Average Error: 0.0 → 0.0
Time: 4.8s
Precision: binary64
Cost: 13504
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1}{-1 - x} \cdot \left(x + -1\right)}\right) \]
(FPCore (x) :precision binary64 (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
↓
(FPCore (x)
 :precision binary64
 (* 2.0 (atan (sqrt (* (/ 1.0 (- -1.0 x)) (+ x -1.0))))))
double code(double x) {
	return 2.0 * atan(sqrt(((1.0 - x) / (1.0 + x))));
}
↓
double code(double x) {
	return 2.0 * atan(sqrt(((1.0 / (-1.0 - x)) * (x + -1.0))));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.0d0 * atan(sqrt(((1.0d0 - x) / (1.0d0 + x))))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.0d0 * atan(sqrt(((1.0d0 / ((-1.0d0) - x)) * (x + (-1.0d0)))))
end function

public static double code(double x) {
	return 2.0 * Math.atan(Math.sqrt(((1.0 - x) / (1.0 + x))));
}
↓
public static double code(double x) {
	return 2.0 * Math.atan(Math.sqrt(((1.0 / (-1.0 - x)) * (x + -1.0))));
}

def code(x):
	return 2.0 * math.atan(math.sqrt(((1.0 - x) / (1.0 + x))))
↓
def code(x):
	return 2.0 * math.atan(math.sqrt(((1.0 / (-1.0 - x)) * (x + -1.0))))

function code(x)
	return Float64(2.0 * atan(sqrt(Float64(Float64(1.0 - x) / Float64(1.0 + x)))))
end
↓
function code(x)
	return Float64(2.0 * atan(sqrt(Float64(Float64(1.0 / Float64(-1.0 - x)) * Float64(x + -1.0)))))
end

function tmp = code(x)
	tmp = 2.0 * atan(sqrt(((1.0 - x) / (1.0 + x))));
end
↓
function tmp = code(x)
	tmp = 2.0 * atan(sqrt(((1.0 / (-1.0 - x)) * (x + -1.0))));
end

code[x_] := N[(2.0 * N[ArcTan[N[Sqrt[N[(N[(1.0 - x), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(2.0 * N[ArcTan[N[Sqrt[N[(N[(1.0 / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\frac{1}{-1 - x} \cdot \left(x + -1\right)}\right)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \]

  2. Applied egg-rr0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\color{blue}{\frac{1}{-1 - x} \cdot \left(x + -1\right)}}\right) \]

Alternatives

Alternative 1
Error0.0
Cost13376
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \]
Alternative 2
Error0.6
Cost6720
\[2 \cdot \tan^{-1} \left(1 - x\right) \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))