Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[\sqrt{1.0 - x \cdot x}\]
↓
\[\sqrt{\sqrt[3]{\left(1.0 - x \cdot x\right) \cdot \left(\left(1.0 - x \cdot x\right) \cdot \left(1.0 - x \cdot x\right)\right)}}\]
\sqrt{1.0 - x \cdot x}
↓
\sqrt{\sqrt[3]{\left(1.0 - x \cdot x\right) \cdot \left(\left(1.0 - x \cdot x\right) \cdot \left(1.0 - x \cdot x\right)\right)}}
double f(double x) {
        double r10436282 = 1.0;
        double r10436283 = x;
        double r10436284 = r10436283 * r10436283;
        double r10436285 = r10436282 - r10436284;
        double r10436286 = sqrt(r10436285);
        return r10436286;
}
↓
double f(double x) {
        double r10436287 = 1.0;
        double r10436288 = x;
        double r10436289 = r10436288 * r10436288;
        double r10436290 = r10436287 - r10436289;
        double r10436291 = r10436290 * r10436290;
        double r10436292 = r10436290 * r10436291;
        double r10436293 = cbrt(r10436292);
        double r10436294 = sqrt(r10436293);
        return r10436294;
}

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

    \[\sqrt{1.0 - x \cdot x}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \sqrt{\color{blue}{\sqrt[3]{\left(\left(1.0 - x \cdot x\right) \cdot \left(1.0 - x \cdot x\right)\right) \cdot \left(1.0 - x \cdot x\right)}}}\]

  4. Final simplification0.0

    \[\leadsto \sqrt{\sqrt[3]{\left(1.0 - x \cdot x\right) \cdot \left(\left(1.0 - x \cdot x\right) \cdot \left(1.0 - x \cdot x\right)\right)}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))