
(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 4 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) (/ x y)) (/ (/ z t) (/ t z))))
double code(double x, double y, double z, double t) {
return ((x / y) * (x / y)) + ((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) * (x / y)) + ((z / t) / (t / z))
end function
public static double code(double x, double y, double z, double t) {
return ((x / y) * (x / y)) + ((z / t) / (t / z));
}
def code(x, y, z, t): return ((x / y) * (x / y)) + ((z / t) / (t / z))
function code(x, y, z, t) return Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(Float64(z / t) / Float64(t / z))) end
function tmp = code(x, y, z, t) tmp = ((x / y) * (x / y)) + ((z / t) / (t / z)); end
code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{y} \cdot \frac{x}{y} + \frac{\frac{z}{t}}{\frac{t}{z}}
\end{array}
Initial program 59.9%
associate-/r*70.9%
div-inv70.8%
pow270.8%
Applied egg-rr70.8%
pow270.8%
associate-*l/77.9%
associate-*r*80.9%
div-inv80.9%
clear-num80.9%
un-div-inv81.0%
Applied egg-rr81.0%
frac-times99.7%
Applied egg-rr99.7%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (/ (* z z) (* t t))))
(if (<= t_1 5e+307)
(+ (* (/ x y) (/ x y)) t_1)
(+ (* x (/ x (* y y))) (* (/ z t) (/ z t))))))
double code(double x, double y, double z, double t) {
double t_1 = (z * z) / (t * t);
double tmp;
if (t_1 <= 5e+307) {
tmp = ((x / y) * (x / y)) + t_1;
} else {
tmp = (x * (x / (y * y))) + ((z / t) * (z / t));
}
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 <= 5d+307) then
tmp = ((x / y) * (x / y)) + t_1
else
tmp = (x * (x / (y * y))) + ((z / t) * (z / t))
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 <= 5e+307) {
tmp = ((x / y) * (x / y)) + t_1;
} else {
tmp = (x * (x / (y * y))) + ((z / t) * (z / t));
}
return tmp;
}
def code(x, y, z, t): t_1 = (z * z) / (t * t) tmp = 0 if t_1 <= 5e+307: tmp = ((x / y) * (x / y)) + t_1 else: tmp = (x * (x / (y * y))) + ((z / t) * (z / t)) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(z * z) / Float64(t * t)) tmp = 0.0 if (t_1 <= 5e+307) tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1); else tmp = Float64(Float64(x * Float64(x / Float64(y * y))) + Float64(Float64(z / t) * Float64(z / t))); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (z * z) / (t * t); tmp = 0.0; if (t_1 <= 5e+307) tmp = ((x / y) * (x / y)) + t_1; else tmp = (x * (x / (y * y))) + ((z / t) * (z / t)); 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, 5e+307], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{z \cdot z}{t \cdot t}\\
\mathbf{if}\;t\_1 \leq 5 \cdot 10^{+307}:\\
\;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\
\mathbf{else}:\\
\;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{z}{t} \cdot \frac{z}{t}\\
\end{array}
\end{array}
if (/.f64 (*.f64 z z) (*.f64 t t)) < 5e307Initial program 68.7%
frac-times99.6%
Applied egg-rr91.5%
if 5e307 < (/.f64 (*.f64 z z) (*.f64 t t)) Initial program 51.3%
associate-/l*60.5%
Simplified60.5%
times-frac96.9%
Applied egg-rr96.9%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (/ (* z z) (* t t))))
(if (<= t_1 2e+264)
(+ t_1 (* x (/ (/ x y) y)))
(+ (* x (/ x (* y y))) (* (/ z t) (/ z t))))))
double code(double x, double y, double z, double t) {
double t_1 = (z * z) / (t * t);
double tmp;
if (t_1 <= 2e+264) {
tmp = t_1 + (x * ((x / y) / y));
} else {
tmp = (x * (x / (y * y))) + ((z / t) * (z / t));
}
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 <= 2d+264) then
tmp = t_1 + (x * ((x / y) / y))
else
tmp = (x * (x / (y * y))) + ((z / t) * (z / t))
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 <= 2e+264) {
tmp = t_1 + (x * ((x / y) / y));
} else {
tmp = (x * (x / (y * y))) + ((z / t) * (z / t));
}
return tmp;
}
def code(x, y, z, t): t_1 = (z * z) / (t * t) tmp = 0 if t_1 <= 2e+264: tmp = t_1 + (x * ((x / y) / y)) else: tmp = (x * (x / (y * y))) + ((z / t) * (z / t)) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(z * z) / Float64(t * t)) tmp = 0.0 if (t_1 <= 2e+264) tmp = Float64(t_1 + Float64(x * Float64(Float64(x / y) / y))); else tmp = Float64(Float64(x * Float64(x / Float64(y * y))) + Float64(Float64(z / t) * Float64(z / t))); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (z * z) / (t * t); tmp = 0.0; if (t_1 <= 2e+264) tmp = t_1 + (x * ((x / y) / y)); else tmp = (x * (x / (y * y))) + ((z / t) * (z / t)); 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, 2e+264], N[(t$95$1 + N[(x * N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{z \cdot z}{t \cdot t}\\
\mathbf{if}\;t\_1 \leq 2 \cdot 10^{+264}:\\
\;\;\;\;t\_1 + x \cdot \frac{\frac{x}{y}}{y}\\
\mathbf{else}:\\
\;\;\;\;x \cdot \frac{x}{y \cdot y} + \frac{z}{t} \cdot \frac{z}{t}\\
\end{array}
\end{array}
if (/.f64 (*.f64 z z) (*.f64 t t)) < 2.00000000000000009e264Initial program 68.9%
associate-/l*72.1%
Simplified72.1%
associate-/r*86.0%
div-inv85.9%
Applied egg-rr85.9%
un-div-inv86.0%
Applied egg-rr86.0%
if 2.00000000000000009e264 < (/.f64 (*.f64 z z) (*.f64 t t)) Initial program 51.7%
associate-/l*61.3%
Simplified61.3%
times-frac96.4%
Applied egg-rr96.4%
Final simplification91.5%
(FPCore (x y z t) :precision binary64 (+ (* x (/ x (* y y))) (* (/ z t) (/ z t))))
double code(double x, double y, double z, double t) {
return (x * (x / (y * y))) + ((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 * (x / (y * y))) + ((z / t) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return (x * (x / (y * y))) + ((z / t) * (z / t));
}
def code(x, y, z, t): return (x * (x / (y * y))) + ((z / t) * (z / t))
function code(x, y, z, t) return Float64(Float64(x * Float64(x / Float64(y * y))) + Float64(Float64(z / t) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = (x * (x / (y * y))) + ((z / t) * (z / t)); end
code[x_, y_, z_, t_] := N[(N[(x * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \frac{x}{y \cdot y} + \frac{z}{t} \cdot \frac{z}{t}
\end{array}
Initial program 59.9%
associate-/l*66.4%
Simplified66.4%
times-frac88.7%
Applied egg-rr88.7%
(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 2024185
(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))))