
(FPCore (x y) :precision binary64 (let* ((t_0 (/ x (* y 2.0)))) (/ (tan t_0) (sin t_0))))
double code(double x, double y) {
double t_0 = x / (y * 2.0);
return tan(t_0) / sin(t_0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
t_0 = x / (y * 2.0d0)
code = tan(t_0) / sin(t_0)
end function
public static double code(double x, double y) {
double t_0 = x / (y * 2.0);
return Math.tan(t_0) / Math.sin(t_0);
}
def code(x, y): t_0 = x / (y * 2.0) return math.tan(t_0) / math.sin(t_0)
function code(x, y) t_0 = Float64(x / Float64(y * 2.0)) return Float64(tan(t_0) / sin(t_0)) end
function tmp = code(x, y) t_0 = x / (y * 2.0); tmp = tan(t_0) / sin(t_0); end
code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{x}{y \cdot 2}\\
\frac{\tan t\_0}{\sin t\_0}
\end{array}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (let* ((t_0 (/ x (* y 2.0)))) (/ (tan t_0) (sin t_0))))
double code(double x, double y) {
double t_0 = x / (y * 2.0);
return tan(t_0) / sin(t_0);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
t_0 = x / (y * 2.0d0)
code = tan(t_0) / sin(t_0)
end function
public static double code(double x, double y) {
double t_0 = x / (y * 2.0);
return Math.tan(t_0) / Math.sin(t_0);
}
def code(x, y): t_0 = x / (y * 2.0) return math.tan(t_0) / math.sin(t_0)
function code(x, y) t_0 = Float64(x / Float64(y * 2.0)) return Float64(tan(t_0) / sin(t_0)) end
function tmp = code(x, y) t_0 = x / (y * 2.0); tmp = tan(t_0) / sin(t_0); end
code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{x}{y \cdot 2}\\
\frac{\tan t\_0}{\sin t\_0}
\end{array}
\end{array}
x_m = (fabs.f64 x) (FPCore (x_m y) :precision binary64 (/ 1.0 (cos (* (sqrt x_m) (* (/ 0.5 y) (sqrt x_m))))))
x_m = fabs(x);
double code(double x_m, double y) {
return 1.0 / cos((sqrt(x_m) * ((0.5 / y) * sqrt(x_m))));
}
x_m = abs(x)
real(8) function code(x_m, y)
real(8), intent (in) :: x_m
real(8), intent (in) :: y
code = 1.0d0 / cos((sqrt(x_m) * ((0.5d0 / y) * sqrt(x_m))))
end function
x_m = Math.abs(x);
public static double code(double x_m, double y) {
return 1.0 / Math.cos((Math.sqrt(x_m) * ((0.5 / y) * Math.sqrt(x_m))));
}
x_m = math.fabs(x) def code(x_m, y): return 1.0 / math.cos((math.sqrt(x_m) * ((0.5 / y) * math.sqrt(x_m))))
x_m = abs(x) function code(x_m, y) return Float64(1.0 / cos(Float64(sqrt(x_m) * Float64(Float64(0.5 / y) * sqrt(x_m))))) end
x_m = abs(x); function tmp = code(x_m, y) tmp = 1.0 / cos((sqrt(x_m) * ((0.5 / y) * sqrt(x_m)))); end
x_m = N[Abs[x], $MachinePrecision] code[x$95$m_, y_] := N[(1.0 / N[Cos[N[(N[Sqrt[x$95$m], $MachinePrecision] * N[(N[(0.5 / y), $MachinePrecision] * N[Sqrt[x$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
x_m = \left|x\right|
\\
\frac{1}{\cos \left(\sqrt{x\_m} \cdot \left(\frac{0.5}{y} \cdot \sqrt{x\_m}\right)\right)}
\end{array}
Initial program 45.5%
Taylor expanded in x around inf 59.2%
add-sqr-sqrt37.4%
unpow237.4%
Applied egg-rr37.4%
sqrt-pow259.2%
associate-*r/59.2%
metadata-eval59.2%
pow159.2%
associate-*l/59.2%
add-sqr-sqrt32.9%
associate-*r*32.9%
Applied egg-rr32.9%
Final simplification32.9%
x_m = (fabs.f64 x) (FPCore (x_m y) :precision binary64 (/ 1.0 (cos (pow (sqrt (* 0.5 (/ x_m y))) 2.0))))
x_m = fabs(x);
double code(double x_m, double y) {
return 1.0 / cos(pow(sqrt((0.5 * (x_m / y))), 2.0));
}
x_m = abs(x)
real(8) function code(x_m, y)
real(8), intent (in) :: x_m
