
(FPCore (x y z t) :precision binary64 (+ (* (/ x y) (- z t)) t))
double code(double x, double y, double z, double t) {
return ((x / y) * (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 / y) * (z - t)) + t
end function
public static double code(double x, double y, double z, double t) {
return ((x / y) * (z - t)) + t;
}
def code(x, y, z, t): return ((x / y) * (z - t)) + t
function code(x, y, z, t) return Float64(Float64(Float64(x / y) * Float64(z - t)) + t) end
function tmp = code(x, y, z, t) tmp = ((x / y) * (z - t)) + t; end
code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{y} \cdot \left(z - t\right) + t
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (+ (* (/ x y) (- z t)) t))
double code(double x, double y, double z, double t) {
return ((x / y) * (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 / y) * (z - t)) + t
end function
public static double code(double x, double y, double z, double t) {
return ((x / y) * (z - t)) + t;
}
def code(x, y, z, t): return ((x / y) * (z - t)) + t
function code(x, y, z, t) return Float64(Float64(Float64(x / y) * Float64(z - t)) + t) end
function tmp = code(x, y, z, t) tmp = ((x / y) * (z - t)) + t; end
code[x_, y_, z_, t_] := N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{y} \cdot \left(z - t\right) + t
\end{array}
(FPCore (x y z t) :precision binary64 (fma (/ x y) (- z t) t))
double code(double x, double y, double z, double t) {
return fma((x / y), (z - t), t);
}
function code(x, y, z, t) return fma(Float64(x / y), Float64(z - t), t) end
code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)
\end{array}
Initial program 98.3%
fma-def98.4%
Simplified98.4%
Final simplification98.4%
(FPCore (x y z t) :precision binary64 (if (or (<= x -6.9e-183) (not (<= x 1.3e-158))) (+ t (* x (/ (- z t) y))) (+ t (/ z (/ y x)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -6.9e-183) || !(x <= 1.3e-158)) {
tmp = t + (x * ((z - t) / y));
} else {
tmp = t + (z / (y / x));
}
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) :: tmp
if ((x <= (-6.9d-183)) .or. (.not. (x <= 1.3d-158))) then
tmp = t + (x * ((z - t) / y))
else
tmp = t + (z / (y / x))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -6.9e-183) || !(x <= 1.3e-158)) {
tmp = t + (x * ((z - t) / y));
} else {
tmp = t + (z / (y / x));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (x <= -6.9e-183) or not (x <= 1.3e-158): tmp = t + (x * ((z - t) / y)) else: tmp = t + (z / (y / x)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((x <= -6.9e-183) || !(x <= 1.3e-158)) tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y))); else tmp = Float64(t + Float64(z / Float64(y / x))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((x <= -6.9e-183) || ~((x <= 1.3e-158))) tmp = t + (x * ((z - t) / y)); else tmp = t + (z / (y / x)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.9e-183], N[Not[LessEqual[x, 1.3e-158]], $MachinePrecision]], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -6.9 \cdot 10^{-183} \lor \neg \left(x \leq 1.3 \cdot 10^{-158}\right):\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\
\mathbf{else}:\\
\;\;\;\;t + \frac{z}{\frac{y}{x}}\\
\end{array}
\end{array}
if x < -6.9000000000000001e-183 or 1.3e-158 < x Initial program 98.4%
Taylor expanded in x around 0 89.7%
associate-*l/96.4%
*-commutative96.4%
Simplified96.4%
if -6.9000000000000001e-183 < x < 1.3e-158Initial program 98.0%
Taylor expanded in z around inf 94.0%
associate-/l*97.6%
Simplified97.6%
Final simplification96.7%
(FPCore (x y z t) :precision binary64 (if (or (<= z -5.4e-106) (not (<= z 3e+31))) (+ t (* (/ x y) z)) (- t (* (/ x y) t))))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -5.4e-106) || !(z <= 3e+31)) {
