Hyperbolic arcsine

Percentage Accurate: 18.0% → 99.7%

Time: 7.1s

Alternatives: 9

Speedup: 207.0×

Specification

Math

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

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)
    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]

Initial Program: 18.0% accurate, 1.0× speedup

Math

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

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)
    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: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0075:\\ \;\;\;\;-\log \left(\mathsf{hypot}\left(1, x\right) - x\right)\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right)\\ \mathbf{else}:\\ \;\;\;\;-\log \left(\frac{0.5}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.0075)
   (- (log (- (hypot 1.0 x) x)))
   (if (<= x 1.35)
     (+ x (+ (* -0.16666666666666666 (pow x 3.0)) (* 0.075 (pow x 5.0))))
     (- (log (/ 0.5 x))))))

C

double code(double x) {
	double tmp;
	if (x <= -0.0075) {
		tmp = -log((hypot(1.0, x) - x));
	} else if (x <= 1.35) {
		tmp = x + ((-0.16666666666666666 * pow(x, 3.0)) + (0.075 * pow(x, 5.0)));
	} else {
		tmp = -log((0.5 / x));
	}
	return tmp;
}

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.0075) {
		tmp = -Math.log((Math.hypot(1.0, x) - x));
	} else if (x <= 1.35) {
		tmp = x + ((-0.16666666666666666 * Math.pow(x, 3.0)) + (0.075 * Math.pow(x, 5.0)));
	} else {
		tmp = -Math.log((0.5 / x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.0075:
		tmp = -math.log((math.hypot(1.0, x) - x))
	elif x <= 1.35:
		tmp = x + ((-0.16666666666666666 * math.pow(x, 3.0)) + (0.075 * math.pow(x, 5.0)))
	else:
		tmp = -math.log((0.5 / x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.0075)
		tmp = Float64(-log(Float64(hypot(1.0, x) - x)));
	elseif (x <= 1.35)
		tmp = Float64(x + Float64(Float64(-0.16666666666666666 * (x ^ 3.0)) + Float64(0.075 * (x ^ 5.0))));
	else
		tmp = Float64(-log(Float64(0.5 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.0075)
		tmp = -log((hypot(1.0, x) - x));
	elseif (x <= 1.35)
		tmp = x + ((-0.16666666666666666 * (x ^ 3.0)) + (0.075 * (x ^ 5.0)));
	else
		tmp = -log((0.5 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.0075], (-N[Log[N[(N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision] - x), $MachinePrecision]], $MachinePrecision]), If[LessEqual[x, 1.35], N[(x + N[(N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(0.075 * N[Power[x, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[Log[N[(0.5 / x), $MachinePrecision]], $MachinePrecision])]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00115:\\ \;\;\;\;-\log \left(\mathsf{hypot}\left(1, x\right) - x\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;x + -0.16666666666666666 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;-\log \left(\frac{0.5}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.00115)
   (- (log (- (hypot 1.0 x) x)))
   (if (<= x 1.3)
     (+ x (* -0.16666666666666666 (pow x 3.0)))
     (- (log (/ 0.5 x))))))

C

double code(double x) {
	double tmp;
	if (x <= -0.00115) {
		tmp = -log((hypot(1.0, x) - x));
	} else if (x <= 1.3) {
		tmp = x + (-0.16666666666666666 * pow(x, 3.0));
	} else {
		tmp = -log((0.5 / x));
	}
	return tmp;
}

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.00115) {
		tmp = -Math.log((Math.hypot(1.0, x) - x));
	} else if (x <= 1.3) {
		tmp = x + (-0.16666666666666666 * Math.pow(x, 3.0));
	} else {
		tmp = -Math.log((0.5 / x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.00115:
		tmp = -math.log((math.hypot(1.0, x) - x))
	elif x <= 1.3:
		tmp = x + (-0.16666666666666666 * math.pow(x, 3.0))
	else:
		tmp = -math.log((0.5 / x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.00115)
		tmp = Float64(-log(Float64(hypot(1.0, x) - x)));
	elseif (x <= 1.3)
		tmp = Float64(x + Float64(-0.16666666666666666 * (x ^ 3.0)));
	else
		tmp = Float64(-log(Float64(0.5 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.00115)
		tmp = -log((hypot(1.0, x) - x));
	elseif (x <= 1.3)
		tmp = x + (-0.16666666666666666 * (x ^ 3.0));
	else
		tmp = -log((0.5 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.00115], (-N[Log[N[(N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision] - x), $MachinePrecision]], $MachinePrecision]), If[LessEqual[x, 1.3], N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[Log[N[(0.5 / x), $MachinePrecision]], $MachinePrecision])]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 99.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25:\\ \;\;\;\;\log \left(\frac{-0.5}{x}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;x + -0.16666666666666666 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;-\log \left(\frac{0.5}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.25)
   (log (/ -0.5 x))
   (if (<= x 1.3)
     (+ x (* -0.16666666666666666 (pow x 3.0)))
     (- (log (/ 0.5 x))))))

