Rust f64::asinh

Percentage Accurate: 30.5% → 99.9%
Time: 9.0s
Alternatives: 14
Speedup: 4.0×

Specification

?
\[\begin{array}{l} \\ \sinh^{-1} x \end{array} \]
(FPCore (x) :precision binary64 (asinh x))
double code(double x) {
	return asinh(x);
}

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

function code(x)
	return asinh(x)
end

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

code[x_] := N[ArcSinh[x], $MachinePrecision]

\begin{array}{l}

\\
\sinh^{-1} x
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 14 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 30.5% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \end{array} \]
(FPCore (x)
 :precision binary64
 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))
double code(double x) {
	return copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x);
}

public static double code(double x) {
	return Math.copySign(Math.log((Math.abs(x) + Math.sqrt(((x * x) + 1.0)))), x);
}

def code(x):
	return math.copysign(math.log((math.fabs(x) + math.sqrt(((x * x) + 1.0)))), x)

function code(x)
	return copysign(log(Float64(abs(x) + sqrt(Float64(Float64(x * x) + 1.0)))), x)
end

function tmp = code(x)
	tmp = sign(x) * abs(log((abs(x) + sqrt(((x * x) + 1.0)))));
end

code[x_] := N[With[{TMP1 = Abs[N[Log[N[(N[Abs[x], $MachinePrecision] + N[Sqrt[N[(N[(x * x), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]

\begin{array}{l}

\\
\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)
\end{array}

Alternative 1: 99.9% accurate, 0.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ \mathbf{if}\;t_0 \leq -0.2:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;t_0 \leq 0.001:\\ \;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left({\left(\sqrt{x + \mathsf{hypot}\left(1, x\right)}\right)}^{2}\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (let* ((t_0 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x)))
   (if (<= t_0 -0.2)
     (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
     (if (<= t_0 0.001)
       (copysign
        (+ x (+ (* -0.16666666666666666 (pow x 3.0)) (* 0.075 (pow x 5.0))))
        x)
       (copysign (log (pow (sqrt (+ x (hypot 1.0 x))) 2.0)) x)))))
double code(double x) {
	double t_0 = copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x);
	double tmp;
	if (t_0 <= -0.2) {
		tmp = copysign(log((fabs(x) + hypot(1.0, x))), x);
	} else if (t_0 <= 0.001) {
		tmp = copysign((x + ((-0.16666666666666666 * pow(x, 3.0)) + (0.075 * pow(x, 5.0)))), x);
	} else {
		tmp = copysign(log(pow(sqrt((x + hypot(1.0, x))), 2.0)), x);
	}
	return tmp;
}

public static double code(double x) {
	double t_0 = Math.copySign(Math.log((Math.abs(x) + Math.sqrt(((x * x) + 1.0)))), x);
	double tmp;
	if (t_0 <= -0.2) {
		tmp = Math.copySign(Math.log((Math.abs(x) + Math.hypot(1.0, x))), x);
	} else if (t_0 <= 0.001) {
		tmp = Math.copySign((x + ((-0.16666666666666666 * Math.pow(x, 3.0)) + (0.075 * Math.pow(x, 5.0)))), x);
	} else {
		tmp = Math.copySign(Math.log(Math.pow(Math.sqrt((x + Math.hypot(1.0, x))), 2.0)), x);
	}
	return tmp;
}

def code(x):
	t_0 = math.copysign(math.log((math.fabs(x) + math.sqrt(((x * x) + 1.0)))), x)
	tmp = 0
	if t_0 <= -0.2:
		tmp = math.copysign(math.log((math.fabs(x) + math.hypot(1.0, x))), x)
	elif t_0 <= 0.001:
		tmp = math.copysign((x + ((-0.16666666666666666 * math.pow(x, 3.0)) + (0.075 * math.pow(x, 5.0)))), x)
	else:
		tmp = math.copysign(math.log(math.pow(math.sqrt((x + math.hypot(1.0, x))), 2.0)), x)
	return tmp

