
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
double code(double x, double y) {
return cosh(x) * (sin(y) / y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = cosh(x) * (sin(y) / y)
end function
public static double code(double x, double y) {
return Math.cosh(x) * (Math.sin(y) / y);
}
def code(x, y): return math.cosh(x) * (math.sin(y) / y)
function code(x, y) return Float64(cosh(x) * Float64(sin(y) / y)) end
function tmp = code(x, y) tmp = cosh(x) * (sin(y) / y); end
code[x_, y_] := N[(N[Cosh[x], $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\cosh x \cdot \frac{\sin y}{y}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
double code(double x, double y) {
return cosh(x) * (sin(y) / y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = cosh(x) * (sin(y) / y)
end function
public static double code(double x, double y) {
return Math.cosh(x) * (Math.sin(y) / y);
}
def code(x, y): return math.cosh(x) * (math.sin(y) / y)
function code(x, y) return Float64(cosh(x) * Float64(sin(y) / y)) end
function tmp = code(x, y) tmp = cosh(x) * (sin(y) / y); end
code[x_, y_] := N[(N[Cosh[x], $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\cosh x \cdot \frac{\sin y}{y}
\end{array}
(FPCore (x y) :precision binary64 (* (/ (sin y) y) (cosh x)))
double code(double x, double y) {
return (sin(y) / y) * cosh(x);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (sin(y) / y) * cosh(x)
end function
public static double code(double x, double y) {
return (Math.sin(y) / y) * Math.cosh(x);
}
def code(x, y): return (math.sin(y) / y) * math.cosh(x)
function code(x, y) return Float64(Float64(sin(y) / y) * cosh(x)) end
function tmp = code(x, y) tmp = (sin(y) / y) * cosh(x); end
code[x_, y_] := N[(N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision] * N[Cosh[x], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{\sin y}{y} \cdot \cosh x
\end{array}
Initial program 99.8%
Final simplification99.8%
(FPCore (x y) :precision binary64 (if (or (<= x 0.00048) (not (<= x 9.2e+252))) (* (sin y) (+ (* 0.5 (* x (/ x y))) (/ 1.0 y))) (cosh x)))
double code(double x, double y) {
double tmp;
if ((x <= 0.00048) || !(x <= 9.2e+252)) {
tmp = sin(y) * ((0.5 * (x * (x / y))) + (1.0 / y));
} else {
tmp = cosh(x);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((x <= 0.00048d0) .or. (.not. (x <= 9.2d+252))) then
tmp = sin(y) * ((0.5d0 * (x * (x / y))) + (1.0d0 / y))
else
tmp = cosh(x)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((x <= 0.00048) || !(x <= 9.2e+252)) {
tmp = Math.sin(y) * ((0.5 * (x * (x / y))) + (1.0 / y));
} else {
tmp = Math.cosh(x);
}
return tmp;
}
def code(x, y): tmp = 0 if (x <= 0.00048) or not (x <= 9.2e+252): tmp = math.sin(y) * ((0.5 * (x * (x / y))) + (1.0 / y)) else: tmp = math.cosh(x) return tmp
function code(x, y) tmp = 0.0 if ((x <= 0.00048) || !(x <= 9.2e+252)) tmp = Float64(sin(y) * Float64(Float64(0.5 * Float64(x * Float64(x / y))) + Float64(1.0 / y))); else tmp = cosh(x); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((x <= 0.00048) || ~((x <= 9.2e+252))) tmp = sin(y) * ((0.5 * (x * (x / y))) + (1.0 / y)); else tmp = cosh(x); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[x, 0.00048], N[Not[LessEqual[x, 9.2e+252]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * N[(N[(0.5 * N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Cosh[x], $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq 0.00048 \lor \neg \left(x \leq 9.2 \cdot 10^{+252}\right):\\
