Rust f64::asinh

Percentage Accurate: 29.1% → 99.8%

Time: 2.8s

Alternatives: 5

Speedup: 5.4×

Specification

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]

Initial Program: 29.1% 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: 99.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\sinh^{-1} x, x\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[With[{TMP1 = Abs[N[ArcSinh[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. lift-log.f64 N/A

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

   2. lift-fabs.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-sqrt.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. pow2 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2}} + 1}\right), x\right) \]

   8. +-commutative N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + {x}^{2}}}\right), x\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2} + 1}}\right), x\right) \]

   10. pow2 N/A

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

   11. sqr-abs-rev N/A

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

   12. asinh-def-rev N/A

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

   13. rem-sqrt-square-rev N/A

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

   14. pow2 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

   15. sqrt-pow1 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

   16. metadata-eval N/A

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

   17. unpow1 N/A

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

   18. lower-asinh.f64 99.8

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

3. Applied rewrites 99.8%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{\sinh^{-1} x}, x\right) \]
4. Add Preprocessing

Alternative 2: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.25:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.25) (copysign x x) (copysign (log (+ x x)) x)))

C

double code(double x) {
	double tmp;
	if (x <= 1.25) {
		tmp = copysign(x, x);
	} else {
		tmp = copysign(log((x + x)), x);
	}
	return tmp;
}

Java

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

Python

def code(x):
	tmp = 0
	if x <= 1.25:
		tmp = math.copysign(x, x)
	else:
		tmp = math.copysign(math.log((x + x)), x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.25)
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float64(x + x)), x);
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_] := If[LessEqual[x, 1.25], 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]]

Derivation

1. Split input into 2 regimes

2. if x < 1.25

   1. Initial program 22.1%

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

      1. lift-log.f64 N/A

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

      2. lift-fabs.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-sqrt.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. pow2 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2}} + 1}\right), x\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + {x}^{2}}}\right), x\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2} + 1}}\right), x\right) \]

      10. pow2 N/A

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

      11. sqr-abs-rev N/A

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

      12. asinh-def-rev N/A

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

      13. rem-sqrt-square-rev N/A

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

      14. pow2 N/A

          \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

      15. sqrt-pow1 N/A

          \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

      16. metadata-eval N/A

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

      17. unpow1 N/A

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

      18. lower-asinh.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. unpow1 68.0

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

      2. metadata-eval 68.0

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

      3. sqrt-pow1 68.0

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

      4. pow2 68.0

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

      5. rem-sqrt-square-rev 68.0

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

      6. asinh-def-rev 68.0

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

      7. sqr-abs-rev 68.0

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

      8. pow2 68.0

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

      9. +-commutative 68.0

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

      10. +-commutative 68.0

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

      11. pow2 68.0

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

   6. Applied rewrites 68.0%

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

   if 1.25 < x

   1. Initial program 50.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 99.3%

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

      1. lift-fabs.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. rem-sqrt-square-rev N/A

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

      5. pow2 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(x + \sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

      6. sqrt-pow1 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(x + \color{blue}{{x}^{\left(\frac{2}{2}\right)}}\right), x\right) \]

      7. metadata-eval N/A

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

      8. unpow1 N/A

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

      9. lower-+.f64 99.3

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

   6. Applied rewrites 99.3%

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

Alternative 3: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \leq 1:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x - -1\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x) 1.0)
   (copysign x x)
   (copysign (log (- x -1.0)) x)))

C

double code(double x) {
	double tmp;
	if (copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x) <= 1.0) {
		tmp = copysign(x, x);
	} else {
		tmp = copysign(log((x - -1.0)), x);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := If[LessEqual[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], 1.0], 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]]

Derivation

1. Split input into 2 regimes

2. if (copysign.f64 (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))) x) < 1

   1. Initial program 22.1%

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

      1. lift-log.f64 N/A

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

      2. lift-fabs.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-sqrt.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. pow2 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2}} + 1}\right), x\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + {x}^{2}}}\right), x\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2} + 1}}\right), x\right) \]

      10. pow2 N/A

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

      11. sqr-abs-rev N/A

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

      12. asinh-def-rev N/A

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

      13. rem-sqrt-square-rev N/A

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

      14. pow2 N/A

          \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

      15. sqrt-pow1 N/A

          \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

      16. metadata-eval N/A

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

      17. unpow1 N/A

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

      18. lower-asinh.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. unpow1 68.0

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

      2. metadata-eval 68.0

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

      3. sqrt-pow1 68.0

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

      4. pow2 68.0

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

      5. rem-sqrt-square-rev 68.0

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

      6. asinh-def-rev 68.0

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

      7. sqr-abs-rev 68.0

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

      8. pow2 68.0

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

      9. +-commutative 68.0

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

      10. +-commutative 68.0

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

      11. pow2 68.0

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

   6. Applied rewrites 68.0%

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

   if 1 < (copysign.f64 (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))) x)

   1. Initial program 50.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 99.3%

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

      1. lift-fabs.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. rem-sqrt-square-rev N/A

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

      5. pow2 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(x + \sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

