Prelude:atanh from fay-base-0.20.0.1

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return (x + 1.0) / (1.0 - x)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return (x + 1.0) / (1.0 - x)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return (x + 1.0) / (1.0 - x)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + 1}{1 - x} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + 1}{1 - x} \leq -0.5:\\ \;\;\;\;-1 - \frac{2}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, x, 2\right), x, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (/ (+ x 1.0) (- 1.0 x)) -0.5)
   (- -1.0 (/ 2.0 x))
   (fma (fma 2.0 x 2.0) x 1.0)))

C

double code(double x) {
	double tmp;
	if (((x + 1.0) / (1.0 - x)) <= -0.5) {
		tmp = -1.0 - (2.0 / x);
	} else {
		tmp = fma(fma(2.0, x, 2.0), x, 1.0);
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x + 1.0) / Float64(1.0 - x)) <= -0.5)
		tmp = Float64(-1.0 - Float64(2.0 / x));
	else
		tmp = fma(fma(2.0, x, 2.0), x, 1.0);
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x + 1.0), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision], -0.5], N[(-1.0 - N[(2.0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x + 2.0), $MachinePrecision] * x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) < -0.5

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. metadata-eval N/A

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

      4. distribute-lft-neg-in N/A

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

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{-1 - 2 \cdot \frac{1}{x}} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{-1 - 2 \cdot \frac{1}{x}} \]

      7. associate-*r/ N/A

         \[\leadsto -1 - \color{blue}{\frac{2 \cdot 1}{x}} \]

      8. metadata-eval N/A

         \[\leadsto -1 - \frac{\color{blue}{2}}{x} \]

      9. lower-/.f64 99.4

         \[\leadsto -1 - \color{blue}{\frac{2}{x}} \]

   5. Applied rewrites 99.4%

      \[\leadsto \color{blue}{-1 - \frac{2}{x}} \]

   if -0.5 < (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. +-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. distribute-lft-neg-out N/A

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

      6. remove-double-neg N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, x, 2\right)}, x, 1\right) \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, x, 2\right), x, 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + 1}{1 - x} \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(2, x, 2\right), x, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (/ (+ x 1.0) (- 1.0 x)) -0.5) -1.0 (fma (fma 2.0 x 2.0) x 1.0)))

C

double code(double x) {
	double tmp;
	if (((x + 1.0) / (1.0 - x)) <= -0.5) {
		tmp = -1.0;
	} else {
		tmp = fma(fma(2.0, x, 2.0), x, 1.0);
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x + 1.0) / Float64(1.0 - x)) <= -0.5)
		tmp = -1.0;
	else
		tmp = fma(fma(2.0, x, 2.0), x, 1.0);
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x + 1.0), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision], -0.5], -1.0, N[(N[(2.0 * x + 2.0), $MachinePrecision] * x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) < -0.5

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.7%

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

   if -0.5 < (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. +-commutative N/A

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

      4. distribute-lft-neg-out N/A

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

      5. distribute-lft-neg-out N/A

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

      6. remove-double-neg N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 100.0

          \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(2, x, 2\right)}, x, 1\right) \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(2, x, 2\right), x, 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + 1}{1 - x} \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (/ (+ x 1.0) (- 1.0 x)) -0.5) -1.0 (fma 2.0 x 1.0)))

C

double code(double x) {
	double tmp;
	if (((x + 1.0) / (1.0 - x)) <= -0.5) {
		tmp = -1.0;
	} else {
		tmp = fma(2.0, x, 1.0);
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x + 1.0) / Float64(1.0 - x)) <= -0.5)
		tmp = -1.0;
	else
		tmp = fma(2.0, x, 1.0);
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x + 1.0), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision], -0.5], -1.0, N[(2.0 * x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) < -0.5

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.7%

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

   if -0.5 < (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 2 \cdot x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot x + 1} \]

      2. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 1\right)} \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + 1}{1 - x} \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (/ (+ x 1.0) (- 1.0 x)) -0.5) -1.0 (+ (+ 1.0 x) x)))

C

double code(double x) {
	double tmp;
	if (((x + 1.0) / (1.0 - x)) <= -0.5) {
		tmp = -1.0;
	} else {
		tmp = (1.0 + x) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x + 1.0d0) / (1.0d0 - x)) <= (-0.5d0)) then
        tmp = -1.0d0
    else
        tmp = (1.0d0 + x) + x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x + 1.0) / (1.0 - x)) <= -0.5) {
		tmp = -1.0;
	} else {
		tmp = (1.0 + x) + x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x + 1.0) / (1.0 - x)) <= -0.5:
		tmp = -1.0
	else:
		tmp = (1.0 + x) + x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x + 1.0) / Float64(1.0 - x)) <= -0.5)
		tmp = -1.0;
	else
		tmp = Float64(Float64(1.0 + x) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x + 1.0) / (1.0 - x)) <= -0.5)
		tmp = -1.0;
	else
		tmp = (1.0 + x) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x + 1.0), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision], -0.5], -1.0, N[(N[(1.0 + x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) < -0.5

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.7%

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

   if -0.5 < (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 2 \cdot x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot x + 1} \]

      2. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 1\right)} \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.7%

      \[\leadsto \left(1 + x\right) + \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + 1}{1 - x} \leq -1 \cdot 10^{-309}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (/ (+ x 1.0) (- 1.0 x)) -1e-309) -1.0 1.0))

C

double code(double x) {
	double tmp;
	if (((x + 1.0) / (1.0 - x)) <= -1e-309) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x + 1.0d0) / (1.0d0 - x)) <= (-1d-309)) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x + 1.0) / (1.0 - x)) <= -1e-309) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x + 1.0) / (1.0 - x)) <= -1e-309:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x + 1.0) / Float64(1.0 - x)) <= -1e-309)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x + 1.0) / (1.0 - x)) <= -1e-309)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x + 1.0), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision], -1e-309], -1.0, 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) < -1.000000000000002e-309

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.7%

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

   if -1.000000000000002e-309 < (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))

   1. Initial program 100.0%

      \[\frac{x + 1}{1 - x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.8%

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

Alternative 7: 50.1% accurate, 18.0× 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 100.0%

   \[\frac{x + 1}{1 - x} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-1} \]
4. Step-by-step derivation

5. Applied rewrites 56.2%

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

Reproduce

herbie shell --seed 2024342 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1.0) (- 1.0 x)))