
(FPCore (x y z t) :precision binary64 (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))
double code(double x, double y, double z, double t) {
return ((x * x) / (y * y)) + ((z * z) / (t * t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((x * x) / (y * y)) + ((z * z) / (t * t))
end function
public static double code(double x, double y, double z, double t) {
return ((x * x) / (y * y)) + ((z * z) / (t * t));
}
def code(x, y, z, t): return ((x * x) / (y * y)) + ((z * z) / (t * t))
function code(x, y, z, t) return Float64(Float64(Float64(x * x) / Float64(y * y)) + Float64(Float64(z * z) / Float64(t * t))) end
function tmp = code(x, y, z, t) tmp = ((x * x) / (y * y)) + ((z * z) / (t * t)); end
code[x_, y_, z_, t_] := N[(N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))
double code(double x, double y, double z, double t) {
return ((x * x) / (y * y)) + ((z * z) / (t * t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((x * x) / (y * y)) + ((z * z) / (t * t))
end function
public static double code(double x, double y, double z, double t) {
return ((x * x) / (y * y)) + ((z * z) / (t * t));
}
def code(x, y, z, t): return ((x * x) / (y * y)) + ((z * z) / (t * t))
function code(x, y, z, t) return Float64(Float64(Float64(x * x) / Float64(y * y)) + Float64(Float64(z * z) / Float64(t * t))) end
function tmp = code(x, y, z, t) tmp = ((x * x) / (y * y)) + ((z * z) / (t * t)); end
code[x_, y_, z_, t_] := N[(N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
\end{array}
(FPCore (x y z t) :precision binary64 (+ (/ (/ x y) (/ y x)) (/ (/ z t) (/ t z))))
double code(double x, double y, double z, double t) {
return ((x / y) / (y / x)) + ((z / t) / (t / z));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((x / y) / (y / x)) + ((z / t) / (t / z))
end function
public static double code(double x, double y, double z, double t) {
return ((x / y) / (y / x)) + ((z / t) / (t / z));
}
def code(x, y, z, t): return ((x / y) / (y / x)) + ((z / t) / (t / z))
function code(x, y, z, t) return Float64(Float64(Float64(x / y) / Float64(y / x)) + Float64(Float64(z / t) / Float64(t / z))) end
function tmp = code(x, y, z, t) tmp = ((x / y) / (y / x)) + ((z / t) / (t / z)); end
code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{\frac{x}{y}}{\frac{y}{x}} + \frac{\frac{z}{t}}{\frac{t}{z}}
\end{array}
Initial program 62.0%
associate-/l*69.3%
Simplified69.3%
frac-times87.5%
Applied egg-rr87.5%
associate-*r/79.0%
times-frac99.6%
clear-num99.7%
un-div-inv99.7%
Applied egg-rr99.7%
clear-num99.7%
un-div-inv99.8%
Applied egg-rr99.8%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (/ (* z z) (* t t))))
(if (<= t_1 1e+279)
(+ t_1 (* (/ x y) (/ x y)))
(+ (/ (/ z t) (/ t z)) (* x (/ x (* y y)))))))
double code(double x, double y, double z, double t) {
double t_1 = (z * z) / (t * t);
double tmp;
if (t_1 <= 1e+279) {
tmp = t_1 + ((x / y) * (x / y));
} else {
tmp = ((z / t) / (t / z)) + (x * (x / (y * y)));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: t_1
real(8) :: tmp
t_1 = (z * z) / (t * t)
if (t_1 <= 1d+279) then
tmp = t_1 + ((x / y) * (x / y))
else
tmp = ((z / t) / (t / z)) + (x * (x / (y * y)))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (z * z) / (t * t);
double tmp;
if (t_1 <= 1e+279) {
tmp = t_1 + ((x / y) * (x / y));
} else {
tmp = ((z / t) / (t / z)) + (x * (x / (y * y)));
}
return tmp;
}
def code(x, y, z, t): t_1 = (z * z) / (t * t) tmp = 0 if t_1 <= 1e+279: tmp = t_1 + ((x / y) * (x / y)) else: tmp = ((z / t) / (t / z)) + (x * (x / (y * y))) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(z * z) / Float64(t * t)) tmp = 0.0 if (t_1 <= 1e+279) tmp = Float64(t_1 + Float64(Float64(x / y) * Float64(x / y))); else tmp = Float64(Float64(Float64(z / t) / Float64(t / z)) + Float64(x * Float64(x / Float64(y * y)))); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (z * z) / (t * t); tmp = 0.0; if (t_1 <= 1e+279) tmp = t_1 + ((x / y) * (x / y)); else tmp = ((z / t) / (t / z)) + (x * (x / (y * y))); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+279], N[(t$95$1 + N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{z \cdot z}{t \cdot t}\\
\mathbf{if}\;t\_1 \leq 10^{+279}:\\
\;\;\;\;t\_1 + \frac{x}{y} \cdot \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}\\
\end{array}
\end{array}
if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.00000000000000006e279Initial program 66.7%
