Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\frac{{1}^{3} - {\left(x \cdot x\right)}^{3}}{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\frac{{1}^{3} - {\left(x \cdot x\right)}^{3}}{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}
double f(double x) {
        double r186075 = 1.0;
        double r186076 = x;
        double r186077 = r186076 * r186076;
        double r186078 = r186075 - r186077;
        double r186079 = sqrt(r186078);
        return r186079;
}
↓
double f(double x) {
        double r186080 = 1.0;
        double r186081 = 3.0;
        double r186082 = pow(r186080, r186081);
        double r186083 = x;
        double r186084 = r186083 * r186083;
        double r186085 = pow(r186084, r186081);
        double r186086 = r186082 - r186085;
        double r186087 = r186080 * r186080;
        double r186088 = r186084 * r186084;
        double r186089 = r186080 * r186084;
        double r186090 = r186088 + r186089;
        double r186091 = r186087 + r186090;
        double r186092 = r186086 / r186091;
        double r186093 = sqrt(r186092);
        return r186093;
}

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 flip3--0.0

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

  4. Applied sqrt-div0.0

    \[\leadsto \color{blue}{\frac{\sqrt{{1}^{3} - {\left(x \cdot x\right)}^{3}}}{\sqrt{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}}\]
  5. Using strategy rm

  6. Applied sqrt-undiv0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))