Rust f64::asinh

Percentage Accurate: 30.3% → 56.8%

Time: 4.4s

Alternatives: 6

Speedup: 2.0×

Specification

Math

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

FPCore

(FPCore (x) :precision binary64 (asinh x))

C

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

Python

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

Julia

function code(x)
	return asinh(x)
end

MATLAB

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

Wolfram

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

Initial Program: 30.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))

C

double code(double x) {
	return copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x);
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 56.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x)
	return copysign(log1p(x), x)
end

Wolfram

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

Derivation

1. Initial program 29.1%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Step-by-step derivation

   1. +-commutative 29.1%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + x \cdot x}}\right), x\right) \]

   2. hypot-1-def 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\mathsf{hypot}\left(1, x\right)}\right), x\right) \]

3. Simplified 55.2%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 19.1%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(1 + \left|x\right|\right)}, x\right) \]
6. Step-by-step derivation

   1. log1p-def 63.7%

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

   2. rem-square-sqrt 28.6%

      \[\leadsto \mathsf{copysign}\left(\mathsf{log1p}\left(\left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right|\right), x\right) \]

   3. fabs-sqr 28.6%

      \[\leadsto \mathsf{copysign}\left(\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right), x\right) \]

   4. rem-square-sqrt 54.6%

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

7. Simplified 54.6%

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

8. Final simplification 54.6%

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

Alternative 2: 31.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\left(1 + \log \left(x + \mathsf{hypot}\left(1, x\right)\right)\right) + -1, x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (copysign (+ (+ 1.0 (log (+ x (hypot 1.0 x)))) -1.0) x))

C

double code(double x) {
	return copysign(((1.0 + log((x + hypot(1.0, x)))) + -1.0), x);
}

Java

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

Python

def code(x):
	return math.copysign(((1.0 + math.log((x + math.hypot(1.0, x)))) + -1.0), x)

Julia

function code(x)
	return copysign(Float64(Float64(1.0 + log(Float64(x + hypot(1.0, x)))) + -1.0), x)
end

MATLAB

function tmp = code(x)
	tmp = sign(x) * abs(((1.0 + log((x + hypot(1.0, x)))) + -1.0));
end

Wolfram

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

Derivation

1. Initial program 29.1%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Step-by-step derivation

   1. +-commutative 29.1%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + x \cdot x}}\right), x\right) \]

   2. hypot-1-def 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\mathsf{hypot}\left(1, x\right)}\right), x\right) \]

3. Simplified 55.2%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. expm1-log1p-u 54.3%

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right)\right)\right)}, x\right) \]

   2. expm1-udef 54.3%

      \[\leadsto \mathsf{copysign}\left(\color{blue}{e^{\mathsf{log1p}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right)\right)} - 1}, x\right) \]

   3. log1p-udef 54.3%

      \[\leadsto \mathsf{copysign}\left(e^{\color{blue}{\log \left(1 + \log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right)\right)}} - 1, x\right) \]

   4. rem-exp-log 55.2%

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\left(1 + \log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right)\right)} - 1, x\right) \]

   5. *-un-lft-identity 55.2%

      \[\leadsto \mathsf{copysign}\left(\left(1 + \log \color{blue}{\left(1 \cdot \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right)\right)}\right) - 1, x\right) \]

   6. *-un-lft-identity 55.2%

      \[\leadsto \mathsf{copysign}\left(\left(1 + \log \color{blue}{\left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right)}\right) - 1, x\right) \]

   7. add-sqr-sqrt 24.6%

      \[\leadsto \mathsf{copysign}\left(\left(1 + \log \left(\left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| + \mathsf{hypot}\left(1, x\right)\right)\right) - 1, x\right) \]

   8. fabs-sqr 24.6%

      \[\leadsto \mathsf{copysign}\left(\left(1 + \log \left(\color{blue}{\sqrt{x} \cdot \sqrt{x}} + \mathsf{hypot}\left(1, x\right)\right)\right) - 1, x\right) \]