function code(x)
	t_0 = copysign(log(Float64(abs(x) + sqrt(Float64(Float64(x * x) + 1.0)))), x)
	tmp = 0.0
	if (t_0 <= -0.2)
		tmp = copysign(log(Float64(abs(x) + hypot(1.0, x))), x);
	elseif (t_0 <= 0.001)
		tmp = copysign(Float64(x + Float64(Float64(-0.16666666666666666 * (x ^ 3.0)) + Float64(0.075 * (x ^ 5.0)))), x);
	else
		tmp = copysign(log((sqrt(Float64(x + hypot(1.0, x))) ^ 2.0)), x);
	end
	return tmp
end

function tmp_2 = code(x)
	t_0 = sign(x) * abs(log((abs(x) + sqrt(((x * x) + 1.0)))));
	tmp = 0.0;
	if (t_0 <= -0.2)
		tmp = sign(x) * abs(log((abs(x) + hypot(1.0, x))));
	elseif (t_0 <= 0.001)
		tmp = sign(x) * abs((x + ((-0.16666666666666666 * (x ^ 3.0)) + (0.075 * (x ^ 5.0)))));
	else
		tmp = sign(x) * abs(log((sqrt((x + hypot(1.0, x))) ^ 2.0)));
	end
	tmp_2 = tmp;
end

code[x_] := Block[{t$95$0 = N[With[{TMP1 = Abs[N[Log[N[(N[Abs[x], $MachinePrecision] + N[Sqrt[N[(N[(x * x), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]}, If[LessEqual[t$95$0, -0.2], N[With[{TMP1 = Abs[N[Log[N[(N[Abs[x], $MachinePrecision] + N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[t$95$0, 0.001], N[With[{TMP1 = Abs[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]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[N[Power[N[Sqrt[N[(x + N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\
\mathbf{if}\;t_0 \leq -0.2:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\

\mathbf{elif}\;t_0 \leq 0.001:\\
\;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\log \left({\left(\sqrt{x + \mathsf{hypot}\left(1, x\right)}\right)}^{2}\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 2: 99.9% accurate, 0.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ \mathbf{if}\;t_0 \leq -0.2:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;t_0 \leq 0.001:\\ \;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(2 \cdot \log \left(\sqrt{x + \mathsf{hypot}\left(1, x\right)}\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (let* ((t_0 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x)))
   (if (<= t_0 -0.2)
     (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
     (if (<= t_0 0.001)
       (copysign
        (+ x (+ (* -0.16666666666666666 (pow x 3.0)) (* 0.075 (pow x 5.0))))
        x)
       (copysign (* 2.0 (log (sqrt (+ x (hypot 1.0 x))))) x)))))
double code(double x) {
	double t_0 = copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x);
	double tmp;
	if (t_0 <= -0.2) {
		tmp = copysign(log((fabs(x) + hypot(1.0, x))), x);
	} else if (t_0 <= 0.001) {
		tmp = copysign((x + ((-0.16666666666666666 * pow(x, 3.0)) + (0.075 * pow(x, 5.0)))), x);
	} else {
		tmp = copysign((2.0 * log(sqrt((x + hypot(1.0, x))))), x);
	}
	return tmp;
}

public static double code(double x) {
	double t_0 = Math.copySign(Math.log((Math.abs(x) + Math.sqrt(((x * x) + 1.0)))), x);
	double tmp;
	if (t_0 <= -0.2) {
		tmp = Math.copySign(Math.log((Math.abs(x) + Math.hypot(1.0, x))), x);
	} else if (t_0 <= 0.001) {
		tmp = Math.copySign((x + ((-0.16666666666666666 * Math.pow(x, 3.0)) + (0.075 * Math.pow(x, 5.0)))), x);
	} else {
		tmp = Math.copySign((2.0 * Math.log(Math.sqrt((x + Math.hypot(1.0, x))))), x);
	}
	return tmp;
}

