ln(1 + x)

Percentage Accurate: 38.4% → 100.0%

Time: 6.5s

Alternatives: 4

Speedup: 17.1×

Specification

Math

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

FPCore

(FPCore (x) :precision binary64 (log (+ 1.0 x)))

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x)
	return log(Float64(1.0 + x))
end

MATLAB

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

Wolfram

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

Initial Program: 38.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (log (+ 1.0 x)))

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x)
	return log(Float64(1.0 + x))
end

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{log1p}\left(x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (log1p x))

C

double code(double x) {
	return log1p(x);
}

Java

public static double code(double x) {
	return Math.log1p(x);
}

Python

def code(x):
	return math.log1p(x)

Julia

function code(x)
	return log1p(x)
end

Wolfram

code[x_] := N[Log[1 + x], $MachinePrecision]

Derivation

1. Initial program 38.4%

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

   1. log1p-def 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{log1p}\left(x\right) \]
6. Add Preprocessing

Alternative 2: 71.3% accurate, 14.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 38.4%

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

   1. log1p-def 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 67.6%

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

   1. expm1-log1p-u 67.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} \]

   2. expm1-udef 6.6%

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

   3. flip-- 6.4%

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

   4. pow2 6.4%

      \[\leadsto \frac{\color{blue}{{\left(e^{\mathsf{log1p}\left(x\right)}\right)}^{2}} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   5. log1p-udef 6.4%

      \[\leadsto \frac{{\left(e^{\color{blue}{\log \left(1 + x\right)}}\right)}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   6. rem-exp-log 6.4%

      \[\leadsto \frac{{\color{blue}{\left(1 + x\right)}}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   7. +-commutative 6.4%

      \[\leadsto \frac{{\color{blue}{\left(x + 1\right)}}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   8. metadata-eval 6.4%

      \[\leadsto \frac{{\left(x + 1\right)}^{2} - \color{blue}{1}}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   9. log1p-udef 6.4%

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

   10. rem-exp-log 6.4%

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

   11. +-commutative 6.4%

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

7. Applied egg-rr 6.4%

   \[\leadsto \color{blue}{\frac{{\left(x + 1\right)}^{2} - 1}{\left(x + 1\right) + 1}} \]
8. Step-by-step derivation

   1. unpow2 6.4%

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

   2. difference-of-sqr-1 6.4%

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

   3. associate-+l+ 6.4%

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

   4. metadata-eval 6.4%

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

   5. associate--l+ 67.5%

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

   6. metadata-eval 67.5%

      \[\leadsto \frac{\left(x + 2\right) \cdot \left(x + \color{blue}{0}\right)}{\left(x + 1\right) + 1} \]

   7. +-rgt-identity 67.5%

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

   8. associate-+l+ 67.5%

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

   9. metadata-eval 67.5%

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

9. Simplified 67.5%

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

10. Taylor expanded in x around 0 71.1%

    \[\leadsto \frac{\color{blue}{2 \cdot x}}{x + 2} \]
11. Step-by-step derivation

    1. *-commutative 71.1%

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

12. Simplified 71.1%

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

13. Final simplification 71.1%

    \[\leadsto \frac{x \cdot 2}{x + 2} \]
14. Add Preprocessing

Alternative 3: 70.6% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 2.0) x 2.0))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = x;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 2.0d0) then
        tmp = x
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = x;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = x
	else:
		tmp = 2.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = x;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = x;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], x, 2.0]

Derivation

1. Split input into 2 regimes

2. if x < 2

   1. Initial program 8.4%

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

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 97.9%

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

   if 2 < x

   1. Initial program 100.0%

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

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 5.6%

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

      1. expm1-log1p-u 5.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} \]

      2. expm1-udef 5.6%

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

      3. flip-- 5.3%

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

      4. pow2 5.3%

         \[\leadsto \frac{\color{blue}{{\left(e^{\mathsf{log1p}\left(x\right)}\right)}^{2}} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

      5. log1p-udef 5.3%

         \[\leadsto \frac{{\left(e^{\color{blue}{\log \left(1 + x\right)}}\right)}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

      6. rem-exp-log 5.3%

         \[\leadsto \frac{{\color{blue}{\left(1 + x\right)}}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

      7. +-commutative 5.3%

         \[\leadsto \frac{{\color{blue}{\left(x + 1\right)}}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

      8. metadata-eval 5.3%

         \[\leadsto \frac{{\left(x + 1\right)}^{2} - \color{blue}{1}}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