\;\;\;\;\sin y \cdot \left(0.5 \cdot \left(x \cdot \frac{x}{y}\right) + \frac{1}{y}\right)\\
\mathbf{else}:\\
\;\;\;\;\cosh x\\
\end{array}
\end{array}
if x < 4.80000000000000012e-4 or 9.1999999999999999e252 < x Initial program 99.8%
*-commutative99.8%
associate-*l/99.8%
associate-/l*99.7%
Simplified99.7%
Taylor expanded in x around 0 89.6%
unpow289.6%
associate-/l*85.8%
Applied egg-rr85.8%
if 4.80000000000000012e-4 < x < 9.1999999999999999e252Initial program 100.0%
clear-num100.0%
un-div-inv100.0%
Applied egg-rr100.0%
Taylor expanded in y around 0 85.7%
Final simplification85.8%
(FPCore (x y) :precision binary64 (if (<= x 0.00018) (/ (sin y) y) (cosh x)))
double code(double x, double y) {
double tmp;
if (x <= 0.00018) {
tmp = sin(y) / y;
} else {
tmp = cosh(x);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (x <= 0.00018d0) then
tmp = sin(y) / y
else
tmp = cosh(x)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (x <= 0.00018) {
tmp = Math.sin(y) / y;
} else {
tmp = Math.cosh(x);
}
return tmp;
}
def code(x, y): tmp = 0 if x <= 0.00018: tmp = math.sin(y) / y else: tmp = math.cosh(x) return tmp
function code(x, y) tmp = 0.0 if (x <= 0.00018) tmp = Float64(sin(y) / y); else tmp = cosh(x); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (x <= 0.00018) tmp = sin(y) / y; else tmp = cosh(x); end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[x, 0.00018], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], N[Cosh[x], $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq 0.00018:\\
\;\;\;\;\frac{\sin y}{y}\\
\mathbf{else}:\\
\;\;\;\;\cosh x\\
\end{array}
\end{array}
if x < 1.80000000000000011e-4Initial program 99.8%
Taylor expanded in x around 0 67.6%
if 1.80000000000000011e-4 < x Initial program 100.0%
clear-num100.0%
un-div-inv100.0%
Applied egg-rr100.0%
Taylor expanded in y around 0 84.8%
Final simplification72.0%
(FPCore (x y) :precision binary64 (cosh x))
double code(double x, double y) {
return cosh(x);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = cosh(x)
end function
public static double code(double x, double y) {
return Math.cosh(x);
}
def code(x, y): return math.cosh(x)
function code(x, y) return cosh(x) end
function tmp = code(x, y) tmp = cosh(x); end
code[x_, y_] := N[Cosh[x], $MachinePrecision]
\begin{array}{l}
\\
\cosh x
\end{array}
Initial program 99.8%
clear-num99.8%
un-div-inv99.8%
Applied egg-rr99.8%
Taylor expanded in y around 0 64.3%
Final simplification64.3%
(FPCore (x y) :precision binary64 (if (<= y 3.3e+249) (* y (+ (* 0.5 (* x (/ x y))) (/ 1.0 y))) (+ 1.0 (* (* y y) -0.16666666666666666))))
double code(double x, double y) {
double tmp;
if (y <= 3.3e+249) {
tmp = y * ((0.5 * (x * (x / y))) + (1.0 / y));
} else {
tmp = 1.0 + ((y * y) * -0.16666666666666666);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= 3.3d+249) then
tmp = y * ((0.5d0 * (x * (x / y))) + (1.0d0 / y))
else
tmp = 1.0d0 + ((y * y) * (-0.16666666666666666d0))
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= 3.3e+249) {
tmp = y * ((0.5 * (x * (x / y))) + (1.0 / y));
} else {
tmp = 1.0 + ((y * y) * -0.16666666666666666);
}
return tmp;
}
def code(x, y): tmp = 0 if y <= 3.3e+249: tmp = y * ((0.5 * (x * (x / y))) + (1.0 / y)) else: tmp = 1.0 + ((y * y) * -0.16666666666666666) return tmp