def code(x):
	t_0 = math.copysign(math.log((math.fabs(x) + math.sqrt(((x * x) + 1.0)))), x)
	tmp = 0
	if t_0 <= -0.2:
		tmp = math.copysign(math.log((math.fabs(x) + math.hypot(1.0, x))), x)
	elif t_0 <= 0.001:
		tmp = math.copysign((x + ((-0.16666666666666666 * math.pow(x, 3.0)) + (0.075 * math.pow(x, 5.0)))), x)
	else:
		tmp = math.copysign((2.0 * math.log(math.sqrt((x + math.hypot(1.0, x))))), x)
	return tmp

function code(x)
	t_0 = copysign(log(Float64(abs(x) + sqrt(Float64(Float64(x * x) + 1.0)))), x)
	tmp = 0.0
	if (t_0 <= -0.2)
		tmp = copysign(log(Float64(abs(x) + hypot(1.0, x))), x);
	elseif (t_0 <= 0.001)
		tmp = copysign(Float64(x + Float64(Float64(-0.16666666666666666 * (x ^ 3.0)) + Float64(0.075 * (x ^ 5.0)))), x);
	else
		tmp = copysign(Float64(2.0 * log(sqrt(Float64(x + hypot(1.0, x))))), x);
	end
	return tmp
end

function tmp_2 = code(x)
	t_0 = sign(x) * abs(log((abs(x) + sqrt(((x * x) + 1.0)))));
	tmp = 0.0;
	if (t_0 <= -0.2)
		tmp = sign(x) * abs(log((abs(x) + hypot(1.0, x))));
	elseif (t_0 <= 0.001)
		tmp = sign(x) * abs((x + ((-0.16666666666666666 * (x ^ 3.0)) + (0.075 * (x ^ 5.0)))));
	else
		tmp = sign(x) * abs((2.0 * log(sqrt((x + hypot(1.0, x))))));
	end
	tmp_2 = tmp;
end

code[x_] := Block[{t$95$0 = N[With[{TMP1 = Abs[N[Log[N[(N[Abs[x], $MachinePrecision] + N[Sqrt[N[(N[(x * x), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]}, If[LessEqual[t$95$0, -0.2], N[With[{TMP1 = Abs[N[Log[N[(N[Abs[x], $MachinePrecision] + N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[t$95$0, 0.001], N[With[{TMP1 = Abs[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]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[(2.0 * N[Log[N[Sqrt[N[(x + N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\
\mathbf{if}\;t_0 \leq -0.2:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\

\mathbf{elif}\;t_0 \leq 0.001:\\
\;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(2 \cdot \log \left(\sqrt{x + \mathsf{hypot}\left(1, x\right)}\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.008:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;x \leq 0.0071:\\ \;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -0.008)
   (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
   (if (<= x 0.0071)
     (copysign
      (+ x (+ (* -0.16666666666666666 (pow x 3.0)) (* 0.075 (pow x 5.0))))
      x)
     (copysign (log1p (+ (hypot 1.0 x) (+ x -1.0))) x))))
double code(double x) {
	double tmp;
	if (x <= -0.008) {
		tmp = copysign(log((fabs(x) + hypot(1.0, x))), x);
	} else if (x <= 0.0071) {
		tmp = copysign((x + ((-0.16666666666666666 * pow(x, 3.0)) + (0.075 * pow(x, 5.0)))), x);
	} else {
		tmp = copysign(log1p((hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

public static double code(double x) {
	double tmp;
	if (x <= -0.008) {
		tmp = Math.copySign(Math.log((Math.abs(x) + Math.hypot(1.0, x))), x);
	} else if (x <= 0.0071) {
		tmp = Math.copySign((x + ((-0.16666666666666666 * Math.pow(x, 3.0)) + (0.075 * Math.pow(x, 5.0)))), x);
	} else {
		tmp = Math.copySign(Math.log1p((Math.hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

