
(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 10 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 (+ t (/ (- z t) (/ y x))))
double code(double x, double y, double z, double t) {
return t + ((z - t) / (y / x));
}
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 + ((z - t) / (y / x))
end function
public static double code(double x, double y, double z, double t) {
return t + ((z - t) / (y / x));
}
def code(x, y, z, t): return t + ((z - t) / (y / x))
function code(x, y, z, t) return Float64(t + Float64(Float64(z - t) / Float64(y / x))) end
function tmp = code(x, y, z, t) tmp = t + ((z - t) / (y / x)); end
code[x_, y_, z_, t_] := N[(t + N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
t + \frac{z - t}{\frac{y}{x}}
\end{array}
(FPCore (x y z t) :precision binary64 (if (or (<= z -6.5e-99) (not (<= z 1.85e-134))) (+ t (* z (/ x y))) (* t (- 1.0 (/ x y)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -6.5e-99) || !(z <= 1.85e-134)) {
tmp = t + (z * (x / y));
} else {
tmp = t * (1.0 - (x / 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) :: tmp
if ((z <= (-6.5d-99)) .or. (.not. (z <= 1.85d-134))) then
tmp = t + (z * (x / y))
else
tmp = t * (1.0d0 - (x / y))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -6.5e-99) || !(z <= 1.85e-134)) {
tmp = t + (z * (x / y));
} else {
tmp = t * (1.0 - (x / y));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -6.5e-99) or not (z <= 1.85e-134): tmp = t + (z * (x / y)) else: tmp = t * (1.0 - (x / y)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -6.5e-99) || !(z <= 1.85e-134)) tmp = Float64(t + Float64(z * Float64(x / y))); else tmp = Float64(t * Float64(1.0 - Float64(x / y))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((z <= -6.5e-99) || ~((z <= 1.85e-134))) tmp = t + (z * (x / y)); else tmp = t * (1.0 - (x / y)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.5e-99], N[Not[LessEqual[z, 1.85e-134]], $MachinePrecision]], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.5 \cdot 10^{-99} \lor \neg \left(z \leq 1.85 \cdot 10^{-134}\right):\\
\;\;\;\;t + z \cdot \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= z -1.05e+26) (+ t (/ (* z x) y)) (+ t (* x (/ (- z t) y)))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -1.05e+26) {
tmp = t + ((z * x) / y);
} else {
tmp = t + (x * ((z - t) / 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) :: tmp
if (z <= (-1.05d+26)) then
tmp = t + ((z * x) / y)
else
tmp = t + (x * ((z - t) / y))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (z <= -1.05e+26) {
tmp = t + ((z * x) / y);
} else {
tmp = t + (x * ((z - t) / y));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -1.05e+26: tmp = t + ((z * x) / y) else: tmp = t + (x * ((z - t) / y)) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -1.05e+26) tmp = Float64(t + Float64(Float64(z * x) / y)); else tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (z <= -1.05e+26) tmp = t + ((z * x) / y); else tmp = t + (x * ((z - t) / y)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+26], N[(t + N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -1.05 \cdot 10^{+26}:\\
\;\;\;\;t + \frac{z \cdot x}{y}\\
\mathbf{else}:\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (or (<= x -5e+150) (not (<= x 3.1e+128))) (* x (- (/ t y))) t))
double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -5e+150) || !(x <= 3.1e+128)) {
tmp = x * -(t / y);
} else {
tmp = 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 ((x <= (-5d+150)) .or. (.not. (x <= 3.1d+128))) then
tmp = x * -(t / y)
else
tmp = t
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -5e+150) || !(x <= 3.1e+128)) {
tmp = x * -(t / y);
} else {
tmp = t;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (x <= -5e+150) or not (x <= 3.1e+128): tmp = x * -(t / y) else: tmp = t return tmp
function code(x, y, z, t) tmp = 0.0 if ((x <= -5e+150) || !(x <= 3.1e+128)) tmp = Float64(x * Float64(-Float64(t / y))); else tmp = t; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((x <= -5e+150) || ~((x <= 3.1e+128))) tmp = x * -(t / y); else tmp = t; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5e+150], N[Not[LessEqual[x, 3.1e+128]], $MachinePrecision]], N[(x * (-N[(t / y), $MachinePrecision])), $MachinePrecision], t]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -5 \cdot 10^{+150} \lor \neg \left(x \leq 3.1 \cdot 10^{+128}\right):\\
\;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\
\mathbf{else}:\\
\;\;\;\;t\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= x -1.22e+117) (* t (/ (- x) y)) (if (<= x 2.3e+131) t (* x (- (/ t y))))))