function code(x, y) tmp = 0.0 if (y <= 3.3e+249) tmp = Float64(y * Float64(Float64(0.5 * Float64(x * Float64(x / y))) + Float64(1.0 / y))); else tmp = Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= 3.3e+249) tmp = y * ((0.5 * (x * (x / y))) + (1.0 / y)); else tmp = 1.0 + ((y * y) * -0.16666666666666666); end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, 3.3e+249], N[(y * N[(N[(0.5 * N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq 3.3 \cdot 10^{+249}:\\
\;\;\;\;y \cdot \left(0.5 \cdot \left(x \cdot \frac{x}{y}\right) + \frac{1}{y}\right)\\
\mathbf{else}:\\
\;\;\;\;1 + \left(y \cdot y\right) \cdot -0.16666666666666666\\
\end{array}
\end{array}
if y < 3.30000000000000014e249Initial program 99.8%
*-commutative99.8%
associate-*l/99.9%
associate-/l*99.8%
Simplified99.8%
Taylor expanded in x around 0 83.6%
unpow283.6%
associate-/l*79.4%
Applied egg-rr79.4%
Taylor expanded in y around 0 54.4%
if 3.30000000000000014e249 < y Initial program 99.6%
Taylor expanded in x around 0 50.5%
Taylor expanded in y around 0 34.1%
*-commutative34.1%
Simplified34.1%
unpow234.1%
Applied egg-rr34.1%
(FPCore (x y) :precision binary64 (+ 1.0 (* (* y y) -0.16666666666666666)))
double code(double x, double y) {
return 1.0 + ((y * y) * -0.16666666666666666);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.0d0 + ((y * y) * (-0.16666666666666666d0))
end function
public static double code(double x, double y) {
return 1.0 + ((y * y) * -0.16666666666666666);
}
def code(x, y): return 1.0 + ((y * y) * -0.16666666666666666)
function code(x, y) return Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)) end
function tmp = code(x, y) tmp = 1.0 + ((y * y) * -0.16666666666666666); end
code[x_, y_] := N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
1 + \left(y \cdot y\right) \cdot -0.16666666666666666
\end{array}
Initial program 99.8%
Taylor expanded in x around 0 50.9%
Taylor expanded in y around 0 26.9%
*-commutative26.9%
Simplified26.9%
unpow226.9%
Applied egg-rr26.9%
(FPCore (x y) :precision binary64 1.0)
double code(double x, double y) {
return 1.0;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.0d0
end function
public static double code(double x, double y) {
return 1.0;
}
def code(x, y): return 1.0
function code(x, y) return 1.0 end
function tmp = code(x, y) tmp = 1.0; end
code[x_, y_] := 1.0
\begin{array}{l}
\\
1
\end{array}
Initial program 99.8%
Taylor expanded in x around 0 50.9%
Taylor expanded in y around 0 23.7%
Taylor expanded in y around 0 23.7%
(FPCore (x y) :precision binary64 (/ (* (cosh x) (sin y)) y))
double code(double x, double y) {
return (cosh(x) * sin(y)) / y;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (cosh(x) * sin(y)) / y
end function
public static double code(double x, double y) {
return (Math.cosh(x) * Math.sin(y)) / y;
}
def code(x, y): return (math.cosh(x) * math.sin(y)) / y
function code(x, y) return Float64(Float64(cosh(x) * sin(y)) / y) end
function tmp = code(x, y) tmp = (cosh(x) * sin(y)) / y; end
code[x_, y_] := N[(N[(N[Cosh[x], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]
\begin{array}{l}
\\
\frac{\cosh x \cdot \sin y}{y}
\end{array}
herbie shell --seed 2024132
(FPCore (x y)
:name "Linear.Quaternion:$csinh from linear-1.19.1.3"
:precision binary64
:alt
(! :herbie-platform default (/ (* (cosh x) (sin y)) y))
(* (cosh x) (/ (sin y) y)))