times-frac94.3%
Applied egg-rr94.3%
if 1.00000000000000006e279 < (/.f64 (*.f64 z z) (*.f64 t t)) Initial program 56.6%
associate-/l*63.4%
Simplified63.4%
frac-times96.6%
Applied egg-rr96.6%
clear-num99.8%
un-div-inv99.9%
Applied egg-rr96.7%
Final simplification95.4%
(FPCore (x y z t) :precision binary64 (+ (/ (/ x y) (/ y x)) (* (/ z t) (/ z t))))
double code(double x, double y, double z, double t) {
return ((x / y) / (y / x)) + ((z / t) * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((x / y) / (y / x)) + ((z / t) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return ((x / y) / (y / x)) + ((z / t) * (z / t));
}
def code(x, y, z, t): return ((x / y) / (y / x)) + ((z / t) * (z / t))
function code(x, y, z, t) return Float64(Float64(Float64(x / y) / Float64(y / x)) + Float64(Float64(z / t) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = ((x / y) / (y / x)) + ((z / t) * (z / t)); end
code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{\frac{x}{y}}{\frac{y}{x}} + \frac{z}{t} \cdot \frac{z}{t}
\end{array}
Initial program 62.0%
associate-/l*69.3%
Simplified69.3%
frac-times87.5%
Applied egg-rr87.5%
associate-*r/79.0%
times-frac99.6%
clear-num99.7%
un-div-inv99.7%
Applied egg-rr99.7%
(FPCore (x y z t) :precision binary64 (+ (/ (/ z t) (/ t z)) (* x (/ x (* y y)))))
double code(double x, double y, double z, double t) {
return ((z / t) / (t / z)) + (x * (x / (y * y)));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((z / t) / (t / z)) + (x * (x / (y * y)))
end function
public static double code(double x, double y, double z, double t) {
return ((z / t) / (t / z)) + (x * (x / (y * y)));
}
def code(x, y, z, t): return ((z / t) / (t / z)) + (x * (x / (y * y)))
function code(x, y, z, t) return Float64(Float64(Float64(z / t) / Float64(t / z)) + Float64(x * Float64(x / Float64(y * y)))) end
function tmp = code(x, y, z, t) tmp = ((z / t) / (t / z)) + (x * (x / (y * y))); end
code[x_, y_, z_, t_] := N[(N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{\frac{z}{t}}{\frac{t}{z}} + x \cdot \frac{x}{y \cdot y}
\end{array}
Initial program 62.0%
associate-/l*69.3%
Simplified69.3%
frac-times87.5%
Applied egg-rr87.5%
clear-num99.7%
un-div-inv99.8%
Applied egg-rr87.5%
Final simplification87.5%
(FPCore (x y z t) :precision binary64 (+ (* (/ z t) (/ z t)) (* x (/ x (* y y)))))
double code(double x, double y, double z, double t) {
return ((z / t) * (z / t)) + (x * (x / (y * y)));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((z / t) * (z / t)) + (x * (x / (y * y)))
end function
public static double code(double x, double y, double z, double t) {
return ((z / t) * (z / t)) + (x * (x / (y * y)));
}
def code(x, y, z, t): return ((z / t) * (z / t)) + (x * (x / (y * y)))
function code(x, y, z, t) return Float64(Float64(Float64(z / t) * Float64(z / t)) + Float64(x * Float64(x / Float64(y * y)))) end
function tmp = code(x, y, z, t) tmp = ((z / t) * (z / t)) + (x * (x / (y * y))); end
code[x_, y_, z_, t_] := N[(N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{z}{t} \cdot \frac{z}{t} + x \cdot \frac{x}{y \cdot y}
\end{array}
Initial program 62.0%
associate-/l*69.3%
Simplified69.3%
frac-times87.5%
Applied egg-rr87.5%
Final simplification87.5%
(FPCore (x y z t) :precision binary64 (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0)))
double code(double x, double y, double z, double t) {
return pow((x / y), 2.0) + pow((z / t), 2.0);
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = ((x / y) ** 2.0d0) + ((z / t) ** 2.0d0)
end function
public static double code(double x, double y, double z, double t) {
return Math.pow((x / y), 2.0) + Math.pow((z / t), 2.0);
}
def code(x, y, z, t): return math.pow((x / y), 2.0) + math.pow((z / t), 2.0)
function code(x, y, z, t) return Float64((Float64(x / y) ^ 2.0) + (Float64(z / t) ^ 2.0)) end
function tmp = code(x, y, z, t) tmp = ((x / y) ^ 2.0) + ((z / t) ^ 2.0); end
code[x_, y_, z_, t_] := N[(N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(z / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}
\end{array}
herbie shell --seed 2024135
(FPCore (x y z t)
:name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
:precision binary64
:alt
(! :herbie-platform default (+ (pow (/ x y) 2) (pow (/ z t) 2)))
(+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))