Rust f64::acosh

Percentage Accurate: 51.4% → 99.9%

Time: 6.2s

Alternatives: 6

Speedup: 2.0×

Specification

\[x \geq 1\]

Math

\[\begin{array}{l} \\ \cosh^{-1} x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (acosh x))

C

double code(double x) {
	return acosh(x);
}

Python

def code(x):
	return math.acosh(x)

Julia

function code(x)
	return acosh(x)
end

MATLAB

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

Wolfram

code[x_] := N[ArcCosh[x], $MachinePrecision]

Initial Program: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(x + \sqrt{x \cdot x - 1}\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \sqrt{x \cdot x + -1} \leq 20000000:\\ \;\;\;\;2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, -1\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (+ x (sqrt (+ (* x x) -1.0))) 20000000.0)
   (* 2.0 (log (sqrt (+ x (sqrt (fma x x -1.0))))))
   (log (+ x x))))

C

double code(double x) {
	double tmp;
	if ((x + sqrt(((x * x) + -1.0))) <= 20000000.0) {
		tmp = 2.0 * log(sqrt((x + sqrt(fma(x, x, -1.0)))));
	} else {
		tmp = log((x + x));
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(x + sqrt(Float64(Float64(x * x) + -1.0))) <= 20000000.0)
		tmp = Float64(2.0 * log(sqrt(Float64(x + sqrt(fma(x, x, -1.0))))));
	else
		tmp = log(Float64(x + x));
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(x + N[Sqrt[N[(N[(x * x), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 20000000.0], N[(2.0 * N[Log[N[Sqrt[N[(x + N[Sqrt[N[(x * x + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Log[N[(x + x), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))) < 2e7

   1. Initial program 99.9%

      \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 99.8%

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

      2. pow2 99.8%

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

      3. log-pow 100.0%

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

      4. fma-neg 100.0%

         \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\color{blue}{\mathsf{fma}\left(x, x, -1\right)}}}\right) \]

      5. metadata-eval 100.0%

         \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, \color{blue}{-1}\right)}}\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, -1\right)}}\right)} \]

   if 2e7 < (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))

   1. Initial program 47.8%

      \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \log \left(x + \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \sqrt{x \cdot x + -1} \leq 20000000:\\ \;\;\;\;2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, -1\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \log \left(x + x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (log (+ x x)))

C

double code(double x) {
	return log((x + x));
}

Fortran

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

Java

public static double code(double x) {
	return Math.log((x + x));
}

Python

def code(x):
	return math.log((x + x))

Julia

function code(x)
	return log(Float64(x + x))
end

MATLAB

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

Wolfram

code[x_] := N[Log[N[(x + x), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 50.4%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 98.4%

   \[\leadsto \log \left(x + \color{blue}{x}\right) \]
4. Add Preprocessing

Alternative 3: 31.4% accurate, 2.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (log x))

C

double code(double x) {
	return log(x);
}

Fortran

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

Java

public static double code(double x) {
	return Math.log(x);
}

Python

def code(x):
	return math.log(x)

Julia

function code(x)
	return log(x)
end

MATLAB

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

Wolfram

code[x_] := N[Log[x], $MachinePrecision]

Derivation

1. Initial program 50.4%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 98.4%

   \[\leadsto \log \left(x + \color{blue}{x}\right) \]

4. Taylor expanded in x around 0 98.1%

   \[\leadsto \color{blue}{\log 2 + \log x} \]

6. Simplified 31.3%

   \[\leadsto \color{blue}{\log x} \]
7. Add Preprocessing

Alternative 4: 14.2% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.3333333333333333)

C

double code(double x) {
	return 1.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.3333333333333333d0
end function

Java

public static double code(double x) {
	return 1.3333333333333333;
}

Python

def code(x):
	return 1.3333333333333333

Julia

function code(x)
	return 1.3333333333333333
end

MATLAB

function tmp = code(x)
	tmp = 1.3333333333333333;
end

Wolfram

code[x_] := 1.3333333333333333

Derivation

1. Initial program 50.4%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 50.4%

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

   2. pow2 50.4%

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

   3. log-pow 50.4%

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

   4. fma-neg 50.4%

      \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\color{blue}{\mathsf{fma}\left(x, x, -1\right)}}}\right) \]

   5. metadata-eval 50.4%

      \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, \color{blue}{-1}\right)}}\right) \]

4. Applied egg-rr 50.4%

   \[\leadsto \color{blue}{2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, -1\right)}}\right)} \]

