expq2 (section 3.11)

Percentage Accurate: 37.2% → 100.0%

Time: 4.5s

Alternatives: 5

Speedup: 68.3×

Specification

\[715 > x\]

Math

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

FPCore

(FPCore (x) :precision binary64 (/ (exp x) (- (exp x) 1.0)))

C

double code(double x) {
	return exp(x) / (exp(x) - 1.0);
}

Fortran

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

Java

public static double code(double x) {
	return Math.exp(x) / (Math.exp(x) - 1.0);
}

Python

def code(x):
	return math.exp(x) / (math.exp(x) - 1.0)

Julia

function code(x)
	return Float64(exp(x) / Float64(exp(x) - 1.0))
end

MATLAB

function tmp = code(x)
	tmp = exp(x) / (exp(x) - 1.0);
end

Wolfram

code[x_] := N[(N[Exp[x], $MachinePrecision] / N[(N[Exp[x], $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 37.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (/ (exp x) (- (exp x) 1.0)))

C

double code(double x) {
	return exp(x) / (exp(x) - 1.0);
}

Fortran

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

Java

public static double code(double x) {
	return Math.exp(x) / (Math.exp(x) - 1.0);
}

Python

def code(x):
	return math.exp(x) / (math.exp(x) - 1.0)

Julia

function code(x)
	return Float64(exp(x) / Float64(exp(x) - 1.0))
end

MATLAB

function tmp = code(x)
	tmp = exp(x) / (exp(x) - 1.0);
end

Wolfram

code[x_] := N[(N[Exp[x], $MachinePrecision] / N[(N[Exp[x], $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{-1}{\mathsf{expm1}\left(-x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ -1.0 (expm1 (- x))))

C

double code(double x) {
	return -1.0 / expm1(-x);
}

Java

public static double code(double x) {
	return -1.0 / Math.expm1(-x);
}

Python

def code(x):
	return -1.0 / math.expm1(-x)

Julia

function code(x)
	return Float64(-1.0 / expm1(Float64(-x)))
end

Wolfram

code[x_] := N[(-1.0 / N[(Exp[(-x)] - 1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 37.9%

   \[\frac{e^{x}}{e^{x} - 1} \]
2. Step-by-step derivation

   1. expm1-def 100.0%

      \[\leadsto \frac{e^{x}}{\color{blue}{\mathsf{expm1}\left(x\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]
4. Step-by-step derivation

   1. add-sqr-sqrt 67.3%

      \[\leadsto \color{blue}{\sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}}} \]

   2. pow1/2 67.3%

      \[\leadsto \color{blue}{{\left(\frac{e^{x}}{\mathsf{expm1}\left(x\right)}\right)}^{0.5}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   3. clear-num 67.3%

      \[\leadsto {\color{blue}{\left(\frac{1}{\frac{\mathsf{expm1}\left(x\right)}{e^{x}}}\right)}}^{0.5} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   4. inv-pow 67.3%

      \[\leadsto {\color{blue}{\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{-1}\right)}}^{0.5} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   5. metadata-eval 67.3%

      \[\leadsto {\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{\color{blue}{\left(-1\right)}}\right)}^{0.5} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   6. pow-pow 67.4%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   7. expm1-udef 37.0%

      \[\leadsto {\left(\frac{\color{blue}{e^{x} - 1}}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   8. div-sub 3.4%

      \[\leadsto {\color{blue}{\left(\frac{e^{x}}{e^{x}} - \frac{1}{e^{x}}\right)}}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   9. pow1 3.4%

      \[\leadsto {\left(\frac{\color{blue}{{\left(e^{x}\right)}^{1}}}{e^{x}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   10. pow1 3.4%

       \[\leadsto {\left(\frac{{\left(e^{x}\right)}^{1}}{\color{blue}{{\left(e^{x}\right)}^{1}}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   11. pow-div 37.0%

       \[\leadsto {\left(\color{blue}{{\left(e^{x}\right)}^{\left(1 - 1\right)}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   12. metadata-eval 37.0%

       \[\leadsto {\left({\left(e^{x}\right)}^{\color{blue}{0}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   13. metadata-eval 37.0%

       \[\leadsto {\left(\color{blue}{1} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   14. rec-exp 37.0%

       \[\leadsto {\left(1 - \color{blue}{e^{-x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   15. metadata-eval 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{\left(\color{blue}{-1} \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   16. metadata-eval 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{\color{blue}{-0.5}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   17. pow1/2 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot \color{blue}{{\left(\frac{e^{x}}{\mathsf{expm1}\left(x\right)}\right)}^{0.5}} \]

   18. clear-num 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot {\color{blue}{\left(\frac{1}{\frac{\mathsf{expm1}\left(x\right)}{e^{x}}}\right)}}^{0.5} \]

   19. inv-pow 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot {\color{blue}{\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{-1}\right)}}^{0.5} \]

   20. metadata-eval 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot {\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{\color{blue}{\left(-1\right)}}\right)}^{0.5} \]