def code(x):
	tmp = 0
	if x <= -0.008:
		tmp = math.copysign(math.log((math.fabs(x) + math.hypot(1.0, x))), x)
	elif x <= 0.0071:
		tmp = math.copysign((x + ((-0.16666666666666666 * math.pow(x, 3.0)) + (0.075 * math.pow(x, 5.0)))), x)
	else:
		tmp = math.copysign(math.log1p((math.hypot(1.0, x) + (x + -1.0))), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= -0.008)
		tmp = copysign(log(Float64(abs(x) + hypot(1.0, x))), x);
	elseif (x <= 0.0071)
		tmp = copysign(Float64(x + Float64(Float64(-0.16666666666666666 * (x ^ 3.0)) + Float64(0.075 * (x ^ 5.0)))), x);
	else
		tmp = copysign(log1p(Float64(hypot(1.0, x) + Float64(x + -1.0))), x);
	end
	return tmp
end

code[x_] := If[LessEqual[x, -0.008], N[With[{TMP1 = Abs[N[Log[N[(N[Abs[x], $MachinePrecision] + N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 0.0071], N[With[{TMP1 = Abs[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]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[1 + N[(N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -0.008:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\

\mathbf{elif}\;x \leq 0.0071:\\
\;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 4: 99.8% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| - x\right) + \frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.0071:\\ \;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -1.0)
   (copysign (log (+ (- (fabs x) x) (/ -0.5 x))) x)
   (if (<= x 0.0071)
     (copysign
      (+ x (+ (* -0.16666666666666666 (pow x 3.0)) (* 0.075 (pow x 5.0))))
      x)
     (copysign (log1p (+ (hypot 1.0 x) (+ x -1.0))) x))))
double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = copysign(log(((fabs(x) - x) + (-0.5 / x))), x);
	} else if (x <= 0.0071) {
		tmp = copysign((x + ((-0.16666666666666666 * pow(x, 3.0)) + (0.075 * pow(x, 5.0)))), x);
	} else {
		tmp = copysign(log1p((hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

public static double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = Math.copySign(Math.log(((Math.abs(x) - x) + (-0.5 / x))), x);
	} else if (x <= 0.0071) {
		tmp = Math.copySign((x + ((-0.16666666666666666 * Math.pow(x, 3.0)) + (0.075 * Math.pow(x, 5.0)))), x);
	} else {
		tmp = Math.copySign(Math.log1p((Math.hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

def code(x):
	tmp = 0
	if x <= -1.0:
		tmp = math.copysign(math.log(((math.fabs(x) - x) + (-0.5 / x))), x)
	elif x <= 0.0071:
		tmp = math.copysign((x + ((-0.16666666666666666 * math.pow(x, 3.0)) + (0.075 * math.pow(x, 5.0)))), x)
	else:
		tmp = math.copysign(math.log1p((math.hypot(1.0, x) + (x + -1.0))), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = copysign(log(Float64(Float64(abs(x) - x) + Float64(-0.5 / x))), x);
	elseif (x <= 0.0071)
		tmp = copysign(Float64(x + Float64(Float64(-0.16666666666666666 * (x ^ 3.0)) + Float64(0.075 * (x ^ 5.0)))), x);
	else
		tmp = copysign(log1p(Float64(hypot(1.0, x) + Float64(x + -1.0))), x);
	end
	return tmp
end