      9. log1p-udef 5.3%

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

      10. rem-exp-log 5.3%

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

      11. +-commutative 5.3%

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

   7. Applied egg-rr 5.3%

      \[\leadsto \color{blue}{\frac{{\left(x + 1\right)}^{2} - 1}{\left(x + 1\right) + 1}} \]
   8. Step-by-step derivation

      1. unpow2 5.3%

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

      2. difference-of-sqr-1 5.3%

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

      3. associate-+l+ 5.3%

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

      4. metadata-eval 5.3%

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

      5. associate--l+ 5.3%

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

      6. metadata-eval 5.3%

         \[\leadsto \frac{\left(x + 2\right) \cdot \left(x + \color{blue}{0}\right)}{\left(x + 1\right) + 1} \]

      7. +-rgt-identity 5.3%

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

      8. associate-+l+ 5.3%

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

      9. metadata-eval 5.3%

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

   9. Simplified 5.3%

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

   10. Taylor expanded in x around 0 14.5%

       \[\leadsto \frac{\color{blue}{2 \cdot x}}{x + 2} \]
   11. Step-by-step derivation

       1. *-commutative 14.5%

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

   12. Simplified 14.5%

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

   13. Taylor expanded in x around inf 14.5%

       \[\leadsto \color{blue}{2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 7.3% accurate, 103.0× 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 38.4%

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

   1. log1p-def 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 67.6%

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

   1. expm1-log1p-u 67.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} \]

   2. expm1-udef 6.6%

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

   3. flip-- 6.4%

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

   4. pow2 6.4%

      \[\leadsto \frac{\color{blue}{{\left(e^{\mathsf{log1p}\left(x\right)}\right)}^{2}} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   5. log1p-udef 6.4%

      \[\leadsto \frac{{\left(e^{\color{blue}{\log \left(1 + x\right)}}\right)}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   6. rem-exp-log 6.4%

      \[\leadsto \frac{{\color{blue}{\left(1 + x\right)}}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   7. +-commutative 6.4%

      \[\leadsto \frac{{\color{blue}{\left(x + 1\right)}}^{2} - 1 \cdot 1}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   8. metadata-eval 6.4%

      \[\leadsto \frac{{\left(x + 1\right)}^{2} - \color{blue}{1}}{e^{\mathsf{log1p}\left(x\right)} + 1} \]

   9. log1p-udef 6.4%

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

   10. rem-exp-log 6.4%

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

   11. +-commutative 6.4%

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

7. Applied egg-rr 6.4%

   \[\leadsto \color{blue}{\frac{{\left(x + 1\right)}^{2} - 1}{\left(x + 1\right) + 1}} \]
8. Step-by-step derivation

   1. unpow2 6.4%

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

   2. difference-of-sqr-1 6.4%

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

   3. associate-+l+ 6.4%

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

   4. metadata-eval 6.4%

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

   5. associate--l+ 67.5%

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

   6. metadata-eval 67.5%

      \[\leadsto \frac{\left(x + 2\right) \cdot \left(x + \color{blue}{0}\right)}{\left(x + 1\right) + 1} \]

   7. +-rgt-identity 67.5%

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

   8. associate-+l+ 67.5%

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

   9. metadata-eval 67.5%

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

9. Simplified 67.5%

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

10. Taylor expanded in x around 0 71.1%

    \[\leadsto \frac{\color{blue}{2 \cdot x}}{x + 2} \]
11. Step-by-step derivation

    1. *-commutative 71.1%

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

12. Simplified 71.1%

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

13. Taylor expanded in x around inf 7.4%

    \[\leadsto \color{blue}{2} \]

14. Final simplification 7.4%

    \[\leadsto 2 \]
15. Add Preprocessing

Developer target: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 + x = 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \log \left(1 + x\right)}{\left(1 + x\right) - 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (== (+ 1.0 x) 1.0) x (/ (* x (log (+ 1.0 x))) (- (+ 1.0 x) 1.0))))

C

double code(double x) {
	double tmp;
	if ((1.0 + x) == 1.0) {
		tmp = x;
	} else {
		tmp = (x * log((1.0 + x))) / ((1.0 + x) - 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((1.0d0 + x) == 1.0d0) then
        tmp = x
    else
        tmp = (x * log((1.0d0 + x))) / ((1.0d0 + x) - 1.0d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x):
	tmp = 0
	if (1.0 + x) == 1.0:
		tmp = x
	else:
		tmp = (x * math.log((1.0 + x))) / ((1.0 + x) - 1.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x)
  :name "ln(1 + x)"
  :precision binary64

  :herbie-target
  (if (== (+ 1.0 x) 1.0) x (/ (* x (log (+ 1.0 x))) (- (+ 1.0 x) 1.0)))

  (log (+ 1.0 x)))