Average Error: 0.0 → 0.0
Time: 1.0s
Precision: binary64
\[\sqrt{1 - x \cdot x} \]
↓
\[e^{0.5 \cdot \mathsf{log1p}\left(x \cdot \left(-x\right)\right)} \]
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
↓
(FPCore (x) :precision binary64 (exp (* 0.5 (log1p (* x (- x))))))
double code(double x) {
	return sqrt((1.0 - (x * x)));
}
↓
double code(double x) {
	return exp((0.5 * log1p((x * -x))));
}

public static double code(double x) {
	return Math.sqrt((1.0 - (x * x)));
}
↓
public static double code(double x) {
	return Math.exp((0.5 * Math.log1p((x * -x))));
}

def code(x):
	return math.sqrt((1.0 - (x * x)))
↓
def code(x):
	return math.exp((0.5 * math.log1p((x * -x))))

function code(x)
	return sqrt(Float64(1.0 - Float64(x * x)))
end
↓
function code(x)
	return exp(Float64(0.5 * log1p(Float64(x * Float64(-x)))))
end

code[x_] := N[Sqrt[N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[x_] := N[Exp[N[(0.5 * N[Log[1 + N[(x * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

\sqrt{1 - x \cdot x}
↓
e^{0.5 \cdot \mathsf{log1p}\left(x \cdot \left(-x\right)\right)}

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 egg-rr0.0

    \[\leadsto \color{blue}{e^{0.5 \cdot \mathsf{log1p}\left(x \cdot \left(-x\right)\right)}} \]

  3. Final simplification0.0

    \[\leadsto e^{0.5 \cdot \mathsf{log1p}\left(x \cdot \left(-x\right)\right)} \]

Reproduce

herbie shell --seed 2022148 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))