Rust f32::acosh

Percentage Accurate: 53.0% → 99.2%

Time: 4.9s

Alternatives: 9

Speedup: 2.0×

Specification

\[x \geq 1\]

Math

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

FPCore

(FPCore (x) :precision binary32 (acosh x))

C

float code(float x) {
	return acoshf(x);
}

Julia

function code(x)
	return acosh(x)
end

MATLAB

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

Initial Program: 53.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary32 (log (+ x (sqrt (- (* x x) 1.0)))))

C

float code(float x) {
	return logf((x + sqrtf(((x * x) - 1.0f))));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = log((x + sqrt(((x * x) - 1.0e0))))
end function

Julia

function code(x)
	return log(Float32(x + sqrt(Float32(Float32(x * x) - Float32(1.0)))))
end

MATLAB

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

Alternative 1: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \sqrt{x \cdot x + -1} \leq 2000:\\ \;\;\;\;\log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{4} + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= (+ x (sqrt (+ (* x x) -1.0))) 2000.0)
   (log (+ x (sqrt (+ (pow (sqrt x) 4.0) -1.0))))
   (log (+ x x))))

C

float code(float x) {
	float tmp;
	if ((x + sqrtf(((x * x) + -1.0f))) <= 2000.0f) {
		tmp = logf((x + sqrtf((powf(sqrtf(x), 4.0f) + -1.0f))));
	} else {
		tmp = logf((x + x));
	}
	return tmp;
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    real(4) :: tmp
    if ((x + sqrt(((x * x) + (-1.0e0)))) <= 2000.0e0) then
        tmp = log((x + sqrt(((sqrt(x) ** 4.0e0) + (-1.0e0)))))
    else
        tmp = log((x + x))
    end if
    code = tmp
end function

Julia

function code(x)
	tmp = Float32(0.0)
	if (Float32(x + sqrt(Float32(Float32(x * x) + Float32(-1.0)))) <= Float32(2000.0))
		tmp = log(Float32(x + sqrt(Float32((sqrt(x) ^ Float32(4.0)) + Float32(-1.0)))));
	else
		tmp = log(Float32(x + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if ((x + sqrt(((x * x) + single(-1.0)))) <= single(2000.0))
		tmp = log((x + sqrt(((sqrt(x) ^ single(4.0)) + single(-1.0)))));
	else
		tmp = log((x + x));
	end
	tmp_2 = tmp;
end

Derivation

1. Split input into 2 regimes

2. if (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))) < 2e3

   1. Initial program 99.9%

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

      1. pow2 99.9%

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

      2. add-sqr-sqrt 100.0%

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

      3. pow2 100.0%

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

      4. pow-pow 100.0%

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

      5. metadata-eval 100.0%

         \[\leadsto \log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{\color{blue}{4}} - 1}\right) \]

   4. Applied egg-rr 100.0%

      \[\leadsto \log \left(x + \sqrt{\color{blue}{{\left(\sqrt{x}\right)}^{4}} - 1}\right) \]

   if 2e3 < (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))

   1. Initial program 45.4%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \sqrt{x \cdot x + -1} \leq 2000:\\ \;\;\;\;\log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{4} + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sqrt{x \cdot x + -1}\\ \mathbf{if}\;t\_0 \leq 2000:\\ \;\;\;\;\log t\_0\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (+ x (sqrt (+ (* x x) -1.0)))))
   (if (<= t_0 2000.0) (log t_0) (log (+ x x)))))

C

float code(float x) {
	float t_0 = x + sqrtf(((x * x) + -1.0f));
	float tmp;
	if (t_0 <= 2000.0f) {
		tmp = logf(t_0);
	} else {
		tmp = logf((x + x));
	}
	return tmp;
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    real(4) :: t_0
    real(4) :: tmp
    t_0 = x + sqrt(((x * x) + (-1.0e0)))
    if (t_0 <= 2000.0e0) then
        tmp = log(t_0)
    else
        tmp = log((x + x))
    end if
    code = tmp
end function