5. Taylor expanded in x around inf 98.4%

   \[\leadsto 2 \cdot \log \left(\sqrt{x + \color{blue}{x}}\right) \]
6. Step-by-step derivation

   1. flip-+ 0.0%

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

   2. sqrt-div 0.0%

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

   3. +-inverses 0.0%

      \[\leadsto 2 \cdot \log \left(\frac{\sqrt{x \cdot x - x \cdot x}}{\sqrt{\color{blue}{0}}}\right) \]

   4. +-inverses 0.0%

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

   5. log-div 0.0%

      \[\leadsto 2 \cdot \color{blue}{\left(\log \left(\sqrt{x \cdot x - x \cdot x}\right) - \log \left(\sqrt{x \cdot x - x \cdot x}\right)\right)} \]

   6. pow1/2 0.0%

      \[\leadsto 2 \cdot \left(\log \color{blue}{\left({\left(x \cdot x - x \cdot x\right)}^{0.5}\right)} - \log \left(\sqrt{x \cdot x - x \cdot x}\right)\right) \]

   7. +-inverses 0.0%

      \[\leadsto 2 \cdot \left(\log \left({\color{blue}{0}}^{0.5}\right) - \log \left(\sqrt{x \cdot x - x \cdot x}\right)\right) \]

   8. metadata-eval 0.0%

      \[\leadsto 2 \cdot \left(\log \color{blue}{0} - \log \left(\sqrt{x \cdot x - x \cdot x}\right)\right) \]

   9. +-inverses 0.0%

      \[\leadsto 2 \cdot \left(\log \color{blue}{\left(x \cdot x - x \cdot x\right)} - \log \left(\sqrt{x \cdot x - x \cdot x}\right)\right) \]

   10. pow1/2 0.0%

       \[\leadsto 2 \cdot \left(\log \left(x \cdot x - x \cdot x\right) - \log \color{blue}{\left({\left(x \cdot x - x \cdot x\right)}^{0.5}\right)}\right) \]

   11. +-inverses 0.0%

       \[\leadsto 2 \cdot \left(\log \left(x \cdot x - x \cdot x\right) - \log \left({\color{blue}{0}}^{0.5}\right)\right) \]

   12. metadata-eval 0.0%

       \[\leadsto 2 \cdot \left(\log \left(x \cdot x - x \cdot x\right) - \log \color{blue}{0}\right) \]

   13. +-inverses 0.0%

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

   14. log-div 0.0%

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

   15. flip-+ 18.7%

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

   16. add-sqr-sqrt 18.7%

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

   17. add-sqr-sqrt 18.7%

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

   18. add-cbrt-cube 8.1%

       \[\leadsto 2 \cdot \log \color{blue}{\left(\sqrt[3]{\left(\left(x + x\right) \cdot \left(x + x\right)\right) \cdot \left(x + x\right)}\right)} \]

7. Applied egg-rr 0.0%

   \[\leadsto 2 \cdot \color{blue}{\left(0.3333333333333333 \cdot \log \left(\frac{0}{0}\right)\right)} \]

9. Simplified 14.3%

   \[\leadsto 2 \cdot \color{blue}{0.6666666666666666} \]
10. Step-by-step derivation

    1. metadata-eval 14.3%

       \[\leadsto \color{blue}{1.3333333333333333} \]

11. Applied egg-rr 14.3%

    \[\leadsto \color{blue}{1.3333333333333333} \]
12. Add Preprocessing

Alternative 5: 14.1% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

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

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 50.4%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 50.4%

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

   2. pow2 50.4%

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

   3. log-pow 50.4%

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

   4. fma-neg 50.4%

      \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\color{blue}{\mathsf{fma}\left(x, x, -1\right)}}}\right) \]

   5. metadata-eval 50.4%

      \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, \color{blue}{-1}\right)}}\right) \]

4. Applied egg-rr 50.4%

   \[\leadsto \color{blue}{2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, -1\right)}}\right)} \]

5. Taylor expanded in x around inf 98.4%

   \[\leadsto 2 \cdot \log \left(\sqrt{x + \color{blue}{x}}\right) \]
6. Step-by-step derivation