   9. add-sqr-sqrt 27.7%

      \[\leadsto \mathsf{copysign}\left(\left(1 + \log \left(\color{blue}{x} + \mathsf{hypot}\left(1, x\right)\right)\right) - 1, x\right) \]

6. Applied egg-rr 27.7%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\left(1 + \log \left(x + \mathsf{hypot}\left(1, x\right)\right)\right) - 1}, x\right) \]

7. Final simplification 27.7%

   \[\leadsto \mathsf{copysign}\left(\left(1 + \log \left(x + \mathsf{hypot}\left(1, x\right)\right)\right) + -1, x\right) \]
8. Add Preprocessing

Alternative 3: 31.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x)
	return copysign(log(Float64(x + hypot(1.0, x))), x)
end

MATLAB

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

Wolfram

code[x_] := 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]

Derivation

1. Initial program 29.1%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Step-by-step derivation

   1. +-commutative 29.1%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + x \cdot x}}\right), x\right) \]

   2. hypot-1-def 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\mathsf{hypot}\left(1, x\right)}\right), x\right) \]

3. Simplified 55.2%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-un-lft-identity 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(1 \cdot \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right)\right)}, x\right) \]

   2. *-commutative 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right) \cdot 1\right)}, x\right) \]

   3. log-prod 55.2%

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right) + \log 1}, x\right) \]

   4. add-sqr-sqrt 24.6%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| + \mathsf{hypot}\left(1, x\right)\right) + \log 1, x\right) \]

   5. fabs-sqr 24.6%

      \[\leadsto \mathsf{copysign}\left(\log \left(\color{blue}{\sqrt{x} \cdot \sqrt{x}} + \mathsf{hypot}\left(1, x\right)\right) + \log 1, x\right) \]

   6. add-sqr-sqrt 27.7%

      \[\leadsto \mathsf{copysign}\left(\log \left(\color{blue}{x} + \mathsf{hypot}\left(1, x\right)\right) + \log 1, x\right) \]

   7. metadata-eval 27.7%

      \[\leadsto \mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right) + \color{blue}{0}, x\right) \]

6. Applied egg-rr 27.7%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(x + \mathsf{hypot}\left(1, x\right)\right) + 0}, x\right) \]
7. Step-by-step derivation

   1. +-rgt-identity 27.7%

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(x + \mathsf{hypot}\left(1, x\right)\right)}, x\right) \]

8. Simplified 27.7%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\log \left(x + \mathsf{hypot}\left(1, x\right)\right)}, x\right) \]

9. Final simplification 27.7%

   \[\leadsto \mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right), x\right) \]
10. Add Preprocessing

Alternative 4: 26.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\log \left(\left(x + x\right) + \frac{0.5}{x}\right), x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (copysign (log (+ (+ x x) (/ 0.5 x))) x))

C

double code(double x) {
	return copysign(log(((x + x) + (0.5 / x))), x);
}

Java

public static double code(double x) {
	return Math.copySign(Math.log(((x + x) + (0.5 / x))), x);
}

Python

def code(x):
	return math.copysign(math.log(((x + x) + (0.5 / x))), x)

Julia

function code(x)
	return copysign(log(Float64(Float64(x + x) + Float64(0.5 / x))), x)
end

MATLAB

function tmp = code(x)
	tmp = sign(x) * abs(log(((x + x) + (0.5 / x))));
end

Wolfram

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

Derivation

1. Initial program 29.1%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Step-by-step derivation

   1. +-commutative 29.1%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + x \cdot x}}\right), x\right) \]

   2. hypot-1-def 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\mathsf{hypot}\left(1, x\right)}\right), x\right) \]

3. Simplified 55.2%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 24.7%

   \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(x + \left(\left|x\right| + 0.5 \cdot \frac{1}{x}\right)\right)}, x\right) \]
6. Step-by-step derivation

   1. rem-square-sqrt 23.9%

      \[\leadsto \mathsf{copysign}\left(\log \left(x + \left(\left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right| + 0.5 \cdot \frac{1}{x}\right)\right), x\right) \]