C

double code(double x) {
	double tmp;
	if (x <= -1.25) {
		tmp = log((-0.5 / x));
	} else if (x <= 1.3) {
		tmp = x + (-0.16666666666666666 * pow(x, 3.0));
	} else {
		tmp = -log((0.5 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.25d0)) then
        tmp = log(((-0.5d0) / x))
    else if (x <= 1.3d0) then
        tmp = x + ((-0.16666666666666666d0) * (x ** 3.0d0))
    else
        tmp = -log((0.5d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.25) {
		tmp = Math.log((-0.5 / x));
	} else if (x <= 1.3) {
		tmp = x + (-0.16666666666666666 * Math.pow(x, 3.0));
	} else {
		tmp = -Math.log((0.5 / x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.25:
		tmp = math.log((-0.5 / x))
	elif x <= 1.3:
		tmp = x + (-0.16666666666666666 * math.pow(x, 3.0))
	else:
		tmp = -math.log((0.5 / x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.25)
		tmp = log(Float64(-0.5 / x));
	elseif (x <= 1.3)
		tmp = Float64(x + Float64(-0.16666666666666666 * (x ^ 3.0)));
	else
		tmp = Float64(-log(Float64(0.5 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.25)
		tmp = log((-0.5 / x));
	elseif (x <= 1.3)
		tmp = x + (-0.16666666666666666 * (x ^ 3.0));
	else
		tmp = -log((0.5 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.25], N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.3], N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[Log[N[(0.5 / x), $MachinePrecision]], $MachinePrecision])]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 99.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;-\log \left(x \cdot -2 - \frac{0.5}{x}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;x + -0.16666666666666666 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;-\log \left(\frac{0.5}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.95)
   (- (log (- (* x -2.0) (/ 0.5 x))))
   (if (<= x 1.3)
     (+ x (* -0.16666666666666666 (pow x 3.0)))
     (- (log (/ 0.5 x))))))

C

double code(double x) {
	double tmp;
	if (x <= -0.95) {
		tmp = -log(((x * -2.0) - (0.5 / x)));
	} else if (x <= 1.3) {
		tmp = x + (-0.16666666666666666 * pow(x, 3.0));
	} else {
		tmp = -log((0.5 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.95d0)) then
        tmp = -log(((x * (-2.0d0)) - (0.5d0 / x)))
    else if (x <= 1.3d0) then
        tmp = x + ((-0.16666666666666666d0) * (x ** 3.0d0))
    else
        tmp = -log((0.5d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.95) {
		tmp = -Math.log(((x * -2.0) - (0.5 / x)));
	} else if (x <= 1.3) {
		tmp = x + (-0.16666666666666666 * Math.pow(x, 3.0));
	} else {
		tmp = -Math.log((0.5 / x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.95:
		tmp = -math.log(((x * -2.0) - (0.5 / x)))
	elif x <= 1.3:
		tmp = x + (-0.16666666666666666 * math.pow(x, 3.0))
	else:
		tmp = -math.log((0.5 / x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.95)
		tmp = Float64(-log(Float64(Float64(x * -2.0) - Float64(0.5 / x))));
	elseif (x <= 1.3)
		tmp = Float64(x + Float64(-0.16666666666666666 * (x ^ 3.0)));
	else
		tmp = Float64(-log(Float64(0.5 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.95)
		tmp = -log(((x * -2.0) - (0.5 / x)));
	elseif (x <= 1.3)
		tmp = x + (-0.16666666666666666 * (x ^ 3.0));
	else
		tmp = -log((0.5 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.95], (-N[Log[N[(N[(x * -2.0), $MachinePrecision] - N[(0.5 / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), If[LessEqual[x, 1.3], N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[Log[N[(0.5 / x), $MachinePrecision]], $MachinePrecision])]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 99.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25:\\ \;\;\;\;\log \left(\frac{-0.5}{x}\right)\\ \mathbf{elif}\;x \leq 1.25:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\log \left(\frac{0.5}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.25) (log (/ -0.5 x)) (if (<= x 1.25) x (- (log (/ 0.5 x))))))

C

double code(double x) {
	double tmp;
	if (x <= -1.25) {
		tmp = log((-0.5 / x));
	} else if (x <= 1.25) {
		tmp = x;
	} else {
		tmp = -log((0.5 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.25d0)) then
        tmp = log(((-0.5d0) / x))
    else if (x <= 1.25d0) then
        tmp = x
    else
        tmp = -log((0.5d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.25) {
		tmp = Math.log((-0.5 / x));
	} else if (x <= 1.25) {
		tmp = x;
	} else {
		tmp = -Math.log((0.5 / x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.25:
		tmp = math.log((-0.5 / x))
	elif x <= 1.25:
		tmp = x
	else:
		tmp = -math.log((0.5 / x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.25)
		tmp = log(Float64(-0.5 / x));
	elseif (x <= 1.25)
		tmp = x;
	else
		tmp = Float64(-log(Float64(0.5 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.25)
		tmp = log((-0.5 / x));
	elseif (x <= 1.25)
		tmp = x;
	else
		tmp = -log((0.5 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.25], N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.25], x, (-N[Log[N[(0.5 / x), $MachinePrecision]], $MachinePrecision])]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 99.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25:\\ \;\;\;\;\log \left(\frac{-0.5}{x}\right)\\ \mathbf{elif}\;x \leq 1.25:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\log \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.25) (log (/ -0.5 x)) (if (<= x 1.25) x (log (* x 2.0)))))