code[x_] := If[LessEqual[x, -1.0], N[With[{TMP1 = Abs[N[Log[N[(N[(N[Abs[x], $MachinePrecision] - x), $MachinePrecision] + N[(-0.5 / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 0.0071], N[With[{TMP1 = Abs[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]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[1 + N[(N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -1:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| - x\right) + \frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;x \leq 0.0071:\\
\;\;\;\;\mathsf{copysign}\left(x + \left(-0.16666666666666666 \cdot {x}^{3} + 0.075 \cdot {x}^{5}\right), x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 5: 99.7% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.00092:\\ \;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -1.3)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 0.00092)
     (copysign (+ x (* -0.16666666666666666 (pow x 3.0))) x)
     (copysign (log1p (+ (hypot 1.0 x) (+ x -1.0))) x))))
double code(double x) {
	double tmp;
	if (x <= -1.3) {
		tmp = copysign(log((-0.5 / x)), x);
	} else if (x <= 0.00092) {
		tmp = copysign((x + (-0.16666666666666666 * pow(x, 3.0))), x);
	} else {
		tmp = copysign(log1p((hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

public static double code(double x) {
	double tmp;
	if (x <= -1.3) {
		tmp = Math.copySign(Math.log((-0.5 / x)), x);
	} else if (x <= 0.00092) {
		tmp = Math.copySign((x + (-0.16666666666666666 * Math.pow(x, 3.0))), x);
	} else {
		tmp = Math.copySign(Math.log1p((Math.hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

def code(x):
	tmp = 0
	if x <= -1.3:
		tmp = math.copysign(math.log((-0.5 / x)), x)
	elif x <= 0.00092:
		tmp = math.copysign((x + (-0.16666666666666666 * math.pow(x, 3.0))), x)
	else:
		tmp = math.copysign(math.log1p((math.hypot(1.0, x) + (x + -1.0))), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= -1.3)
		tmp = copysign(log(Float64(-0.5 / x)), x);
	elseif (x <= 0.00092)
		tmp = copysign(Float64(x + Float64(-0.16666666666666666 * (x ^ 3.0))), x);
	else
		tmp = copysign(log1p(Float64(hypot(1.0, x) + Float64(x + -1.0))), x);
	end
	return tmp
end

code[x_] := If[LessEqual[x, -1.3], N[With[{TMP1 = Abs[N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 0.00092], N[With[{TMP1 = Abs[N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[1 + N[(N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.3:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;x \leq 0.00092:\\
\;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 6: 99.8% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.96:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| - x\right) + \frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.00092:\\ \;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -0.96)
   (copysign (log (+ (- (fabs x) x) (/ -0.5 x))) x)
   (if (<= x 0.00092)
     (copysign (+ x (* -0.16666666666666666 (pow x 3.0))) x)
     (copysign (log1p (+ (hypot 1.0 x) (+ x -1.0))) x))))
double code(double x) {
	double tmp;
	if (x <= -0.96) {
		tmp = copysign(log(((fabs(x) - x) + (-0.5 / x))), x);
	} else if (x <= 0.00092) {
		tmp = copysign((x + (-0.16666666666666666 * pow(x, 3.0))), x);
	} else {
		tmp = copysign(log1p((hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

public static double code(double x) {
	double tmp;
	if (x <= -0.96) {
		tmp = Math.copySign(Math.log(((Math.abs(x) - x) + (-0.5 / x))), x);
	} else if (x <= 0.00092) {
		tmp = Math.copySign((x + (-0.16666666666666666 * Math.pow(x, 3.0))), x);
	} else {
		tmp = Math.copySign(Math.log1p((Math.hypot(1.0, x) + (x + -1.0))), x);
	}
	return tmp;
}

def code(x):
	tmp = 0
	if x <= -0.96:
		tmp = math.copysign(math.log(((math.fabs(x) - x) + (-0.5 / x))), x)
	elif x <= 0.00092:
		tmp = math.copysign((x + (-0.16666666666666666 * math.pow(x, 3.0))), x)
	else:
		tmp = math.copysign(math.log1p((math.hypot(1.0, x) + (x + -1.0))), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= -0.96)
		tmp = copysign(log(Float64(Float64(abs(x) - x) + Float64(-0.5 / x))), x);
	elseif (x <= 0.00092)
		tmp = copysign(Float64(x + Float64(-0.16666666666666666 * (x ^ 3.0))), x);
	else
		tmp = copysign(log1p(Float64(hypot(1.0, x) + Float64(x + -1.0))), x);
	end
	return tmp
end

