bug333 (missed optimization)

Percentage Accurate: 8.2% → 100.0%

Time: 4.6s

Alternatives: 4

Speedup: 207.0×

Specification

\[-1 \leq x \land x \leq 1\]

Math

\[\begin{array}{l} \\ \sqrt{1 + x} - \sqrt{1 - x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))

C

double code(double x) {
	return sqrt((1.0 + x)) - sqrt((1.0 - x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((1.0d0 + x)) - sqrt((1.0d0 - x))
end function

Java

public static double code(double x) {
	return Math.sqrt((1.0 + x)) - Math.sqrt((1.0 - x));
}

Python

def code(x):
	return math.sqrt((1.0 + x)) - math.sqrt((1.0 - x))

Julia

function code(x)
	return Float64(sqrt(Float64(1.0 + x)) - sqrt(Float64(1.0 - x)))
end

MATLAB

function tmp = code(x)
	tmp = sqrt((1.0 + x)) - sqrt((1.0 - x));
end

Wolfram

code[x_] := N[(N[Sqrt[N[(1.0 + x), $MachinePrecision]], $MachinePrecision] - N[Sqrt[N[(1.0 - x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 8.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{1 + x} - \sqrt{1 - x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))

C

double code(double x) {
	return sqrt((1.0 + x)) - sqrt((1.0 - x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((1.0d0 + x)) - sqrt((1.0d0 - x))
end function

Java

public static double code(double x) {
	return Math.sqrt((1.0 + x)) - Math.sqrt((1.0 - x));
}

Python

def code(x):
	return math.sqrt((1.0 + x)) - math.sqrt((1.0 - x))

Julia

function code(x)
	return Float64(sqrt(Float64(1.0 + x)) - sqrt(Float64(1.0 - x)))
end

MATLAB

function tmp = code(x)
	tmp = sqrt((1.0 + x)) - sqrt((1.0 - x));
end

Wolfram

code[x_] := N[(N[Sqrt[N[(1.0 + x), $MachinePrecision]], $MachinePrecision] - N[Sqrt[N[(1.0 - x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + x}{\sqrt{x + 1} + \sqrt{1 - x}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (+ x x) (+ (sqrt (+ x 1.0)) (sqrt (- 1.0 x)))))

C

double code(double x) {
	return (x + x) / (sqrt((x + 1.0)) + sqrt((1.0 - x)));
}

Fortran

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

Java

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

Python

def code(x):
	return (x + x) / (math.sqrt((x + 1.0)) + math.sqrt((1.0 - x)))

Julia

function code(x)
	return Float64(Float64(x + x) / Float64(sqrt(Float64(x + 1.0)) + sqrt(Float64(1.0 - x))))
end

MATLAB

function tmp = code(x)
	tmp = (x + x) / (sqrt((x + 1.0)) + sqrt((1.0 - x)));
end

Wolfram

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

Derivation

1. Initial program 8.6%

   \[\sqrt{1 + x} - \sqrt{1 - x} \]
2. Step-by-step derivation

   1. flip-- 8.6%

      \[\leadsto \color{blue}{\frac{\sqrt{1 + x} \cdot \sqrt{1 + x} - \sqrt{1 - x} \cdot \sqrt{1 - x}}{\sqrt{1 + x} + \sqrt{1 - x}}} \]

   2. div-inv 8.6%

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

   3. add-sqr-sqrt 8.6%

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

   4. add-sqr-sqrt 8.6%

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

   5. associate--r- 21.3%

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

   6. add-exp-log 21.3%

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

   7. log1p-udef 21.3%

      \[\leadsto \left(\left(e^{\color{blue}{\mathsf{log1p}\left(x\right)}} - 1\right) + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   8. expm1-udef 100.0%

      \[\leadsto \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   9. expm1-log1p-u 100.0%

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

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(x + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}}} \]
4. Step-by-step derivation