C

double code(double x) {
	double tmp;
	if (x <= -1.25) {
		tmp = log((-0.5 / x));
	} else if (x <= 1.25) {
		tmp = x;
	} else {
		tmp = log((x * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.25d0)) then
        tmp = log(((-0.5d0) / x))
    else if (x <= 1.25d0) then
        tmp = x
    else
        tmp = log((x * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.25) {
		tmp = Math.log((-0.5 / x));
	} else if (x <= 1.25) {
		tmp = x;
	} else {
		tmp = Math.log((x * 2.0));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.25:
		tmp = math.log((-0.5 / x))
	elif x <= 1.25:
		tmp = x
	else:
		tmp = math.log((x * 2.0))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.25)
		tmp = log(Float64(-0.5 / x));
	elseif (x <= 1.25)
		tmp = x;
	else
		tmp = log(Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.25)
		tmp = log((-0.5 / x));
	elseif (x <= 1.25)
		tmp = x;
	else
		tmp = log((x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.25], N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.25], x, N[Log[N[(x * 2.0), $MachinePrecision]], $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 75.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.25:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\log \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.25) x (log (* x 2.0))))

C

double code(double x) {
	double tmp;
	if (x <= 1.25) {
		tmp = x;
	} else {
		tmp = log((x * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.25d0) then
        tmp = x
    else
        tmp = log((x * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.25) {
		tmp = x;
	} else {
		tmp = Math.log((x * 2.0));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.25:
		tmp = x
	else:
		tmp = math.log((x * 2.0))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.25)
		tmp = x;
	else
		tmp = log(Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.25)
		tmp = x;
	else
		tmp = log((x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.25], x, N[Log[N[(x * 2.0), $MachinePrecision]], $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 59.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.6:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.6) x (log1p x)))

C

double code(double x) {
	double tmp;
	if (x <= 1.6) {
		tmp = x;
	} else {
		tmp = log1p(x);
	}
	return tmp;
}

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.6) {
		tmp = x;
	} else {
		tmp = Math.log1p(x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.6:
		tmp = x
	else:
		tmp = math.log1p(x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.6)
		tmp = x;
	else
		tmp = log1p(x);
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[x, 1.6], x, N[Log[1 + x], $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 52.8% accurate, 207.0× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 x)

C

double code(double x) {
	return x;
}

Fortran

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

Java

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

Python

def code(x):
	return x

Julia

function code(x)
	return x
end

MATLAB

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

Wolfram

code[x_] := x

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 30.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x \cdot x + 1}\\ \mathbf{if}\;x < 0:\\ \;\;\;\;\log \left(\frac{-1}{x - t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + t_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sqrt (+ (* x x) 1.0))))
   (if (< x 0.0) (log (/ -1.0 (- x t_0))) (log (+ x t_0)))))

C

double code(double x) {
	double t_0 = sqrt(((x * x) + 1.0));
	double tmp;
	if (x < 0.0) {
		tmp = log((-1.0 / (x - t_0)));
	} else {
		tmp = log((x + t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(((x * x) + 1.0d0))
    if (x < 0.0d0) then
        tmp = log(((-1.0d0) / (x - t_0)))
    else
        tmp = log((x + t_0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = Math.sqrt(((x * x) + 1.0));
	double tmp;
	if (x < 0.0) {
		tmp = Math.log((-1.0 / (x - t_0)));
	} else {
		tmp = Math.log((x + t_0));
	}
	return tmp;
}

Python

def code(x):
	t_0 = math.sqrt(((x * x) + 1.0))
	tmp = 0
	if x < 0.0:
		tmp = math.log((-1.0 / (x - t_0)))
	else:
		tmp = math.log((x + t_0))
	return tmp

Julia

function code(x)
	t_0 = sqrt(Float64(Float64(x * x) + 1.0))
	tmp = 0.0
	if (x < 0.0)
		tmp = log(Float64(-1.0 / Float64(x - t_0)));
	else
		tmp = log(Float64(x + t_0));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_] := Block[{t$95$0 = N[Sqrt[N[(N[(x * x), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]}, If[Less[x, 0.0], N[Log[N[(-1.0 / N[(x - t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Log[N[(x + t$95$0), $MachinePrecision]], $MachinePrecision]]]

Reproduce

herbie shell --seed 2024010 
(FPCore (x)
  :name "Hyperbolic arcsine"
  :precision binary64

  :herbie-target
  (if (< x 0.0) (log (/ -1.0 (- x (sqrt (+ (* x x) 1.0))))) (log (+ x (sqrt (+ (* x x) 1.0)))))

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