?

Average Error: 45.6 → 30.0
Time: 27.4s
Precision: binary64
Cost: 78728

?

\[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
\[\begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;t_0 \leq 10:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| + 1\right) + \left(\sqrt{1 + x \cdot x} + -1\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + \left|x\right|\right)\right), x\right)\\ \end{array} \]
(FPCore (x)
 :precision binary64
 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))
(FPCore (x)
 :precision binary64
 (let* ((t_0 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x)))
   (if (<= t_0 (- INFINITY))
     (copysign (log (/ -0.5 x)) x)
     (if (<= t_0 10.0)
       (copysign (log (+ (+ (fabs x) 1.0) (+ (sqrt (+ 1.0 (* x x))) -1.0))) x)
       (copysign (log (+ (/ 0.5 x) (+ x (fabs x)))) x)))))
double code(double x) {
	return copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x);
}
double code(double x) {
	double t_0 = copysign(log((fabs(x) + sqrt(((x * x) + 1.0)))), x);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = copysign(log((-0.5 / x)), x);
	} else if (t_0 <= 10.0) {
		tmp = copysign(log(((fabs(x) + 1.0) + (sqrt((1.0 + (x * x))) + -1.0))), x);
	} else {
		tmp = copysign(log(((0.5 / x) + (x + fabs(x)))), x);
	}
	return tmp;
}
public static double code(double x) {
	return Math.copySign(Math.log((Math.abs(x) + Math.sqrt(((x * x) + 1.0)))), x);
}
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 <= -Double.POSITIVE_INFINITY) {
		tmp = Math.copySign(Math.log((-0.5 / x)), x);
	} else if (t_0 <= 10.0) {
		tmp = Math.copySign(Math.log(((Math.abs(x) + 1.0) + (Math.sqrt((1.0 + (x * x))) + -1.0))), x);
	} else {
		tmp = Math.copySign(Math.log(((0.5 / x) + (x + Math.abs(x)))), x);
	}
	return tmp;
}
def code(x):
	return math.copysign(math.log((math.fabs(x) + math.sqrt(((x * x) + 1.0)))), x)
def code(x):
	t_0 = math.copysign(math.log((math.fabs(x) + math.sqrt(((x * x) + 1.0)))), x)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = math.copysign(math.log((-0.5 / x)), x)
	elif t_0 <= 10.0:
		tmp = math.copysign(math.log(((math.fabs(x) + 1.0) + (math.sqrt((1.0 + (x * x))) + -1.0))), x)
	else:
		tmp = math.copysign(math.log(((0.5 / x) + (x + math.fabs(x)))), x)
	return tmp
function code(x)
	return copysign(log(Float64(abs(x) + sqrt(Float64(Float64(x * x) + 1.0)))), x)
end
function code(x)
	t_0 = copysign(log(Float64(abs(x) + sqrt(Float64(Float64(x * x) + 1.0)))), x)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = copysign(log(Float64(-0.5 / x)), x);
	elseif (t_0 <= 10.0)
		tmp = copysign(log(Float64(Float64(abs(x) + 1.0) + Float64(sqrt(Float64(1.0 + Float64(x * x))) + -1.0))), x);
	else
		tmp = copysign(log(Float64(Float64(0.5 / x) + Float64(x + abs(x)))), x);
	end
	return tmp
end
function tmp = code(x)
	tmp = sign(x) * abs(log((abs(x) + sqrt(((x * x) + 1.0)))));
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 <= -Inf)
		tmp = sign(x) * abs(log((-0.5 / x)));
	elseif (t_0 <= 10.0)
		tmp = sign(x) * abs(log(((abs(x) + 1.0) + (sqrt((1.0 + (x * x))) + -1.0))));
	else
		tmp = sign(x) * abs(log(((0.5 / x) + (x + abs(x)))));
	end
	tmp_2 = tmp;
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]
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, (-Infinity)], N[With[{TMP1 = Abs[N[Log[N[(-0.5 / x), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision], If[LessEqual[t$95$0, 10.0], N[With[{TMP1 = Abs[N[Log[N[(N[(N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision] + N[(N[Sqrt[N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -1.0), $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 + N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]]]]
\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)
\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 -\infty:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\

\mathbf{elif}\;t_0 \leq 10:\\
\;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| + 1\right) + \left(\sqrt{1 + x \cdot x} + -1\right)\right), x\right)\\

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


\end{array}

Error?

Target

Original45.6
Target0.0
Herbie30.0
\[\mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right| + \frac{\left|x\right|}{\mathsf{hypot}\left(1, \frac{1}{\left|x\right|}\right) + \frac{1}{\left|x\right|}}\right), x\right) \]

Derivation?

  1. Split input into 3 regimes
  2. if (copysign.f64 (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) 1)))) x) < -inf.0

    1. Initial program 64.0

      \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
    2. Applied egg-rr64.0

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left(\sqrt{x \cdot x + 1} + \left|x\right| \cdot 0.5\right) - \left|x\right| \cdot -0.5\right)}, x\right) \]
    3. Taylor expanded in x around -inf 0

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left(-1 \cdot x + 0.5 \cdot \left|x\right|\right) - \left(0.5 \cdot \frac{1}{x} + -0.5 \cdot \left|x\right|\right)\right)}, x\right) \]
    4. Simplified0

