Average Error: 0.0 → 0.0
Time: 8.4s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\log \left(\sqrt{e^{\sqrt{1 - x \cdot x}}}\right) + \log \left(\sqrt{e^{\sqrt{1 - x \cdot x}}}\right)\]
\sqrt{1 - x \cdot x}
↓
\log \left(\sqrt{e^{\sqrt{1 - x \cdot x}}}\right) + \log \left(\sqrt{e^{\sqrt{1 - x \cdot x}}}\right)
double f(double x) {
        double r8120992 = 1.0;
        double r8120993 = x;
        double r8120994 = r8120993 * r8120993;
        double r8120995 = r8120992 - r8120994;
        double r8120996 = sqrt(r8120995);
        return r8120996;
}
↓
double f(double x) {
        double r8120997 = 1.0;
        double r8120998 = x;
        double r8120999 = r8120998 * r8120998;
        double r8121000 = r8120997 - r8120999;
        double r8121001 = sqrt(r8121000);
        double r8121002 = exp(r8121001);
        double r8121003 = sqrt(r8121002);
        double r8121004 = log(r8121003);
        double r8121005 = r8121004 + r8121004;
        return r8121005;
}

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-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\sqrt{1 - x \cdot x}}\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.0

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

  6. Applied log-prod0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))