tmp = t + ((x / y) * z);
} else {
tmp = t - ((x / y) * 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) :: tmp
if ((z <= (-5.4d-106)) .or. (.not. (z <= 3d+31))) then
tmp = t + ((x / y) * z)
else
tmp = t - ((x / y) * t)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -5.4e-106) || !(z <= 3e+31)) {
tmp = t + ((x / y) * z);
} else {
tmp = t - ((x / y) * t);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -5.4e-106) or not (z <= 3e+31): tmp = t + ((x / y) * z) else: tmp = t - ((x / y) * t) return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -5.4e-106) || !(z <= 3e+31)) tmp = Float64(t + Float64(Float64(x / y) * z)); else tmp = Float64(t - Float64(Float64(x / y) * t)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((z <= -5.4e-106) || ~((z <= 3e+31))) tmp = t + ((x / y) * z); else tmp = t - ((x / y) * t); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.4e-106], N[Not[LessEqual[z, 3e+31]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -5.4 \cdot 10^{-106} \lor \neg \left(z \leq 3 \cdot 10^{+31}\right):\\
\;\;\;\;t + \frac{x}{y} \cdot z\\
\mathbf{else}:\\
\;\;\;\;t - \frac{x}{y} \cdot t\\
\end{array}
\end{array}
if z < -5.40000000000000043e-106 or 2.99999999999999989e31 < z Initial program 98.5%
Taylor expanded in z around inf 83.4%
associate-*r/91.7%
Simplified91.7%
if -5.40000000000000043e-106 < z < 2.99999999999999989e31Initial program 98.1%
Taylor expanded in z around 0 86.5%
mul-1-neg86.5%
unsub-neg86.5%
associate-*r/89.1%
Simplified89.1%
Final simplification90.5%
(FPCore (x y z t) :precision binary64 (if (or (<= z -5.4e-104) (not (<= z 1.25e+30))) (+ t (* (/ x y) z)) (- t (/ t (/ y x)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -5.4e-104) || !(z <= 1.25e+30)) {
tmp = t + ((x / y) * z);
} else {
tmp = t - (t / (y / x));
}
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) :: tmp
if ((z <= (-5.4d-104)) .or. (.not. (z <= 1.25d+30))) then
tmp = t + ((x / y) * z)
else
tmp = t - (t / (y / x))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -5.4e-104) || !(z <= 1.25e+30)) {
tmp = t + ((x / y) * z);
} else {
tmp = t - (t / (y / x));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -5.4e-104) or not (z <= 1.25e+30): tmp = t + ((x / y) * z) else: tmp = t - (t / (y / x)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -5.4e-104) || !(z <= 1.25e+30)) tmp = Float64(t + Float64(Float64(x / y) * z)); else tmp = Float64(t - Float64(t / Float64(y / x))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((z <= -5.4e-104) || ~((z <= 1.25e+30))) tmp = t + ((x / y) * z); else tmp = t - (t / (y / x)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.4e-104], N[Not[LessEqual[z, 1.25e+30]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -5.4 \cdot 10^{-104} \lor \neg \left(z \leq 1.25 \cdot 10^{+30}\right):\\
\;\;\;\;t + \frac{x}{y} \cdot z\\
\mathbf{else}:\\
\;\;\;\;t - \frac{t}{\frac{y}{x}}\\
\end{array}
\end{array}
if z < -5.3999999999999997e-104 or 1.25e30 < z Initial program 98.5%
Taylor expanded in z around inf 83.4%
associate-*r/91.7%
Simplified91.7%
if -5.3999999999999997e-104 < z < 1.25e30Initial program 98.1%
Taylor expanded in z around 0 86.5%
mul-1-neg86.5%
unsub-neg86.5%
associate-/l*89.8%
associate-/r/85.2%
Simplified85.2%
associate-*l/86.5%
associate-/l*89.8%
Applied egg-rr89.8%
Final simplification90.9%
(FPCore (x y z t) :precision binary64 (+ t (* (/ x y) (- z t))))
double code(double x, double y, double z, double t) {
return t + ((x / y) * (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 = t + ((x / y) * (z - t))
end function
