Average Error: 0.0 → 0.0
Time: 14.8s
Precision: binary64
Cost: 512
\[\sqrt{1 - x \cdot x}\]
↓
\[e^{\log \left(\sqrt{1 - x \cdot x}\right)}\]
\sqrt{1 - x \cdot x}
↓
e^{\log \left(\sqrt{1 - x \cdot x}\right)}
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
↓
(FPCore (x) :precision binary64 (exp (log (sqrt (- 1.0 (* x x))))))
double code(double x) {
	return sqrt(1.0 - (x * x));
}
↓
double code(double x) {
	return exp(log(sqrt(1.0 - (x * x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs
Alternative 1
Accuracy0.0
Cost576
\[\sqrt[3]{{\left(\sqrt{1 - x \cdot x}\right)}^{3}}\]

Derivation

  1. Initial program 0.0

    \[\sqrt{1 - x \cdot x}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity_binary64_55340.0

    \[\leadsto \color{blue}{1 \cdot \sqrt{1 - x \cdot x}}\]
  4. Using strategy rm

  5. Applied add-exp-log_binary64_55720.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020322 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))