2sqrt (example 3.1)

Percentage Accurate: 7.0% → 99.7%

Time: 15.6s

Alternatives: 3

Speedup: 1.0×

Specification

\[x > 1 \land x < 10^{+308}\]

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 7.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\mathsf{fma}\left(\frac{1}{\sqrt{1 + x}}, 1 + x, \sqrt{x}\right)} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 7.3%

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

   1. flip-- N/A

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

   2. /-lowering-/.f64 N/A

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

   3. rem-square-sqrt N/A

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

   4. rem-square-sqrt N/A

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

   5. associate--l+ N/A

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

   6. metadata-eval N/A

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

   7. *-rgt-identity N/A

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

   8. +-lowering-+.f64 N/A

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

   9. metadata-eval N/A

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

   10. *-rgt-identity N/A

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

   11. --lowering--.f64 N/A

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

   12. +-lowering-+.f64 N/A

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

   13. sqrt-lowering-sqrt.f64 N/A

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

   14. +-lowering-+.f64 N/A

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

   15. sqrt-lowering-sqrt.f64 9.5

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

4. Applied egg-rr 9.5%

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

   1. +-commutative N/A

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

   2. associate-+l- N/A

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

   3. --lowering--.f64 N/A

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

   4. --lowering--.f64 99.6

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

6. Applied egg-rr 99.6%

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

   1. pow1/2 N/A

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

   2. metadata-eval N/A

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

   3. metadata-eval N/A

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

   4. pow-plus N/A

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

   5. pow-pow N/A

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

   6. pow1/2 N/A

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

   7. inv-pow N/A

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

   8. accelerator-lowering-fma.f64 N/A

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

   9. /-lowering-/.f64 N/A

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

   10. sqrt-lowering-sqrt.f64 N/A

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

   11. +-lowering-+.f64 N/A

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

   12. +-lowering-+.f64 N/A

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

   13. sqrt-lowering-sqrt.f64 99.7

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

8. Applied egg-rr 99.7%

   \[\leadsto \frac{1 - \left(x - x\right)}{\color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt{x + 1}}, x + 1, \sqrt{x}\right)}} \]
9. Step-by-step derivation

   1. +-inverses N/A

      \[\leadsto \frac{1 - \color{blue}{0}}{\mathsf{fma}\left(\frac{1}{\sqrt{x + 1}}, x + 1, \sqrt{x}\right)} \]

   2. metadata-eval 99.7

      \[\leadsto \frac{\color{blue}{1}}{\mathsf{fma}\left(\frac{1}{\sqrt{x + 1}}, x + 1, \sqrt{x}\right)} \]

10. Applied egg-rr 99.7%

    \[\leadsto \frac{\color{blue}{1}}{\mathsf{fma}\left(\frac{1}{\sqrt{x + 1}}, x + 1, \sqrt{x}\right)} \]

11. Final simplification 99.7%

    \[\leadsto \frac{1}{\mathsf{fma}\left(\frac{1}{\sqrt{1 + x}}, 1 + x, \sqrt{x}\right)} \]
12. Add Preprocessing

Alternative 2: 99.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 7.3%

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

   1. flip-- N/A

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

   2. /-lowering-/.f64 N/A

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

   3. rem-square-sqrt N/A

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

   4. rem-square-sqrt N/A

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

   5. associate--l+ N/A

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

   6. metadata-eval N/A

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

   7. *-rgt-identity N/A

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

   8. +-lowering-+.f64 N/A

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

   9. metadata-eval N/A

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

   10. *-rgt-identity N/A

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

   11. --lowering--.f64 N/A

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

   12. +-lowering-+.f64 N/A

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

   13. sqrt-lowering-sqrt.f64 N/A

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

   14. +-lowering-+.f64 N/A

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

   15. sqrt-lowering-sqrt.f64 9.5

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

4. Applied egg-rr 9.5%

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

   1. flip-+ N/A

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

   2. associate-/l/ N/A

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

   3. /-lowering-/.f64 N/A

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

6. Applied egg-rr 9.5%

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

   1. times-frac N/A

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

   2. associate-+r- N/A

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

   3. +-commutative N/A

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

   4. associate--r- N/A

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

   5. +-inverses N/A

      \[\leadsto \frac{1 - \color{blue}{0}}{\sqrt{x + 1} + \sqrt{x}} \cdot \frac{\left(x + -1\right) + x}{\left(x + -1\right) + x} \]

   6. metadata-eval N/A

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

   7. *-inverses N/A

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

   8. *-commutative N/A

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

   9. div-inv N/A

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

   10. /-lowering-/.f64 N/A

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

   11. +-lowering-+.f64 N/A

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

   12. sqrt-lowering-sqrt.f64 N/A

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

   13. +-lowering-+.f64 N/A

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

   14. sqrt-lowering-sqrt.f64 99.6

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

8. Applied egg-rr 99.6%

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

9. Final simplification 99.6%

   \[\leadsto \frac{1}{\sqrt{1 + x} + \sqrt{x}} \]
10. Add Preprocessing

Alternative 3: 7.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 7.3%

   \[\sqrt{x + 1} - \sqrt{x} \]
2. Add Preprocessing

3. Final simplification 7.3%

   \[\leadsto \sqrt{1 + x} - \sqrt{x} \]
4. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Developer Target 2: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot {x}^{-0.5} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 0.5 (pow x -0.5)))

C

double code(double x) {
	return 0.5 * pow(x, -0.5);
}

Fortran

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

Java

public static double code(double x) {
	return 0.5 * Math.pow(x, -0.5);
}

Python

def code(x):
	return 0.5 * math.pow(x, -0.5)

Julia

function code(x)
	return Float64(0.5 * (x ^ -0.5))
end

MATLAB

function tmp = code(x)
	tmp = 0.5 * (x ^ -0.5);
end

Wolfram

code[x_] := N[(0.5 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024207 
(FPCore (x)
  :name "2sqrt (example 3.1)"
  :precision binary64
  :pre (and (> x 1.0) (< x 1e+308))

  :alt
  (! :herbie-platform default (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

  :alt
  (! :herbie-platform default (* 1/2 (pow x -1/2)))

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