   1. associate-*r/ 100.0%

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

   2. *-rgt-identity 100.0%

      \[\leadsto \frac{\color{blue}{x + x}}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   3. +-commutative 100.0%

      \[\leadsto \frac{x + x}{\sqrt{\color{blue}{x + 1}} + \sqrt{1 - x}} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{x + x}{\sqrt{x + 1} + \sqrt{1 - x}}} \]

6. Final simplification 100.0%

   \[\leadsto \frac{x + x}{\sqrt{x + 1} + \sqrt{1 - x}} \]

Alternative 2: 99.6% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 0.5\right) \cdot \left(2 + x \cdot \left(x \cdot 0.25\right)\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (* x 0.5) (+ 2.0 (* x (* x 0.25)))))

C

double code(double x) {
	return (x * 0.5) * (2.0 + (x * (x * 0.25)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 0.5d0) * (2.0d0 + (x * (x * 0.25d0)))
end function

Java

public static double code(double x) {
	return (x * 0.5) * (2.0 + (x * (x * 0.25)));
}

Python

def code(x):
	return (x * 0.5) * (2.0 + (x * (x * 0.25)))

Julia

function code(x)
	return Float64(Float64(x * 0.5) * Float64(2.0 + Float64(x * Float64(x * 0.25))))
end

MATLAB

function tmp = code(x)
	tmp = (x * 0.5) * (2.0 + (x * (x * 0.25)));
end

Wolfram

code[x_] := N[(N[(x * 0.5), $MachinePrecision] * N[(2.0 + N[(x * N[(x * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 8.6%

   \[\sqrt{1 + x} - \sqrt{1 - x} \]
2. Step-by-step derivation

   1. flip-- 8.6%

      \[\leadsto \color{blue}{\frac{\sqrt{1 + x} \cdot \sqrt{1 + x} - \sqrt{1 - x} \cdot \sqrt{1 - x}}{\sqrt{1 + x} + \sqrt{1 - x}}} \]

   2. div-inv 8.6%

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

   3. add-sqr-sqrt 8.6%

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

   4. add-sqr-sqrt 8.6%

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

   5. associate--r- 21.3%

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

   6. add-exp-log 21.3%

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

   7. log1p-udef 21.3%

      \[\leadsto \left(\left(e^{\color{blue}{\mathsf{log1p}\left(x\right)}} - 1\right) + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   8. expm1-udef 100.0%

      \[\leadsto \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   9. expm1-log1p-u 100.0%

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

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(x + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}}} \]
4. Step-by-step derivation

   1. associate-*r/ 100.0%

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

   2. *-rgt-identity 100.0%

      \[\leadsto \frac{\color{blue}{x + x}}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   3. +-commutative 100.0%

      \[\leadsto \frac{x + x}{\sqrt{\color{blue}{x + 1}} + \sqrt{1 - x}} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{x + x}{\sqrt{x + 1} + \sqrt{1 - x}}} \]

6. Taylor expanded in x around 0 99.9%

   \[\leadsto \frac{x + x}{\color{blue}{2 + -0.25 \cdot {x}^{2}}} \]

8. Simplified 99.9%

   \[\leadsto \frac{x + x}{\color{blue}{2 + \left(x \cdot x\right) \cdot -0.25}} \]
9. Step-by-step derivation

   1. flip-+ 99.9%

      \[\leadsto \frac{x + x}{\color{blue}{\frac{2 \cdot 2 - \left(\left(x \cdot x\right) \cdot -0.25\right) \cdot \left(\left(x \cdot x\right) \cdot -0.25\right)}{2 - \left(x \cdot x\right) \cdot -0.25}}} \]

   2. associate-/r/ 99.9%

      \[\leadsto \color{blue}{\frac{x + x}{2 \cdot 2 - \left(\left(x \cdot x\right) \cdot -0.25\right) \cdot \left(\left(x \cdot x\right) \cdot -0.25\right)} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right)} \]