public static double code(double x, double y, double z, double t) {
return t + ((x / y) * (z - t));
}
def code(x, y, z, t): return t + ((x / y) * (z - t))
function code(x, y, z, t) return Float64(t + Float64(Float64(x / y) * Float64(z - t))) end
function tmp = code(x, y, z, t) tmp = t + ((x / y) * (z - t)); end
code[x_, y_, z_, t_] := N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
t + \frac{x}{y} \cdot \left(z - t\right)
\end{array}
Initial program 98.3%
Final simplification98.3%
(FPCore (x y z t) :precision binary64 (+ t (* (/ x y) z)))
double code(double x, double y, double z, double t) {
return t + ((x / y) * 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 = t + ((x / y) * z)
end function
public static double code(double x, double y, double z, double t) {
return t + ((x / y) * z);
}
def code(x, y, z, t): return t + ((x / y) * z)
function code(x, y, z, t) return Float64(t + Float64(Float64(x / y) * z)) end
function tmp = code(x, y, z, t) tmp = t + ((x / y) * z); end
code[x_, y_, z_, t_] := N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
t + \frac{x}{y} \cdot z
\end{array}
Initial program 98.3%
Taylor expanded in z around inf 70.4%
associate-*r/77.2%
Simplified77.2%
Final simplification77.2%
(FPCore (x y z t) :precision binary64 t)
double code(double x, double y, double z, double t) {
return 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 = t
end function
public static double code(double x, double y, double z, double t) {
return t;
}
def code(x, y, z, t): return t
function code(x, y, z, t) return t end
function tmp = code(x, y, z, t) tmp = t; end
code[x_, y_, z_, t_] := t
\begin{array}{l}
\\
t
\end{array}
Initial program 98.3%
Taylor expanded in x around 0 36.3%
Final simplification36.3%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (+ (* (/ x y) (- z t)) t)))
(if (< z 2.759456554562692e-282)
t_1
(if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))
double code(double x, double y, double z, double t) {
double t_1 = ((x / y) * (z - t)) + t;
double tmp;
if (z < 2.759456554562692e-282) {
tmp = t_1;
} else if (z < 2.326994450874436e-110) {
tmp = (x * ((z - t) / y)) + t;
} else {
tmp = t_1;
}
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 = ((x / y) * (z - t)) + t
if (z < 2.759456554562692d-282) then
tmp = t_1
else if (z < 2.326994450874436d-110) then
tmp = (x * ((z - t) / y)) + t
else
tmp = t_1
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = ((x / y) * (z - t)) + t;
double tmp;
if (z < 2.759456554562692e-282) {
tmp = t_1;
} else if (z < 2.326994450874436e-110) {
tmp = (x * ((z - t) / y)) + t;
} else {
tmp = t_1;
}
return tmp;
}
def code(x, y, z, t): t_1 = ((x / y) * (z - t)) + t tmp = 0 if z < 2.759456554562692e-282: tmp = t_1 elif z < 2.326994450874436e-110: tmp = (x * ((z - t) / y)) + t else: tmp = t_1 return tmp
function code(x, y, z, t) t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t) tmp = 0.0 if (z < 2.759456554562692e-282) tmp = t_1; elseif (z < 2.326994450874436e-110) tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t); else tmp = t_1; end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = ((x / y) * (z - t)) + t; tmp = 0.0; if (z < 2.759456554562692e-282) tmp = t_1; elseif (z < 2.326994450874436e-110) tmp = (x * ((z - t) / y)) + t; else tmp = t_1; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\
\mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
\end{array}
herbie shell --seed 2023200
(FPCore (x y z t)
:name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
:precision binary64
:herbie-target
(if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))
(+ (* (/ x y) (- z t)) t))