Julia

function code(x)
	t_0 = Float32(x + sqrt(Float32(Float32(x * x) + Float32(-1.0))))
	tmp = Float32(0.0)
	if (t_0 <= Float32(2000.0))
		tmp = log(t_0);
	else
		tmp = log(Float32(x + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x + sqrt(((x * x) + single(-1.0)));
	tmp = single(0.0);
	if (t_0 <= single(2000.0))
		tmp = log(t_0);
	else
		tmp = log((x + x));
	end
	tmp_2 = tmp;
end

Derivation

1. Split input into 2 regimes

2. if (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))) < 2e3

   1. Initial program 99.9%

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

   if 2e3 < (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))

   1. Initial program 45.4%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \sqrt{x \cdot x + -1} \leq 2000:\\ \;\;\;\;\log \left(x + \sqrt{x \cdot x + -1}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.0% accurate, 2.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary32 (log (+ x x)))

C

float code(float x) {
	return logf((x + x));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = log((x + x))
end function

Julia

function code(x)
	return log(Float32(x + x))
end

MATLAB

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

Derivation

1. Initial program 50.3%

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

3. Taylor expanded in x around inf 96.7%

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

Alternative 4: 44.1% accurate, 2.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary32 (log x))

C

float code(float x) {
	return logf(x);
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = log(x)
end function

Julia

function code(x)
	return log(x)
end

MATLAB

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

Derivation

1. Initial program 50.3%

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

3. Taylor expanded in x around inf 96.7%

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

4. Taylor expanded in x around 0 95.9%

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

6. Simplified 44.0%

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

Alternative 5: 11.2% accurate, 29.6× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(0.9083333333333333 - \frac{2}{x}\right) \end{array} \]

FPCore

(FPCore (x) :precision binary32 (* x (- 0.9083333333333333 (/ 2.0 x))))

C

float code(float x) {
	return x * (0.9083333333333333f - (2.0f / x));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = x * (0.9083333333333333e0 - (2.0e0 / x))
end function

Julia

function code(x)
	return Float32(x * Float32(Float32(0.9083333333333333) - Float32(Float32(2.0) / x)))
end

MATLAB

function tmp = code(x)
	tmp = x * (single(0.9083333333333333) - (single(2.0) / x));
end

Derivation

1. Initial program 50.3%

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

   1. pow2 50.3%

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

   2. add-sqr-sqrt 50.3%

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

   3. pow2 50.3%

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

   4. pow-pow 50.3%

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

   5. metadata-eval 50.3%

      \[\leadsto \log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{\color{blue}{4}} - 1}\right) \]

4. Applied egg-rr 50.3%

   \[\leadsto \log \left(x + \sqrt{\color{blue}{{\left(\sqrt{x}\right)}^{4}} - 1}\right) \]

5. Taylor expanded in x around 0 -0.0%

   \[\leadsto \color{blue}{\log \left(\sqrt{-1}\right) + x \cdot \left({x}^{2} \cdot \left(0.075 \cdot \frac{{x}^{2}}{{\left(\sqrt{-1}\right)}^{5}} - 0.16666666666666666 \cdot \frac{1}{{\left(\sqrt{-1}\right)}^{3}}\right) + \frac{1}{\sqrt{-1}}\right)} \]

7. Simplified 11.6%

   \[\leadsto \color{blue}{-2 + x \cdot 0.9083333333333333} \]

8. Taylor expanded in x around inf 11.6%

   \[\leadsto \color{blue}{x \cdot \left(0.9083333333333333 - 2 \cdot \frac{1}{x}\right)} \]
9. Step-by-step derivation

   1. associate-*r/ 11.6%

      \[\leadsto x \cdot \left(0.9083333333333333 - \color{blue}{\frac{2 \cdot 1}{x}}\right) \]

   2. metadata-eval 11.6%

      \[\leadsto x \cdot \left(0.9083333333333333 - \frac{\color{blue}{2}}{x}\right) \]

10. Simplified 11.6%

    \[\leadsto \color{blue}{x \cdot \left(0.9083333333333333 - \frac{2}{x}\right)} \]
11. Add Preprocessing