   2. fabs-sqr 23.9%

      \[\leadsto \mathsf{copysign}\left(\log \left(x + \left(\color{blue}{\sqrt{x} \cdot \sqrt{x}} + 0.5 \cdot \frac{1}{x}\right)\right), x\right) \]

   3. rem-square-sqrt 23.9%

      \[\leadsto \mathsf{copysign}\left(\log \left(x + \left(\color{blue}{x} + 0.5 \cdot \frac{1}{x}\right)\right), x\right) \]

   4. associate-+r+ 23.9%

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left(x + x\right) + 0.5 \cdot \frac{1}{x}\right)}, x\right) \]

   5. associate-*r/ 23.9%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left(x + x\right) + \color{blue}{\frac{0.5 \cdot 1}{x}}\right), x\right) \]

   6. metadata-eval 23.9%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left(x + x\right) + \frac{\color{blue}{0.5}}{x}\right), x\right) \]

7. Simplified 23.9%

   \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left(x + x\right) + \frac{0.5}{x}\right)}, x\right) \]

8. Final simplification 23.9%

   \[\leadsto \mathsf{copysign}\left(\log \left(\left(x + x\right) + \frac{0.5}{x}\right), x\right) \]
9. Add Preprocessing

Alternative 5: 26.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x) {
	return copysign(log((x + x)), x);
}

Java

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

Python

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

Julia

function code(x)
	return copysign(log(Float64(x + x)), x)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 29.1%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Step-by-step derivation

   1. +-commutative 29.1%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + x \cdot x}}\right), x\right) \]

   2. hypot-1-def 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\mathsf{hypot}\left(1, x\right)}\right), x\right) \]

3. Simplified 55.2%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 25.2%

   \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(x + \left|x\right|\right)}, x\right) \]
6. Step-by-step derivation

   1. rem-square-sqrt 23.7%

      \[\leadsto \mathsf{copysign}\left(\log \left(x + \left|\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right|\right), x\right) \]

   2. fabs-sqr 23.7%

      \[\leadsto \mathsf{copysign}\left(\log \left(x + \color{blue}{\sqrt{x} \cdot \sqrt{x}}\right), x\right) \]

   3. rem-square-sqrt 23.7%

      \[\leadsto \mathsf{copysign}\left(\log \left(x + \color{blue}{x}\right), x\right) \]

7. Simplified 23.7%

   \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(x + x\right)}, x\right) \]

8. Final simplification 23.7%

   \[\leadsto \mathsf{copysign}\left(\log \left(x + x\right), x\right) \]
9. Add Preprocessing

Alternative 6: 9.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\log x, x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (copysign (log x) x))

C

double code(double x) {
	return copysign(log(x), x);
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 29.1%

   \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
2. Step-by-step derivation

   1. +-commutative 29.1%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + x \cdot x}}\right), x\right) \]

   2. hypot-1-def 55.2%

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \color{blue}{\mathsf{hypot}\left(1, x\right)}\right), x\right) \]

3. Simplified 55.2%

   \[\leadsto \color{blue}{\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 8.5%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{-1 \cdot \log \left(\frac{1}{x}\right)}, x\right) \]
6. Step-by-step derivation

   1. mul-1-neg 8.5%

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

   2. log-rec 8.5%

      \[\leadsto \mathsf{copysign}\left(-\color{blue}{\left(-\log x\right)}, x\right) \]

   3. remove-double-neg 8.5%

      \[\leadsto \mathsf{copysign}\left(\color{blue}{\log x}, x\right) \]

7. Simplified 8.5%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\log x}, x\right) \]

8. Final simplification 8.5%

   \[\leadsto \mathsf{copysign}\left(\log x, x\right) \]
9. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\left|x\right|}\\ \mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right| + \frac{\left|x\right|}{\mathsf{hypot}\left(1, t\_0\right) + t\_0}\right), x\right) \end{array} \end{array} \]

FPCore

(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)))

C

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);
}

Java

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);
}

Python

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)

Julia

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

Wolfram

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]]

Reproduce

herbie shell --seed 2024033 
(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))