Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\log \left(e^{\sqrt{1 - x \cdot x}}\right)\]
\sqrt{1 - x \cdot x}
↓
\log \left(e^{\sqrt{1 - x \cdot x}}\right)
double f(double x) {
        double r198659 = 1.0;
        double r198660 = x;
        double r198661 = r198660 * r198660;
        double r198662 = r198659 - r198661;
        double r198663 = sqrt(r198662);
        return r198663;
}
↓
double f(double x) {
        double r198664 = 1.0;
        double r198665 = x;
        double r198666 = r198665 * r198665;
        double r198667 = r198664 - r198666;
        double r198668 = sqrt(r198667);
        double r198669 = exp(r198668);
        double r198670 = log(r198669);
        return r198670;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))