   3. metadata-eval 99.9%

      \[\leadsto \frac{x + x}{\color{blue}{4} - \left(\left(x \cdot x\right) \cdot -0.25\right) \cdot \left(\left(x \cdot x\right) \cdot -0.25\right)} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   4. *-commutative 99.9%

      \[\leadsto \frac{x + x}{4 - \color{blue}{\left(-0.25 \cdot \left(x \cdot x\right)\right)} \cdot \left(\left(x \cdot x\right) \cdot -0.25\right)} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   5. *-commutative 99.9%

      \[\leadsto \frac{x + x}{4 - \left(-0.25 \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{\left(-0.25 \cdot \left(x \cdot x\right)\right)}} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   6. swap-sqr 99.9%

      \[\leadsto \frac{x + x}{4 - \color{blue}{\left(-0.25 \cdot -0.25\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   7. metadata-eval 99.9%

      \[\leadsto \frac{x + x}{4 - \color{blue}{0.0625} \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   8. pow2 99.9%

      \[\leadsto \frac{x + x}{4 - 0.0625 \cdot \left(\color{blue}{{x}^{2}} \cdot \left(x \cdot x\right)\right)} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   9. pow2 99.9%

      \[\leadsto \frac{x + x}{4 - 0.0625 \cdot \left({x}^{2} \cdot \color{blue}{{x}^{2}}\right)} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   10. pow-prod-up 99.9%

       \[\leadsto \frac{x + x}{4 - 0.0625 \cdot \color{blue}{{x}^{\left(2 + 2\right)}}} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   11. metadata-eval 99.9%

       \[\leadsto \frac{x + x}{4 - 0.0625 \cdot {x}^{\color{blue}{4}}} \cdot \left(2 - \left(x \cdot x\right) \cdot -0.25\right) \]

   12. *-commutative 99.9%

       \[\leadsto \frac{x + x}{4 - 0.0625 \cdot {x}^{4}} \cdot \left(2 - \color{blue}{-0.25 \cdot \left(x \cdot x\right)}\right) \]

   13. cancel-sign-sub-inv 99.9%

       \[\leadsto \frac{x + x}{4 - 0.0625 \cdot {x}^{4}} \cdot \color{blue}{\left(2 + \left(--0.25\right) \cdot \left(x \cdot x\right)\right)} \]

   14. metadata-eval 99.9%

       \[\leadsto \frac{x + x}{4 - 0.0625 \cdot {x}^{4}} \cdot \left(2 + \color{blue}{0.25} \cdot \left(x \cdot x\right)\right) \]

10. Applied egg-rr 99.9%

    \[\leadsto \color{blue}{\frac{x + x}{4 - 0.0625 \cdot {x}^{4}} \cdot \left(2 + 0.25 \cdot \left(x \cdot x\right)\right)} \]
11. Step-by-step derivation

    1. associate-*r* 99.9%

       \[\leadsto \frac{x + x}{4 - 0.0625 \cdot {x}^{4}} \cdot \left(2 + \color{blue}{\left(0.25 \cdot x\right) \cdot x}\right) \]

12. Simplified 99.9%

    \[\leadsto \color{blue}{\frac{x + x}{4 - 0.0625 \cdot {x}^{4}} \cdot \left(2 + \left(0.25 \cdot x\right) \cdot x\right)} \]

13. Taylor expanded in x around 0 99.8%

    \[\leadsto \color{blue}{\left(0.5 \cdot x\right)} \cdot \left(2 + \left(0.25 \cdot x\right) \cdot x\right) \]
14. Step-by-step derivation

    1. *-commutative 99.8%

       \[\leadsto \color{blue}{\left(x \cdot 0.5\right)} \cdot \left(2 + \left(0.25 \cdot x\right) \cdot x\right) \]

15. Simplified 99.8%

    \[\leadsto \color{blue}{\left(x \cdot 0.5\right)} \cdot \left(2 + \left(0.25 \cdot x\right) \cdot x\right) \]

16. Final simplification 99.8%

    \[\leadsto \left(x \cdot 0.5\right) \cdot \left(2 + x \cdot \left(x \cdot 0.25\right)\right) \]