5. Applied egg-rr 37.1%

   \[\leadsto \color{blue}{{\left(1 - e^{-x}\right)}^{-0.5} \cdot {\left(1 - e^{-x}\right)}^{-0.5}} \]
6. Step-by-step derivation

   1. pow-sqr 37.9%

      \[\leadsto \color{blue}{{\left(1 - e^{-x}\right)}^{\left(2 \cdot -0.5\right)}} \]

   2. metadata-eval 37.9%

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

   3. unpow-1 37.9%

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

7. Simplified 37.9%

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

8. Taylor expanded in x around -inf 37.9%

   \[\leadsto \frac{1}{\color{blue}{1 - e^{-1 \cdot x}}} \]
9. Step-by-step derivation

   1. sub-neg 37.9%

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

   2. neg-mul-1 37.9%

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

   3. +-commutative 37.9%

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

   4. neg-sub0 37.9%

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

   5. associate-+l- 37.9%

      \[\leadsto \frac{1}{\color{blue}{0 - \left(e^{-x} - 1\right)}} \]

   6. sub0-neg 37.9%

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

   7. expm1-def 100.0%

      \[\leadsto \frac{1}{-\color{blue}{\mathsf{expm1}\left(-x\right)}} \]

10. Simplified 100.0%

    \[\leadsto \frac{1}{\color{blue}{-\mathsf{expm1}\left(-x\right)}} \]

11. Taylor expanded in x around inf 37.9%

    \[\leadsto \color{blue}{\frac{-1}{e^{-x} - 1}} \]
12. Step-by-step derivation

    1. expm1-def 100.0%

       \[\leadsto \frac{-1}{\color{blue}{\mathsf{expm1}\left(-x\right)}} \]

13. Simplified 100.0%

    \[\leadsto \color{blue}{\frac{-1}{\mathsf{expm1}\left(-x\right)}} \]

14. Final simplification 100.0%

    \[\leadsto \frac{-1}{\mathsf{expm1}\left(-x\right)} \]

Alternative 2: 98.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{e^{x}}{x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (exp x) x))

C

double code(double x) {
	return exp(x) / x;
}

Fortran

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

Java

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

Python

def code(x):
	return math.exp(x) / x

Julia

function code(x)
	return Float64(exp(x) / x)
end

MATLAB

function tmp = code(x)
	tmp = exp(x) / x;
end

Wolfram

code[x_] := N[(N[Exp[x], $MachinePrecision] / x), $MachinePrecision]

Derivation

1. Initial program 37.9%

   \[\frac{e^{x}}{e^{x} - 1} \]

2. Taylor expanded in x around 0 98.3%

   \[\leadsto \frac{e^{x}}{\color{blue}{x}} \]

3. Final simplification 98.3%

   \[\leadsto \frac{e^{x}}{x} \]

Alternative 3: 67.2% accurate, 68.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return 1.0 / x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 37.9%

   \[\frac{e^{x}}{e^{x} - 1} \]
2. Step-by-step derivation

   1. expm1-def 100.0%

      \[\leadsto \frac{e^{x}}{\color{blue}{\mathsf{expm1}\left(x\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

4. Taylor expanded in x around 0 66.5%

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

5. Final simplification 66.5%

   \[\leadsto \frac{1}{x} \]

Alternative 4: 3.2% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.5)

C

double code(double x) {
	return 0.5;
}

Fortran

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

Java

public static double code(double x) {
	return 0.5;
}

Python

def code(x):
	return 0.5

Julia

function code(x)
	return 0.5
end

MATLAB

function tmp = code(x)
	tmp = 0.5;
end

Wolfram

code[x_] := 0.5

Derivation

1. Initial program 37.9%

   \[\frac{e^{x}}{e^{x} - 1} \]
2. Step-by-step derivation

   1. expm1-def 100.0%

      \[\leadsto \frac{e^{x}}{\color{blue}{\mathsf{expm1}\left(x\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

4. Taylor expanded in x around 0 66.5%

   \[\leadsto \color{blue}{0.5 + \frac{1}{x}} \]
5. Step-by-step derivation

   1. +-commutative 66.5%

      \[\leadsto \color{blue}{\frac{1}{x} + 0.5} \]

6. Simplified 66.5%

   \[\leadsto \color{blue}{\frac{1}{x} + 0.5} \]

7. Taylor expanded in x around inf 3.3%

   \[\leadsto \color{blue}{0.5} \]

8. Final simplification 3.3%

   \[\leadsto 0.5 \]

Alternative 5: 3.2% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 4.5 \end{array} \]

FPCore

(FPCore (x) :precision binary64 4.5)

C

double code(double x) {
	return 4.5;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 4.5d0
end function

