Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt[3]{\left(1 - x \cdot x\right) \cdot \sqrt{1 - x \cdot x}}
double f(double x) {
        double r5644204 = 1.0;
        double r5644205 = x;
        double r5644206 = r5644205 * r5644205;
        double r5644207 = r5644204 - r5644206;
        double r5644208 = sqrt(r5644207);
        return r5644208;
}
↓
double f(double x) {
        double r5644209 = 1.0;
        double r5644210 = x;
        double r5644211 = r5644210 * r5644210;
        double r5644212 = r5644209 - r5644211;
        double r5644213 = sqrt(r5644212);
        double r5644214 = r5644212 * r5644213;
        double r5644215 = cbrt(r5644214);
        return r5644215;
}

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

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))