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

      [Start]0

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

      rational_best-simplify-3 [=>]0

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

      rational_best-simplify-57 [=>]0

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

      rational_best-simplify-59 [=>]0

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

      rational_best-simplify-1 [=>]0

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

      rational_best-simplify-48 [<=]0

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

      rational_best-simplify-1 [<=]0

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

      rational_best-simplify-1 [=>]0

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

      rational_best-simplify-62 [=>]0

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

      metadata-eval [=>]0

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

      rational_best-simplify-7 [=>]0

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

      rational_best-simplify-56 [=>]0

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

      rational_best-simplify-14 [=>]0

      \[ \mathsf{copysign}\left(\log \left(\left|x\right| - \left(\color{blue}{\left(0 - -1 \cdot x\right)} + 0.5 \cdot \frac{1}{x}\right)\right), x\right) \]

      metadata-eval [<=]0

      \[ \mathsf{copysign}\left(\log \left(\left|x\right| - \left(\left(\color{blue}{\frac{0}{-1}} - -1 \cdot x\right) + 0.5 \cdot \frac{1}{x}\right)\right), x\right) \]

      rational_best-simplify-37 [=>]0

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

      metadata-eval [=>]0

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

      rational_best-simplify-8 [=>]0

      \[ \mathsf{copysign}\left(\log \left(\left|x\right| - \left(\color{blue}{x} + 0.5 \cdot \frac{1}{x}\right)\right), x\right) \]
    5. Taylor expanded in x around 0 0

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

    if -inf.0 < (copysign.f64 (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) 1)))) x) < 10

    1. Initial program 47.1

      \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
    2. Applied egg-rr47.2

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left(\sqrt{x \cdot x + 1} + \left|x\right| \cdot 0.5\right) - \left|x\right| \cdot -0.5\right)}, x\right) \]
    3. Applied egg-rr47.2

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(\left(-1 - \left(-\left|x\right|\right)\right) + \left(1 - \left(-\sqrt{x \cdot x + 1}\right)\right)\right)}, x\right) \]
    4. Simplified47.1

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

      [Start]47.2

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

      rational_best-simplify-14 [=>]47.2

      \[ \mathsf{copysign}\left(\log \left(\left(-1 - \color{blue}{\left(0 - \left|x\right|\right)}\right) + \left(1 - \left(-\sqrt{x \cdot x + 1}\right)\right)\right), x\right) \]

      rational_best-simplify-51 [=>]47.2

      \[ \mathsf{copysign}\left(\log \left(\color{blue}{\left(\left|x\right| - \left(0 - -1\right)\right)} + \left(1 - \left(-\sqrt{x \cdot x + 1}\right)\right)\right), x\right) \]

      metadata-eval [=>]47.2

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

      rational_best-simplify-85 [=>]47.1

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

      rational_best-simplify-85 [<=]47.1

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

      rational_best-simplify-20 [=>]47.1

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

      rational_best-simplify-14 [=>]47.1

      \[ \mathsf{copysign}\left(\log \left(\left(\left|x\right| + 1\right) + \left(-1 - \color{blue}{\left(0 - \sqrt{x \cdot x + 1}\right)}\right)\right), x\right) \]

      rational_best-simplify-51 [=>]47.1

      \[ \mathsf{copysign}\left(\log \left(\left(\left|x\right| + 1\right) + \color{blue}{\left(\sqrt{x \cdot x + 1} - \left(0 - -1\right)\right)}\right), x\right) \]

      metadata-eval [=>]47.1

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

      rational_best-simplify-18 [=>]47.1

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

      rational_best-simplify-3 [=>]47.1

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

    if 10 < (copysign.f64 (log.f64 (+.f64 (fabs.f64 x) (sqrt.f64 (+.f64 (*.f64 x x) 1)))) x)

    1. Initial program 31.8

      \[\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \]
    2. Taylor expanded in x around inf 0.1

      \[\leadsto \mathsf{copysign}\left(\log \color{blue}{\left(0.5 \cdot \frac{1}{x} + \left(\left|x\right| + x\right)\right)}, x\right) \]
    3. Simplified0.1

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

      [Start]0.1

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

      rational_best-simplify-55 [=>]0.1

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

      rational_best-simplify-1 [=>]0.1

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

      rational_best-simplify-7 [=>]0.1

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

      rational_best-simplify-3 [=>]0.1

      \[ \mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \color{blue}{\left(x + \left|x\right|\right)}\right), x\right) \]
  3. Recombined 3 regimes into one program.
  4. Final simplification30.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \leq -\infty:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;\mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \leq 10:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| + 1\right) + \left(\sqrt{1 + x \cdot x} + -1\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + \left|x\right|\right)\right), x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error30.0
Cost78472
\[\begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;t_0 \leq 10:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + \left|x\right|\right)\right), x\right)\\ \end{array} \]
Alternative 2
Error31.1
Cost20100
\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| - \left(x + \frac{0.5}{x}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{1}{x} + \left(\left|x\right| + \left(x + \frac{-0.5}{x}\right)\right)\right), x\right)\\ \end{array} \]
Alternative 3
Error31.2
Cost19844
\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + \left|x\right|\right)\right), x\right)\\ \end{array} \]
Alternative 4
Error31.1
Cost19844
\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| - \left(x + \frac{0.5}{x}\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + \left|x\right|\right)\right), x\right)\\ \end{array} \]
Alternative 5
Error41.7
Cost13188
\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log x, x\right)\\ \end{array} \]
Alternative 6
Error31.2
Cost13188
\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-309}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x}\right), x\right)\\ \end{array} \]
Alternative 7
Error52.4
Cost13124
\[\begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(-x\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log x, x\right)\\ \end{array} \]
Alternative 8
Error58.3
Cost12928
\[\mathsf{copysign}\left(\log x, x\right) \]

Error

Reproduce?

herbie shell --seed 2023099 
(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))