Alternative 6: 11.2% accurate, 41.4× speedup

Math

\[\begin{array}{l} \\ -2 + x \cdot 0.9083333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary32 (+ -2.0 (* x 0.9083333333333333)))

C

float code(float x) {
	return -2.0f + (x * 0.9083333333333333f);
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = (-2.0e0) + (x * 0.9083333333333333e0)
end function

Julia

function code(x)
	return Float32(Float32(-2.0) + Float32(x * Float32(0.9083333333333333)))
end

MATLAB

function tmp = code(x)
	tmp = single(-2.0) + (x * single(0.9083333333333333));
end

Derivation

1. Initial program 50.3%

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

   1. pow2 50.3%

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

   2. add-sqr-sqrt 50.3%

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

   3. pow2 50.3%

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

   4. pow-pow 50.3%

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

   5. metadata-eval 50.3%

      \[\leadsto \log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{\color{blue}{4}} - 1}\right) \]

4. Applied egg-rr 50.3%

   \[\leadsto \log \left(x + \sqrt{\color{blue}{{\left(\sqrt{x}\right)}^{4}} - 1}\right) \]

5. Taylor expanded in x around 0 -0.0%

   \[\leadsto \color{blue}{\log \left(\sqrt{-1}\right) + x \cdot \left({x}^{2} \cdot \left(0.075 \cdot \frac{{x}^{2}}{{\left(\sqrt{-1}\right)}^{5}} - 0.16666666666666666 \cdot \frac{1}{{\left(\sqrt{-1}\right)}^{3}}\right) + \frac{1}{\sqrt{-1}}\right)} \]

7. Simplified 11.6%

   \[\leadsto \color{blue}{-2 + x \cdot 0.9083333333333333} \]
8. Add Preprocessing

Alternative 7: 11.2% accurate, 41.4× speedup

Math

\[\begin{array}{l} \\ -2 + x \cdot 0.8333333333333334 \end{array} \]

FPCore

(FPCore (x) :precision binary32 (+ -2.0 (* x 0.8333333333333334)))

C

float code(float x) {
	return -2.0f + (x * 0.8333333333333334f);
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = (-2.0e0) + (x * 0.8333333333333334e0)
end function

Julia

function code(x)
	return Float32(Float32(-2.0) + Float32(x * Float32(0.8333333333333334)))
end

MATLAB

function tmp = code(x)
	tmp = single(-2.0) + (x * single(0.8333333333333334));
end

Derivation

1. Initial program 50.3%

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

   1. pow2 50.3%

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

   2. add-sqr-sqrt 50.3%

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

   3. pow2 50.3%

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

   4. pow-pow 50.3%

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

   5. metadata-eval 50.3%

      \[\leadsto \log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{\color{blue}{4}} - 1}\right) \]

4. Applied egg-rr 50.3%

   \[\leadsto \log \left(x + \sqrt{\color{blue}{{\left(\sqrt{x}\right)}^{4}} - 1}\right) \]

5. Taylor expanded in x around 0 -0.0%

   \[\leadsto \color{blue}{\log \left(\sqrt{-1}\right) + x \cdot \left(-0.16666666666666666 \cdot \frac{{x}^{2}}{{\left(\sqrt{-1}\right)}^{3}} + \frac{1}{\sqrt{-1}}\right)} \]

7. Simplified 11.6%

   \[\leadsto \color{blue}{-2 + x \cdot 0.8333333333333334} \]
8. Add Preprocessing

Alternative 8: 11.4% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.8333333333333334 \end{array} \]

FPCore

(FPCore (x) :precision binary32 (* x 0.8333333333333334))

C

float code(float x) {
	return x * 0.8333333333333334f;
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = x * 0.8333333333333334e0
end function

