)}}}\]

  4. Simplified0.0

    \[\leadsto \sqrt{\sqrt[3]{\color{blue}{{\left(1 - x \cdot x\right)}^{3}}}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt{\sqrt[3]{{\left(1 - x \cdot x\right)}^{3}}}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))