Java

public static double code(double x) {
	return 4.5;
}

Python

def code(x):
	return 4.5

Julia

function code(x)
	return 4.5
end

MATLAB

function tmp = code(x)
	tmp = 4.5;
end

Wolfram

code[x_] := 4.5

Derivation

1. Initial program 37.9%

   \[\frac{e^{x}}{e^{x} - 1} \]
2. Step-by-step derivation

   1. expm1-def 100.0%

      \[\leadsto \frac{e^{x}}{\color{blue}{\mathsf{expm1}\left(x\right)}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]
4. Step-by-step derivation

   1. add-sqr-sqrt 67.3%

      \[\leadsto \color{blue}{\sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}}} \]

   2. pow1/2 67.3%

      \[\leadsto \color{blue}{{\left(\frac{e^{x}}{\mathsf{expm1}\left(x\right)}\right)}^{0.5}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   3. clear-num 67.3%

      \[\leadsto {\color{blue}{\left(\frac{1}{\frac{\mathsf{expm1}\left(x\right)}{e^{x}}}\right)}}^{0.5} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   4. inv-pow 67.3%

      \[\leadsto {\color{blue}{\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{-1}\right)}}^{0.5} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   5. metadata-eval 67.3%

      \[\leadsto {\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{\color{blue}{\left(-1\right)}}\right)}^{0.5} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   6. pow-pow 67.4%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   7. expm1-udef 37.0%

      \[\leadsto {\left(\frac{\color{blue}{e^{x} - 1}}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   8. div-sub 3.4%

      \[\leadsto {\color{blue}{\left(\frac{e^{x}}{e^{x}} - \frac{1}{e^{x}}\right)}}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   9. pow1 3.4%

      \[\leadsto {\left(\frac{\color{blue}{{\left(e^{x}\right)}^{1}}}{e^{x}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   10. pow1 3.4%

       \[\leadsto {\left(\frac{{\left(e^{x}\right)}^{1}}{\color{blue}{{\left(e^{x}\right)}^{1}}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   11. pow-div 37.0%

       \[\leadsto {\left(\color{blue}{{\left(e^{x}\right)}^{\left(1 - 1\right)}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   12. metadata-eval 37.0%

       \[\leadsto {\left({\left(e^{x}\right)}^{\color{blue}{0}} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   13. metadata-eval 37.0%

       \[\leadsto {\left(\color{blue}{1} - \frac{1}{e^{x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   14. rec-exp 37.0%

       \[\leadsto {\left(1 - \color{blue}{e^{-x}}\right)}^{\left(\left(-1\right) \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   15. metadata-eval 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{\left(\color{blue}{-1} \cdot 0.5\right)} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   16. metadata-eval 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{\color{blue}{-0.5}} \cdot \sqrt{\frac{e^{x}}{\mathsf{expm1}\left(x\right)}} \]

   17. pow1/2 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot \color{blue}{{\left(\frac{e^{x}}{\mathsf{expm1}\left(x\right)}\right)}^{0.5}} \]

   18. clear-num 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot {\color{blue}{\left(\frac{1}{\frac{\mathsf{expm1}\left(x\right)}{e^{x}}}\right)}}^{0.5} \]

   19. inv-pow 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot {\color{blue}{\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{-1}\right)}}^{0.5} \]

   20. metadata-eval 37.0%

       \[\leadsto {\left(1 - e^{-x}\right)}^{-0.5} \cdot {\left({\left(\frac{\mathsf{expm1}\left(x\right)}{e^{x}}\right)}^{\color{blue}{\left(-1\right)}}\right)}^{0.5} \]

5. Applied egg-rr 37.1%

   \[\leadsto \color{blue}{{\left(1 - e^{-x}\right)}^{-0.5} \cdot {\left(1 - e^{-x}\right)}^{-0.5}} \]
6. Step-by-step derivation

   1. pow-sqr 37.9%

      \[\leadsto \color{blue}{{\left(1 - e^{-x}\right)}^{\left(2 \cdot -0.5\right)}} \]

   2. metadata-eval 37.9%

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

   3. unpow-1 37.9%

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

7. Simplified 37.9%

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

9. Applied egg-rr 3.4%

   \[\leadsto \frac{1}{\color{blue}{0.2222222222222222}} \]

10. Final simplification 3.4%

    \[\leadsto 4.5 \]

Developer target: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{-1}{\mathsf{expm1}\left(-x\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (- 1.0) (expm1 (- x))))

C

double code(double x) {
	return -1.0 / expm1(-x);
}

Java

public static double code(double x) {
	return -1.0 / Math.expm1(-x);
}

Python

def code(x):
	return -1.0 / math.expm1(-x)

Julia

function code(x)
	return Float64(Float64(-1.0) / expm1(Float64(-x)))
end

Wolfram

code[x_] := N[((-1.0) / N[(Exp[(-x)] - 1), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023306 
(FPCore (x)
  :name "expq2 (section 3.11)"
  :precision binary64
  :pre (> 715.0 x)

  :herbie-target
  (/ (- 1.0) (expm1 (- x)))

  (/ (exp x) (- (exp x) 1.0)))