Julia

function code(x)
	return Float32(x * Float32(0.8333333333333334))
end

MATLAB

function tmp = code(x)
	tmp = x * single(0.8333333333333334);
end

Derivation

1. Initial program 50.3%

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

   1. pow2 50.3%

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

   2. add-sqr-sqrt 50.3%

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

   3. pow2 50.3%

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

   4. pow-pow 50.3%

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

   5. metadata-eval 50.3%

      \[\leadsto \log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{\color{blue}{4}} - 1}\right) \]

4. Applied egg-rr 50.3%

   \[\leadsto \log \left(x + \sqrt{\color{blue}{{\left(\sqrt{x}\right)}^{4}} - 1}\right) \]

5. Taylor expanded in x around 0 -0.0%

   \[\leadsto \color{blue}{\log \left(\sqrt{-1}\right) + x \cdot \left(-0.16666666666666666 \cdot \frac{{x}^{2}}{{\left(\sqrt{-1}\right)}^{3}} + \frac{1}{\sqrt{-1}}\right)} \]

7. Simplified 11.6%

   \[\leadsto \color{blue}{-2 + x \cdot 0.8333333333333334} \]

8. Taylor expanded in x around inf 11.6%

   \[\leadsto \color{blue}{x \cdot \left(0.8333333333333334 - 2 \cdot \frac{1}{x}\right)} \]
9. Step-by-step derivation

   1. associate-*r/ 11.6%

      \[\leadsto x \cdot \left(0.8333333333333334 - \color{blue}{\frac{2 \cdot 1}{x}}\right) \]

   2. metadata-eval 11.6%

      \[\leadsto x \cdot \left(0.8333333333333334 - \frac{\color{blue}{2}}{x}\right) \]

10. Simplified 11.6%

    \[\leadsto \color{blue}{x \cdot \left(0.8333333333333334 - \frac{2}{x}\right)} \]

11. Taylor expanded in x around inf 11.6%

    \[\leadsto x \cdot \color{blue}{0.8333333333333334} \]
12. Add Preprocessing

Alternative 9: 3.1% accurate, 207.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary32 -2.0)

C

float code(float x) {
	return -2.0f;
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = -2.0e0
end function

Julia

function code(x)
	return Float32(-2.0)
end

MATLAB

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

Derivation

1. Initial program 50.3%

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

   1. pow2 50.3%

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

   2. add-sqr-sqrt 50.3%

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

   3. pow2 50.3%

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

   4. pow-pow 50.3%

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

   5. metadata-eval 50.3%

      \[\leadsto \log \left(x + \sqrt{{\left(\sqrt{x}\right)}^{\color{blue}{4}} - 1}\right) \]

4. Applied egg-rr 50.3%

   \[\leadsto \log \left(x + \sqrt{\color{blue}{{\left(\sqrt{x}\right)}^{4}} - 1}\right) \]

5. Taylor expanded in x around 0 -0.0%

   \[\leadsto \color{blue}{\log \left(\sqrt{-1}\right) + x \cdot \left(-0.16666666666666666 \cdot \frac{{x}^{2}}{{\left(\sqrt{-1}\right)}^{3}} + \frac{1}{\sqrt{-1}}\right)} \]

7. Simplified 11.6%

   \[\leadsto \color{blue}{-2 + x \cdot 0.8333333333333334} \]

8. Taylor expanded in x around 0 3.1%

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

Developer Target 1: 99.2% 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 binary32
 (log (+ x (* (sqrt (- x 1.0)) (sqrt (+ x 1.0))))))

C

float code(float x) {
	return logf((x + (sqrtf((x - 1.0f)) * sqrtf((x + 1.0f)))));
}

Fortran

real(4) function code(x)
    real(4), intent (in) :: x
    code = log((x + (sqrt((x - 1.0e0)) * sqrt((x + 1.0e0)))))
end function

Julia

function code(x)
	return log(Float32(x + Float32(sqrt(Float32(x - Float32(1.0))) * sqrt(Float32(x + Float32(1.0))))))
end

MATLAB

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

Reproduce

herbie shell --seed 2024144 
(FPCore (x)
  :name "Rust f32::acosh"
  :precision binary32
  :pre (>= x 1.0)

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

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