      6. sqrt-pow1 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(x + \color{blue}{{x}^{\left(\frac{2}{2}\right)}}\right), x\right) \]

      7. metadata-eval N/A

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

      8. unpow1 N/A

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

      9. lower-+.f64 99.3

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

   6. Applied rewrites 99.3%

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

   7. Taylor expanded in x around -inf

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\frac{\frac{-1}{2}}{x}\right)}, x\right) \]
   8. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\frac{\color{blue}{\frac{-1}{2}}}{x}\right), x\right) \]

      2. unpow1 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\frac{\frac{-1}{2}}{x}\right), x\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\frac{\frac{-1}{2}}{x}\right), x\right) \]

      4. sqrt-pow1 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\frac{\frac{-1}{2}}{x}\right), x\right) \]

      5. pow2 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\frac{\frac{-1}{2}}{x}\right), x\right) \]

      6. rem-sqrt-square-rev N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\frac{\frac{-1}{2}}{x}\right), x\right) \]

      7. lower-/.f64 0.0

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

   9. Applied rewrites 0.0%

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

   10. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. rem-sqrt-square-rev N/A

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

       3. pow2 N/A

          \[\leadsto \mathsf{copysign}\left(\log \left(\sqrt{{x}^{2}} + 1\right), x\right) \]

       4. sqrt-pow1 N/A

          \[\leadsto \mathsf{copysign}\left(\log \left({x}^{\left(\frac{2}{2}\right)} + 1\right), x\right) \]

       5. metadata-eval N/A

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

       6. unpow1 N/A

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

       7. metadata-eval N/A

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

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

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

       9. metadata-eval N/A

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

       10. metadata-eval N/A

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

       11. lower--.f64 31.5

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

   12. Applied rewrites 31.5%

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

Alternative 4: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \leq 1:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log x, x\right)\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x) {
	double tmp;
	if (copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x) <= 1.0) {
		tmp = copysign(x, x);
	} else {
		tmp = copysign(log(x), x);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (copysign.f64 (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))) x) < 1

   1. Initial program 22.1%

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

      1. lift-log.f64 N/A

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

      2. lift-fabs.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-sqrt.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. pow2 N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2}} + 1}\right), x\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + {x}^{2}}}\right), x\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2} + 1}}\right), x\right) \]

      10. pow2 N/A

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

      11. sqr-abs-rev N/A

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

      12. asinh-def-rev N/A

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

      13. rem-sqrt-square-rev N/A

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

      14. pow2 N/A

          \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

      15. sqrt-pow1 N/A

          \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

      16. metadata-eval N/A

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

      17. unpow1 N/A

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

      18. lower-asinh.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. unpow1 68.0

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

      2. metadata-eval 68.0

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

      3. sqrt-pow1 68.0

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

      4. pow2 68.0

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

      5. rem-sqrt-square-rev 68.0

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

      6. asinh-def-rev 68.0

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

      7. sqr-abs-rev 68.0

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

      8. pow2 68.0

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

      9. +-commutative 68.0

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

      10. +-commutative 68.0

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

      11. pow2 68.0

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

   6. Applied rewrites 68.0%

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

   if 1 < (copysign.f64 (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))) x)

   1. Initial program 50.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 31.5%

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

Alternative 5: 52.4% accurate, 5.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[With[{TMP1 = Abs[x], 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. lift-log.f64 N/A

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

   2. lift-fabs.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-sqrt.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. pow2 N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2}} + 1}\right), x\right) \]

   8. +-commutative N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{1 + {x}^{2}}}\right), x\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{\color{blue}{{x}^{2} + 1}}\right), x\right) \]

   10. pow2 N/A

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

   11. sqr-abs-rev N/A

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

   12. asinh-def-rev N/A

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

   13. rem-sqrt-square-rev N/A

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

   14. pow2 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \left(\sqrt{\color{blue}{{x}^{2}}}\right), x\right) \]

   15. sqrt-pow1 N/A

       \[\leadsto \mathsf{copysign}\left(\sinh^{-1} \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}, x\right) \]

   16. metadata-eval N/A

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

   17. unpow1 N/A

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

   18. lower-asinh.f64 99.8

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

3. Applied rewrites 99.8%

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

4. Taylor expanded in x around 0

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

   1. unpow1 52.4

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

   2. metadata-eval 52.4

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

   3. sqrt-pow1 52.4

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

   4. pow2 52.4

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

   5. rem-sqrt-square-rev 52.4

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

   6. asinh-def-rev 52.4

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

   7. sqr-abs-rev 52.4

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

   8. pow2 52.4

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

   9. +-commutative 52.4

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

   10. +-commutative 52.4

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

   11. pow2 52.4

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

6. Applied rewrites 52.4%

   \[\leadsto \mathsf{copysign}\left(\color{blue}{x}, x\right) \]
7. Add Preprocessing

Developer Target 1: 99.9% accurate, 0.4× 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 2025124 
(FPCore (x)
  :name "Rust f64::asinh"
  :precision binary64

  :alt
  (! :herbie-platform c (let* ((ax (fabs x)) (ix (/ 1 ax))) (copysign (log1p (+ ax (/ ax (+ (hypot 1 ix) ix)))) x)))

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