(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:
Herbie found 2 alternatives:
Alternative | Accuracy | Speedup |
---|
(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}
(FPCore (x) :precision binary64 (copysign (asinh x) x))
double code(double x) { return copysign(asinh(x), x); }
def code(x): return math.copysign(math.asinh(x), x)
function code(x) return copysign(asinh(x), x) end
function tmp = code(x) tmp = sign(x) * abs(asinh(x)); end
code[x_] := N[With[{TMP1 = Abs[N[ArcSinh[x], $MachinePrecision]], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
\begin{array}{l} \\ \mathsf{copysign}\left(\sinh^{-1} x, x\right) \end{array}
Initial program 27.2%
lift-log.f64
N/A
lift-+.f64
N/A
lift-fabs.f64
N/A
lift-sqrt.f64
N/A
lift-+.f64
N/A
lift-*.f64
N/A
pow2
N/A
+-commutative
N/A
+-commutative
N/A
pow2
N/A
sqr-abs-rev
N/A
asinh-def-rev
N/A
rem-sqrt-square-rev
N/A
pow2
N/A
sqrt-pow1
N/A
metadata-eval
N/A
unpow1
N/A
lower-asinh.f64
99.9
Applied rewrites99.9%
(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}
Initial program 27.2%
lift-log.f64
N/A
lift-+.f64
N/A
lift-fabs.f64
N/A
lift-sqrt.f64
N/A
lift-+.f64
N/A
lift-*.f64
N/A
pow2
N/A
+-commutative
N/A
+-commutative
N/A
pow2
N/A
sqr-abs-rev
N/A
asinh-def-rev
N/A
rem-sqrt-square-rev
N/A
pow2
N/A
sqrt-pow1
N/A
metadata-eval
N/A
unpow1
N/A
lower-asinh.f64
99.9
Applied rewrites99.9%
Taylor expanded in x around 0
unpow1
58.1
metadata-eval
58.1
sqrt-pow1
58.1
pow2
58.1
rem-sqrt-square-rev
58.1
asinh-def-rev
58.1
sqr-abs-rev
58.1
pow2
58.1
+-commutative
58.1
+-commutative
58.1
pow2
58.1
Applied rewrites58.1%
(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}
herbie shell --seed 2025051
(FPCore (x)
:name "Rust f64::asinh"
:precision binary64
:alt
(! :herbie-platform default (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))