code[x_] := If[LessEqual[x, -0.96], N[With[{TMP1 = Abs[N[Log[N[(N[(N[Abs[x], $MachinePrecision] - x), $MachinePrecision] + N[(-0.5 / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 0.00092], N[With[{TMP1 = Abs[N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[1 + N[(N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -0.96:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| - x\right) + \frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;x \leq 0.00092:\\
\;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\mathsf{hypot}\left(1, x\right) + \left(x + -1\right)\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 7: 99.7% accurate, 1.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.00094:\\ \;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -1.3)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 0.00094)
     (copysign (+ x (* -0.16666666666666666 (pow x 3.0))) x)
     (copysign (log (+ x (hypot 1.0 x))) x))))
double code(double x) {
	double tmp;
	if (x <= -1.3) {
		tmp = copysign(log((-0.5 / x)), x);
	} else if (x <= 0.00094) {
		tmp = copysign((x + (-0.16666666666666666 * pow(x, 3.0))), x);
	} else {
		tmp = copysign(log((x + hypot(1.0, x))), x);
	}
	return tmp;
}

public static double code(double x) {
	double tmp;
	if (x <= -1.3) {
		tmp = Math.copySign(Math.log((-0.5 / x)), x);
	} else if (x <= 0.00094) {
		tmp = Math.copySign((x + (-0.16666666666666666 * Math.pow(x, 3.0))), x);
	} else {
		tmp = Math.copySign(Math.log((x + Math.hypot(1.0, x))), x);
	}
	return tmp;
}

def code(x):
	tmp = 0
	if x <= -1.3:
		tmp = math.copysign(math.log((-0.5 / x)), x)
	elif x <= 0.00094:
		tmp = math.copysign((x + (-0.16666666666666666 * math.pow(x, 3.0))), x)
	else:
		tmp = math.copysign(math.log((x + math.hypot(1.0, x))), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= -1.3)
		tmp = copysign(log(Float64(-0.5 / x)), x);
	elseif (x <= 0.00094)
		tmp = copysign(Float64(x + Float64(-0.16666666666666666 * (x ^ 3.0))), x);
	else
		tmp = copysign(log(Float64(x + hypot(1.0, x))), x);
	end
	return tmp
end

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.3)
		tmp = sign(x) * abs(log((-0.5 / x)));
	elseif (x <= 0.00094)
		tmp = sign(x) * abs((x + (-0.16666666666666666 * (x ^ 3.0))));
	else
		tmp = sign(x) * abs(log((x + hypot(1.0, x))));
	end
	tmp_2 = tmp;
end

code[x_] := If[LessEqual[x, -1.3], N[With[{TMP1 = Abs[N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 0.00094], N[With[{TMP1 = Abs[N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[N[(x + N[Sqrt[1.0 ^ 2 + x ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.3:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;x \leq 0.00094:\\
\;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 8: 99.5% accurate, 1.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.95:\\ \;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + x\right)\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -1.3)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 0.95)
     (copysign (+ x (* -0.16666666666666666 (pow x 3.0))) x)
     (copysign (log (+ (/ 0.5 x) (+ x x))) x))))
double code(double x) {
	double tmp;
	if (x <= -1.3) {
		tmp = copysign(log((-0.5 / x)), x);
	} else if (x <= 0.95) {
		tmp = copysign((x + (-0.16666666666666666 * pow(x, 3.0))), x);
	} else {
		tmp = copysign(log(((0.5 / x) + (x + x))), x);
	}
	return tmp;
}