real(8), intent (in) :: y
code = 1.0d0 / cos((sqrt((0.5d0 * (x_m / y))) ** 2.0d0))
end function
x_m = Math.abs(x);
public static double code(double x_m, double y) {
return 1.0 / Math.cos(Math.pow(Math.sqrt((0.5 * (x_m / y))), 2.0));
}
x_m = math.fabs(x) def code(x_m, y): return 1.0 / math.cos(math.pow(math.sqrt((0.5 * (x_m / y))), 2.0))
x_m = abs(x) function code(x_m, y) return Float64(1.0 / cos((sqrt(Float64(0.5 * Float64(x_m / y))) ^ 2.0))) end
x_m = abs(x); function tmp = code(x_m, y) tmp = 1.0 / cos((sqrt((0.5 * (x_m / y))) ^ 2.0)); end
x_m = N[Abs[x], $MachinePrecision] code[x$95$m_, y_] := N[(1.0 / N[Cos[N[Power[N[Sqrt[N[(0.5 * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
x_m = \left|x\right|
\\
\frac{1}{\cos \left({\left(\sqrt{0.5 \cdot \frac{x\_m}{y}}\right)}^{2}\right)}
\end{array}
Initial program 45.5%
Taylor expanded in x around inf 59.2%
add-sqr-sqrt37.4%
unpow237.4%
Applied egg-rr37.4%
Final simplification37.4%
x_m = (fabs.f64 x) (FPCore (x_m y) :precision binary64 (/ 1.0 (cos (/ 1.0 (/ 2.0 (/ x_m y))))))
x_m = fabs(x);
double code(double x_m, double y) {
return 1.0 / cos((1.0 / (2.0 / (x_m / y))));
}
x_m = abs(x)
real(8) function code(x_m, y)
real(8), intent (in) :: x_m
real(8), intent (in) :: y
code = 1.0d0 / cos((1.0d0 / (2.0d0 / (x_m / y))))
end function
x_m = Math.abs(x);
public static double code(double x_m, double y) {
return 1.0 / Math.cos((1.0 / (2.0 / (x_m / y))));
}
x_m = math.fabs(x) def code(x_m, y): return 1.0 / math.cos((1.0 / (2.0 / (x_m / y))))
x_m = abs(x) function code(x_m, y) return Float64(1.0 / cos(Float64(1.0 / Float64(2.0 / Float64(x_m / y))))) end
x_m = abs(x); function tmp = code(x_m, y) tmp = 1.0 / cos((1.0 / (2.0 / (x_m / y)))); end
x_m = N[Abs[x], $MachinePrecision] code[x$95$m_, y_] := N[(1.0 / N[Cos[N[(1.0 / N[(2.0 / N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
x_m = \left|x\right|
\\
\frac{1}{\cos \left(\frac{1}{\frac{2}{\frac{x\_m}{y}}}\right)}
\end{array}
Initial program 45.5%
Taylor expanded in x around inf 59.2%
*-commutative59.2%
metadata-eval59.2%
div-inv59.2%
clear-num59.3%
Applied egg-rr59.3%
Final simplification59.3%
x_m = (fabs.f64 x) (FPCore (x_m y) :precision binary64 (/ 1.0 (cos (* 0.5 (/ x_m y)))))
x_m = fabs(x);
double code(double x_m, double y) {
return 1.0 / cos((0.5 * (x_m / y)));
}
x_m = abs(x)
real(8) function code(x_m, y)
real(8), intent (in) :: x_m
real(8), intent (in) :: y
code = 1.0d0 / cos((0.5d0 * (x_m / y)))
end function
x_m = Math.abs(x);
public static double code(double x_m, double y) {
return 1.0 / Math.cos((0.5 * (x_m / y)));
}
x_m = math.fabs(x) def code(x_m, y): return 1.0 / math.cos((0.5 * (x_m / y)))
x_m = abs(x) function code(x_m, y) return Float64(1.0 / cos(Float64(0.5 * Float64(x_m / y)))) end
x_m = abs(x); function tmp = code(x_m, y) tmp = 1.0 / cos((0.5 * (x_m / y))); end
x_m = N[Abs[x], $MachinePrecision] code[x$95$m_, y_] := N[(1.0 / N[Cos[N[(0.5 * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
x_m = \left|x\right|
\\
\frac{1}{\cos \left(0.5 \cdot \frac{x\_m}{y}\right)}
\end{array}
Initial program 45.5%
Taylor expanded in x around inf 59.2%
Final simplification59.2%
x_m = (fabs.f64 x) (FPCore (x_m y) :precision binary64 1.0)
x_m = fabs(x);
double code(double x_m, double y) {
return 1.0;
}
x_m = abs(x)
real(8) function code(x_m, y)
real(8), intent (in) :: x_m
real(8), intent (in) :: y
