Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[\sqrt{1 - x \cdot x} \]
↓
\[\sqrt{e^{\mathsf{log1p}\left(-x \cdot x\right)}} \]
\sqrt{1 - x \cdot x}
↓
\sqrt{e^{\mathsf{log1p}\left(-x \cdot x\right)}}

(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
↓
(FPCore (x) :precision binary64 (sqrt (exp (log1p (- (* x x))))))
double code(double x) {
	return sqrt(1.0 - (x * x));
}
↓
double code(double x) {
	return sqrt(exp(log1p(-(x * x))));
}

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. Applied add-exp-log_binary640.0

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

  3. Simplified0.0

    \[\leadsto \sqrt{e^{\color{blue}{\mathsf{log1p}\left(-x \cdot x\right)}}} \]

  4. Final simplification0.0

    \[\leadsto \sqrt{e^{\mathsf{log1p}\left(-x \cdot x\right)}} \]

Reproduce

herbie shell --seed 2021357 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))