   1. pow1/2 98.4%

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

   2. sqr-pow 98.4%

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

   3. unpow-prod-down 48.9%

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

   4. flip-+ 0.0%

      \[\leadsto 2 \cdot \log \left({\left(\left(x + x\right) \cdot \color{blue}{\frac{x \cdot x - x \cdot x}{x - x}}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   5. +-inverses 0.0%

      \[\leadsto 2 \cdot \log \left({\left(\left(x + x\right) \cdot \frac{x \cdot x - x \cdot x}{\color{blue}{0}}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   6. +-inverses 0.0%

      \[\leadsto 2 \cdot \log \left({\left(\left(x + x\right) \cdot \frac{x \cdot x - x \cdot x}{\color{blue}{x \cdot x - x \cdot x}}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   7. associate-*r/ 0.0%

      \[\leadsto 2 \cdot \log \left({\color{blue}{\left(\frac{\left(x + x\right) \cdot \left(x \cdot x - x \cdot x\right)}{x \cdot x - x \cdot x}\right)}}^{\left(\frac{0.5}{2}\right)}\right) \]

   8. +-inverses 0.0%

      \[\leadsto 2 \cdot \log \left({\left(\frac{\left(x + x\right) \cdot \color{blue}{0}}{x \cdot x - x \cdot x}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   9. +-inverses 0.0%

      \[\leadsto 2 \cdot \log \left({\left(\frac{\left(x + x\right) \cdot \color{blue}{\left(x - x\right)}}{x \cdot x - x \cdot x}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   10. difference-of-squares 0.0%

       \[\leadsto 2 \cdot \log \left({\left(\frac{\color{blue}{x \cdot x - x \cdot x}}{x \cdot x - x \cdot x}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   11. +-inverses 0.0%

       \[\leadsto 2 \cdot \log \left({\left(\frac{x \cdot x - x \cdot x}{\color{blue}{0}}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   12. +-inverses 0.0%

       \[\leadsto 2 \cdot \log \left({\left(\frac{x \cdot x - x \cdot x}{\color{blue}{x - x}}\right)}^{\left(\frac{0.5}{2}\right)}\right) \]

   13. flip-+ 18.8%

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

   14. log-pow 18.8%

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

   15. metadata-eval 18.8%

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

   16. flip-+ 0.0%

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

   17. log-div 0.0%

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

   18. +-inverses 0.0%

       \[\leadsto 2 \cdot \left(0.25 \cdot \left(\log \left(x \cdot x - x \cdot x\right) - \log \color{blue}{0}\right)\right) \]

   19. +-inverses 0.0%

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

7. Applied egg-rr 0.0%

   \[\leadsto 2 \cdot \color{blue}{\left(0.25 \cdot \log \left(\frac{0}{0}\right)\right)} \]

9. Simplified 14.2%

   \[\leadsto 2 \cdot \color{blue}{0.5} \]
10. Step-by-step derivation

    1. metadata-eval 14.2%

       \[\leadsto \color{blue}{1} \]

11. Applied egg-rr 14.2%

    \[\leadsto \color{blue}{1} \]
12. Add Preprocessing

Alternative 6: 1.6% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -2.0)

C

double code(double x) {
	return -2.0;
}

Fortran

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

Java

public static double code(double x) {
	return -2.0;
}

Python

def code(x):
	return -2.0

Julia

function code(x)
	return -2.0
end

MATLAB

function tmp = code(x)
	tmp = -2.0;
end

Wolfram

code[x_] := -2.0

Derivation

1. Initial program 50.4%

   \[\log \left(x + \sqrt{x \cdot x - 1}\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 50.4%

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

   2. pow2 50.4%

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

   3. log-pow 50.4%

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

   4. fma-neg 50.4%

      \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\color{blue}{\mathsf{fma}\left(x, x, -1\right)}}}\right) \]

   5. metadata-eval 50.4%

      \[\leadsto 2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, \color{blue}{-1}\right)}}\right) \]

4. Applied egg-rr 50.4%

   \[\leadsto \color{blue}{2 \cdot \log \left(\sqrt{x + \sqrt{\mathsf{fma}\left(x, x, -1\right)}}\right)} \]

5. Taylor expanded in x around 0 0.0%

   \[\leadsto \color{blue}{2 \cdot \log \left(\sqrt{\sqrt{-1}}\right)} \]

7. Simplified 1.6%

   \[\leadsto \color{blue}{-2} \]
8. Add Preprocessing

Developer Target 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \log \left(x + \sqrt{x - 1} \cdot \sqrt{x + 1}\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(FPCore (x)
  :name "Rust f64::acosh"
  :precision binary64
  :pre (>= x 1.0)

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

  (log (+ x (sqrt (- (* x x) 1.0)))))