Rust f64::acosh

Percentage Accurate: 13.2% → 99.1%

Time: 1.9s

Alternatives: 3

Speedup: 4.3×

• Could not converge on a ground truth

  1. x = -1.7030234586554808e+258

Specification

\[x \geq 1\]

Math

\[\cosh^{-1} x \]

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: 13.2% accurate, 1.0× speedup

Math

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

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)
use fmin_fmax_functions
    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: 99.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 12000000000000:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + x\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 12000000000000.0) (* 0.0 1.0) (log (+ x x))))

C

double code(double x) {
	double tmp;
	if (x <= 12000000000000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = log((x + x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 12000000000000.0d0) then
        tmp = 0.0d0 * 1.0d0
    else
        tmp = log((x + x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 12000000000000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = Math.log((x + x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 12000000000000.0:
		tmp = 0.0 * 1.0
	else:
		tmp = math.log((x + x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 12000000000000.0)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = log(Float64(x + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 12000000000000.0)
		tmp = 0.0 * 1.0;
	else
		tmp = log((x + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 12000000000000.0], N[(0.0 * 1.0), $MachinePrecision], N[Log[N[(x + x), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.2e13

   1. Initial program 13.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. difference-of-sqr-1 N/A

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

      5. sqrt-prod N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. fabs-sub N/A

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

      10. lower-fabs.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-sqrt.f64 N/A

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

      13. add-flip N/A

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

      14. fabs-sub N/A

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

      15. lower-fabs.f64 N/A

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

      16. lower--.f64 N/A

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

      17. metadata-eval 73.1%

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

   3. Applied rewrites 73.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 3.4%

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

   6. Applied rewrites 3.4%

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

   7. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot \left(\color{blue}{1} + -1 \cdot x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 76.1%

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

   10. Taylor expanded in undef-var around zero

       \[\leadsto 0 \cdot \left(1 + -1 \cdot 0\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 76.1%

       \[\leadsto 0 \cdot \left(1 + -1 \cdot 0\right) \]

   13. Taylor expanded in x around 0

       \[\leadsto 0 \cdot 1 \]
   14. Step-by-step derivation

   15. Applied rewrites 76.1%

       \[\leadsto 0 \cdot 1 \]

   if 1.2e13 < x

   1. Initial program 13.2%

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

   2. Taylor expanded in x around -inf

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

      1. lower-*.f64 1.3%

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

   4. Applied rewrites 1.3%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 25.3%

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

   7. Applied rewrites 25.3%

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

      1. lift-*.f64 N/A

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

      2. count-2-rev N/A

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

      3. lower-+.f64 25.3%

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

   9. Applied rewrites 25.3%

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

Alternative 2: 99.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 12000000000000:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\cosh^{-1} x\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 12000000000000.0) (* 0.0 1.0) (acosh x)))

C

double code(double x) {
	double tmp;
	if (x <= 12000000000000.0) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = acosh(x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 12000000000000.0:
		tmp = 0.0 * 1.0
	else:
		tmp = math.acosh(x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 12000000000000.0)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = acosh(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 12000000000000.0)
		tmp = 0.0 * 1.0;
	else
		tmp = acosh(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 12000000000000.0], N[(0.0 * 1.0), $MachinePrecision], N[ArcCosh[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.2e13

   1. Initial program 13.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. difference-of-sqr-1 N/A

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

      5. sqrt-prod N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. fabs-sub N/A

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

      10. lower-fabs.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-sqrt.f64 N/A

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

      13. add-flip N/A

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

      14. fabs-sub N/A

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

      15. lower-fabs.f64 N/A

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

      16. lower--.f64 N/A

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

      17. metadata-eval 73.1%

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

   3. Applied rewrites 73.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 3.4%

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

   6. Applied rewrites 3.4%

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

   7. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot \left(\color{blue}{1} + -1 \cdot x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 76.1%

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

   10. Taylor expanded in undef-var around zero

       \[\leadsto 0 \cdot \left(1 + -1 \cdot 0\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 76.1%

       \[\leadsto 0 \cdot \left(1 + -1 \cdot 0\right) \]

   13. Taylor expanded in x around 0

       \[\leadsto 0 \cdot 1 \]
   14. Step-by-step derivation

   15. Applied rewrites 76.1%

       \[\leadsto 0 \cdot 1 \]

   if 1.2e13 < x

   1. Initial program 13.2%

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

      1. lift-log.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sqrt.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. acosh-def-rev N/A

         \[\leadsto \color{blue}{\cosh^{-1} x} \]

      7. lower-acosh.f64 24.6%

         \[\leadsto \color{blue}{\cosh^{-1} x} \]

   3. Applied rewrites 24.6%

      \[\leadsto \color{blue}{\cosh^{-1} x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 76.1% accurate, 4.3× speedup

Math

\[0 \cdot 1 \]

FPCore

(FPCore (x)
  :precision binary64
  (* 0.0 1.0))

C

double code(double x) {
	return 0.0 * 1.0;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = 0.0d0 * 1.0d0
end function

Java

public static double code(double x) {
	return 0.0 * 1.0;
}

Python

def code(x):
	return 0.0 * 1.0

Julia

function code(x)
	return Float64(0.0 * 1.0)
end

MATLAB

function tmp = code(x)
	tmp = 0.0 * 1.0;
end

Wolfram

code[x_] := N[(0.0 * 1.0), $MachinePrecision]

Derivation

1. Initial program 13.2%

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

   1. lift-sqrt.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. difference-of-sqr-1 N/A

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

   5. sqrt-prod N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. fabs-sub N/A

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

   10. lower-fabs.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lower-sqrt.f64 N/A

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

   13. add-flip N/A

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

   14. fabs-sub N/A

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

   15. lower-fabs.f64 N/A

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

   16. lower--.f64 N/A

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

   17. metadata-eval 73.1%

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

3. Applied rewrites 73.1%

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

4. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 3.4%

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

6. Applied rewrites 3.4%

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

7. Taylor expanded in undef-var around zero

   \[\leadsto 0 \cdot \left(\color{blue}{1} + -1 \cdot x\right) \]
8. Step-by-step derivation

9. Applied rewrites 76.1%

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

10. Taylor expanded in undef-var around zero

    \[\leadsto 0 \cdot \left(1 + -1 \cdot 0\right) \]
11. Step-by-step derivation

12. Applied rewrites 76.1%

    \[\leadsto 0 \cdot \left(1 + -1 \cdot 0\right) \]

13. Taylor expanded in x around 0

    \[\leadsto 0 \cdot 1 \]
14. Step-by-step derivation

15. Applied rewrites 76.1%

    \[\leadsto 0 \cdot 1 \]
16. Add Preprocessing

Developer Target 1: 24.7% accurate, 0.8× speedup

Math

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

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)
use fmin_fmax_functions
    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 2025313 -o setup:search
(FPCore (x)
  :name "Rust f64::acosh"
  :precision binary64
  :pre (>= x 1.0)

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

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