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

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

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

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

code[x_] := If[LessEqual[x, -1.3], N[With[{TMP1 = Abs[N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 0.95], N[With[{TMP1 = Abs[N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[N[(N[(0.5 / x), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.3:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;x \leq 0.95:\\
\;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + x\right)\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 9: 99.4% accurate, 1.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -1.3)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 1.3)
     (copysign (+ x (* -0.16666666666666666 (pow x 3.0))) x)
     (copysign (log (+ x x)) x))))
double code(double x) {
	double tmp;
	if (x <= -1.3) {
		tmp = copysign(log((-0.5 / x)), x);
	} else if (x <= 1.3) {
		tmp = copysign((x + (-0.16666666666666666 * pow(x, 3.0))), x);
	} else {
		tmp = copysign(log((x + x)), x);
	}
	return tmp;
}

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

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

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

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

code[x_] := If[LessEqual[x, -1.3], N[With[{TMP1 = Abs[N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 1.3], N[With[{TMP1 = Abs[N[(x + N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[N[(x + x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.3:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;x \leq 1.3:\\
\;\;\;\;\mathsf{copysign}\left(x + -0.16666666666666666 \cdot {x}^{3}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 10: 99.2% accurate, 2.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x -1.3)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 1.3) (copysign x x) (copysign (log (+ x x)) x))))
double code(double x) {
	double tmp;
	if (x <= -1.3) {
		tmp = copysign(log((-0.5 / x)), x);
	} else if (x <= 1.3) {
		tmp = copysign(x, x);
	} else {
		tmp = copysign(log((x + x)), x);
	}
	return tmp;
}

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

def code(x):
	tmp = 0
	if x <= -1.3:
		tmp = math.copysign(math.log((-0.5 / x)), x)
	elif x <= 1.3:
		tmp = math.copysign(x, x)
	else:
		tmp = math.copysign(math.log((x + x)), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= -1.3)
		tmp = copysign(log(Float64(-0.5 / x)), x);
	elseif (x <= 1.3)
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float64(x + x)), x);
	end
	return tmp
end

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.3)
		tmp = sign(x) * abs(log((-0.5 / x)));
	elseif (x <= 1.3)
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + x)));
	end
	tmp_2 = tmp;
end

code[x_] := If[LessEqual[x, -1.3], N[With[{TMP1 = Abs[N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[x, 1.3], N[With[{TMP1 = Abs[x], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[N[(x + x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.3:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;x \leq 1.3:\\
\;\;\;\;\mathsf{copysign}\left(x, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 11: 59.2% accurate, 2.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.6:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + 1\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x 1.6) (copysign x x) (copysign (log (+ x 1.0)) x)))
double code(double x) {
	double tmp;
	if (x <= 1.6) {
		tmp = copysign(x, x);
	} else {
		tmp = copysign(log((x + 1.0)), x);
	}
	return tmp;
}

public static double code(double x) {
	double tmp;
	if (x <= 1.6) {
		tmp = Math.copySign(x, x);
	} else {
		tmp = Math.copySign(Math.log((x + 1.0)), x);
	}
	return tmp;
}

def code(x):
	tmp = 0
	if x <= 1.6:
		tmp = math.copysign(x, x)
	else:
		tmp = math.copysign(math.log((x + 1.0)), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= 1.6)
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float64(x + 1.0)), x);
	end
	return tmp
end

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.6)
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + 1.0)));
	end
	tmp_2 = tmp;
end

code[x_] := If[LessEqual[x, 1.6], N[With[{TMP1 = Abs[x], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq 1.6:\\
\;\;\;\;\mathsf{copysign}\left(x, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(x + 1\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 12: 76.1% accurate, 2.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.3:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x 1.3) (copysign x x) (copysign (log (+ x x)) x)))
double code(double x) {
	double tmp;
	if (x <= 1.3) {
		tmp = copysign(x, x);
	} else {
		tmp = copysign(log((x + x)), x);
	}
	return tmp;
}

public static double code(double x) {
	double tmp;
	if (x <= 1.3) {
		tmp = Math.copySign(x, x);
	} else {
		tmp = Math.copySign(Math.log((x + x)), x);
	}
	return tmp;
}

def code(x):
	tmp = 0
	if x <= 1.3:
		tmp = math.copysign(x, x)
	else:
		tmp = math.copysign(math.log((x + x)), x)
	return tmp

function code(x)
	tmp = 0.0
	if (x <= 1.3)
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float64(x + x)), x);
	end
	return tmp
end