Alternative 3: 99.6% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \frac{x + x}{2 + \left(x \cdot x\right) \cdot -0.25} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (+ x x) (+ 2.0 (* (* x x) -0.25))))

C

double code(double x) {
	return (x + x) / (2.0 + ((x * x) * -0.25));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + x) / (2.0d0 + ((x * x) * (-0.25d0)))
end function

Java

public static double code(double x) {
	return (x + x) / (2.0 + ((x * x) * -0.25));
}

Python

def code(x):
	return (x + x) / (2.0 + ((x * x) * -0.25))

Julia

function code(x)
	return Float64(Float64(x + x) / Float64(2.0 + Float64(Float64(x * x) * -0.25)))
end

MATLAB

function tmp = code(x)
	tmp = (x + x) / (2.0 + ((x * x) * -0.25));
end

Wolfram

code[x_] := N[(N[(x + x), $MachinePrecision] / N[(2.0 + N[(N[(x * x), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 8.6%

   \[\sqrt{1 + x} - \sqrt{1 - x} \]
2. Step-by-step derivation

   1. flip-- 8.6%

      \[\leadsto \color{blue}{\frac{\sqrt{1 + x} \cdot \sqrt{1 + x} - \sqrt{1 - x} \cdot \sqrt{1 - x}}{\sqrt{1 + x} + \sqrt{1 - x}}} \]

   2. div-inv 8.6%

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

   3. add-sqr-sqrt 8.6%

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

   4. add-sqr-sqrt 8.6%

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

   5. associate--r- 21.3%

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

   6. add-exp-log 21.3%

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

   7. log1p-udef 21.3%

      \[\leadsto \left(\left(e^{\color{blue}{\mathsf{log1p}\left(x\right)}} - 1\right) + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   8. expm1-udef 100.0%

      \[\leadsto \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   9. expm1-log1p-u 100.0%

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

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(x + x\right) \cdot \frac{1}{\sqrt{1 + x} + \sqrt{1 - x}}} \]
4. Step-by-step derivation

   1. associate-*r/ 100.0%

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

   2. *-rgt-identity 100.0%

      \[\leadsto \frac{\color{blue}{x + x}}{\sqrt{1 + x} + \sqrt{1 - x}} \]

   3. +-commutative 100.0%

      \[\leadsto \frac{x + x}{\sqrt{\color{blue}{x + 1}} + \sqrt{1 - x}} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{x + x}{\sqrt{x + 1} + \sqrt{1 - x}}} \]

6. Taylor expanded in x around 0 99.9%

   \[\leadsto \frac{x + x}{\color{blue}{2 + -0.25 \cdot {x}^{2}}} \]

8. Simplified 99.9%

   \[\leadsto \frac{x + x}{\color{blue}{2 + \left(x \cdot x\right) \cdot -0.25}} \]

9. Final simplification 99.9%

   \[\leadsto \frac{x + x}{2 + \left(x \cdot x\right) \cdot -0.25} \]

Alternative 4: 99.1% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x) :precision binary64 x)

C

double code(double x) {
	return x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x
end function

Java

public static double code(double x) {
	return x;
}

Python

def code(x):
	return x

Julia

function code(x)
	return x
end

MATLAB

function tmp = code(x)
	tmp = x;
end

Wolfram

code[x_] := x

Derivation

1. Initial program 8.6%

   \[\sqrt{1 + x} - \sqrt{1 - x} \]

2. Taylor expanded in x around 0 99.2%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 99.2%

   \[\leadsto x \]

Developer target: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2 \cdot x}{\sqrt{1 + x} + \sqrt{1 - x}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (* 2.0 x) (+ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x)))))

C

double code(double x) {
	return (2.0 * x) / (sqrt((1.0 + x)) + sqrt((1.0 - x)));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023293 
(FPCore (x)
  :name "bug333 (missed optimization)"
  :precision binary64
  :pre (and (<= -1.0 x) (<= x 1.0))

  :herbie-target
  (/ (* 2.0 x) (+ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))

  (- (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))