code = 1.0d0
end function
x_m = Math.abs(x);
public static double code(double x_m, double y) {
return 1.0;
}
x_m = math.fabs(x) def code(x_m, y): return 1.0
x_m = abs(x) function code(x_m, y) return 1.0 end
x_m = abs(x); function tmp = code(x_m, y) tmp = 1.0; end
x_m = N[Abs[x], $MachinePrecision] code[x$95$m_, y_] := 1.0
\begin{array}{l}
x_m = \left|x\right|
\\
1
\end{array}
Initial program 45.5%
remove-double-neg45.5%
distribute-frac-neg45.5%
tan-neg45.5%
distribute-frac-neg245.5%
distribute-lft-neg-out45.5%
distribute-frac-neg245.5%
distribute-lft-neg-out45.5%
distribute-frac-neg245.5%
distribute-frac-neg45.5%
neg-mul-145.5%
*-commutative45.5%
associate-/l*45.2%
*-commutative45.2%
associate-/r*45.2%
metadata-eval45.2%
sin-neg45.2%
distribute-frac-neg45.2%
Simplified45.9%
Taylor expanded in x around 0 58.3%
Final simplification58.3%
(FPCore (x y)
:precision binary64
(let* ((t_0 (/ x (* y 2.0))) (t_1 (sin t_0)))
(if (< y -1.2303690911306994e+114)
1.0
(if (< y -9.102852406811914e-222)
(/ t_1 (* t_1 (log (exp (cos t_0)))))
1.0))))
double code(double x, double y) {
double t_0 = x / (y * 2.0);
double t_1 = sin(t_0);
double tmp;
if (y < -1.2303690911306994e+114) {
tmp = 1.0;
} else if (y < -9.102852406811914e-222) {
tmp = t_1 / (t_1 * log(exp(cos(t_0))));
} else {
tmp = 1.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: t_1
real(8) :: tmp
t_0 = x / (y * 2.0d0)
t_1 = sin(t_0)
if (y < (-1.2303690911306994d+114)) then
tmp = 1.0d0
else if (y < (-9.102852406811914d-222)) then
tmp = t_1 / (t_1 * log(exp(cos(t_0))))
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = x / (y * 2.0);
double t_1 = Math.sin(t_0);
double tmp;
if (y < -1.2303690911306994e+114) {
tmp = 1.0;
} else if (y < -9.102852406811914e-222) {
tmp = t_1 / (t_1 * Math.log(Math.exp(Math.cos(t_0))));
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): t_0 = x / (y * 2.0) t_1 = math.sin(t_0) tmp = 0 if y < -1.2303690911306994e+114: tmp = 1.0 elif y < -9.102852406811914e-222: tmp = t_1 / (t_1 * math.log(math.exp(math.cos(t_0)))) else: tmp = 1.0 return tmp
function code(x, y) t_0 = Float64(x / Float64(y * 2.0)) t_1 = sin(t_0) tmp = 0.0 if (y < -1.2303690911306994e+114) tmp = 1.0; elseif (y < -9.102852406811914e-222) tmp = Float64(t_1 / Float64(t_1 * log(exp(cos(t_0))))); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) t_0 = x / (y * 2.0); t_1 = sin(t_0); tmp = 0.0; if (y < -1.2303690911306994e+114) tmp = 1.0; elseif (y < -9.102852406811914e-222) tmp = t_1 / (t_1 * log(exp(cos(t_0)))); else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, If[Less[y, -1.2303690911306994e+114], 1.0, If[Less[y, -9.102852406811914e-222], N[(t$95$1 / N[(t$95$1 * N[Log[N[Exp[N[Cos[t$95$0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{x}{y \cdot 2}\\
t_1 := \sin t\_0\\
\mathbf{if}\;y < -1.2303690911306994 \cdot 10^{+114}:\\
\;\;\;\;1\\
\mathbf{elif}\;y < -9.102852406811914 \cdot 10^{-222}:\\
\;\;\;\;\frac{t\_1}{t\_1 \cdot \log \left(e^{\cos t\_0}\right)}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
herbie shell --seed 2024059
(FPCore (x y)
:name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
:precision binary64
:herbie-target
(if (< y -1.2303690911306994e+114) 1.0 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (log (exp (cos (/ x (* y 2.0))))))) 1.0))
(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))