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.3)
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + x)));
	end
	tmp_2 = tmp;
end

code[x_] := If[LessEqual[x, 1.3], N[With[{TMP1 = Abs[x], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[N[(x + x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq 1.3:\\
\;\;\;\;\mathsf{copysign}\left(x, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 13: 59.2% accurate, 2.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.6:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(x\right), x\right)\\ \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (if (<= x 1.6) (copysign x x) (copysign (log1p x) x)))
double code(double x) {
	double tmp;
	if (x <= 1.6) {
		tmp = copysign(x, x);
	} else {
		tmp = copysign(log1p(x), x);
	}
	return tmp;
}

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

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

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

code[x_] := If[LessEqual[x, 1.6], N[With[{TMP1 = Abs[x], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], N[With[{TMP1 = Abs[N[Log[1 + x], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq 1.6:\\
\;\;\;\;\mathsf{copysign}\left(x, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(x\right), x\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 14: 52.7% accurate, 4.0× speedup?

\[\begin{array}{l} \\ \mathsf{copysign}\left(x, x\right) \end{array} \]
(FPCore (x) :precision binary64 (copysign x x))
double code(double x) {
	return copysign(x, x);
}

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

def code(x):
	return math.copysign(x, x)

function code(x)
	return copysign(x, x)
end

function tmp = code(x)
	tmp = sign(x) * abs(x);
end

code[x_] := N[With[{TMP1 = Abs[x], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]

\begin{array}{l}

\\
\mathsf{copysign}\left(x, x\right)
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\left|x\right|}\\ \mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right| + \frac{\left|x\right|}{\mathsf{hypot}\left(1, t_0\right) + t_0}\right), x\right) \end{array} \end{array} \]
(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (fabs x))))
   (copysign (log1p (+ (fabs x) (/ (fabs x) (+ (hypot 1.0 t_0) t_0)))) x)))
double code(double x) {
	double t_0 = 1.0 / fabs(x);
	return copysign(log1p((fabs(x) + (fabs(x) / (hypot(1.0, t_0) + t_0)))), x);
}

public static double code(double x) {
	double t_0 = 1.0 / Math.abs(x);
	return Math.copySign(Math.log1p((Math.abs(x) + (Math.abs(x) / (Math.hypot(1.0, t_0) + t_0)))), x);
}

def code(x):
	t_0 = 1.0 / math.fabs(x)
	return math.copysign(math.log1p((math.fabs(x) + (math.fabs(x) / (math.hypot(1.0, t_0) + t_0)))), x)

function code(x)
	t_0 = Float64(1.0 / abs(x))
	return copysign(log1p(Float64(abs(x) + Float64(abs(x) / Float64(hypot(1.0, t_0) + t_0)))), x)
end

code[x_] := Block[{t$95$0 = N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]}, N[With[{TMP1 = Abs[N[Log[1 + N[(N[Abs[x], $MachinePrecision] + N[(N[Abs[x], $MachinePrecision] / N[(N[Sqrt[1.0 ^ 2 + t$95$0 ^ 2], $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \frac{1}{\left|x\right|}\\
\mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right| + \frac{\left|x\right|}{\mathsf{hypot}\left(1, t_0\right) + t_0}\right), x\right)
\end{array}
\end{array}

Reproduce

?
herbie shell --seed 2023341 
(FPCore (x)
  :name "Rust f64::asinh"
  :precision binary64

  :herbie-target
  (copysign (log1p (+ (fabs x) (/ (fabs x) (+ (hypot 1.0 (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))))) x)

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