double code(double x, double y, double z, double t) {
double tmp;
if (x <= -1.22e+117) {
tmp = t * (-x / y);
} else if (x <= 2.3e+131) {
tmp = t;
} else {
tmp = x * -(t / 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) :: tmp
if (x <= (-1.22d+117)) then
tmp = t * (-x / y)
else if (x <= 2.3d+131) then
tmp = t
else
tmp = x * -(t / y)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (x <= -1.22e+117) {
tmp = t * (-x / y);
} else if (x <= 2.3e+131) {
tmp = t;
} else {
tmp = x * -(t / y);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if x <= -1.22e+117: tmp = t * (-x / y) elif x <= 2.3e+131: tmp = t else: tmp = x * -(t / y) return tmp
function code(x, y, z, t) tmp = 0.0 if (x <= -1.22e+117) tmp = Float64(t * Float64(Float64(-x) / y)); elseif (x <= 2.3e+131) tmp = t; else tmp = Float64(x * Float64(-Float64(t / y))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (x <= -1.22e+117) tmp = t * (-x / y); elseif (x <= 2.3e+131) tmp = t; else tmp = x * -(t / y); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[x, -1.22e+117], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+131], t, N[(x * (-N[(t / y), $MachinePrecision])), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.22 \cdot 10^{+117}:\\
\;\;\;\;t \cdot \frac{-x}{y}\\
\mathbf{elif}\;x \leq 2.3 \cdot 10^{+131}:\\
\;\;\;\;t\\
\mathbf{else}:\\
\;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (+ t (* (- z t) (/ x y))))
double code(double x, double y, double z, double t) {
return t + ((z - t) * (x / 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 = t + ((z - t) * (x / y))
end function
public static double code(double x, double y, double z, double t) {
return t + ((z - t) * (x / y));
}
def code(x, y, z, t): return t + ((z - t) * (x / y))
function code(x, y, z, t) return Float64(t + Float64(Float64(z - t) * Float64(x / y))) end
function tmp = code(x, y, z, t) tmp = t + ((z - t) * (x / y)); end
code[x_, y_, z_, t_] := N[(t + N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
t + \left(z - t\right) \cdot \frac{x}{y}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= x -6.1e+187) (* x (/ t y)) t))
double code(double x, double y, double z, double t) {
double tmp;
if (x <= -6.1e+187) {
tmp = x * (t / y);
} else {
tmp = 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 (x <= (-6.1d+187)) then
tmp = x * (t / y)
else
tmp = t
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (x <= -6.1e+187) {
tmp = x * (t / y);
} else {
tmp = t;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if x <= -6.1e+187: tmp = x * (t / y) else: tmp = t return tmp
function code(x, y, z, t) tmp = 0.0 if (x <= -6.1e+187) tmp = Float64(x * Float64(t / y)); else tmp = t; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (x <= -6.1e+187) tmp = x * (t / y); else tmp = t; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[x, -6.1e+187], N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision], t]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -6.1 \cdot 10^{+187}:\\
\;\;\;\;x \cdot \frac{t}{y}\\
\mathbf{else}:\\
\;\;\;\;t\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= x -3.45e+165) (/ t (/ y x)) t))
double code(double x, double y, double z, double t) {
double tmp;
if (x <= -3.45e+165) {
tmp = t / (y / x);
} else {
tmp = 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 (x <= (-3.45d+165)) then
tmp = t / (y / x)
else
tmp = t
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (x <= -3.45e+165) {
tmp = t / (y / x);
} else {
tmp = t;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if x <= -3.45e+165: tmp = t / (y / x) else: tmp = t return tmp
function code(x, y, z, t) tmp = 0.0 if (x <= -3.45e+165) tmp = Float64(t / Float64(y / x)); else tmp = t; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (x <= -3.45e+165) tmp = t / (y / x); else tmp = t; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[x, -3.45e+165], N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision], t]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.45 \cdot 10^{+165}:\\
\;\;\;\;\frac{t}{\frac{y}{x}}\\
\mathbf{else}:\\
\;\;\;\;t\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (* t (- 1.0 (/ x y))))
double code(double x, double y, double z, double t) {
return t * (1.0 - (x / 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 = t * (1.0d0 - (x / y))
end function
public static double code(double x, double y, double z, double t) {
return t * (1.0 - (x / y));
}
def code(x, y, z, t): return t * (1.0 - (x / y))
function code(x, y, z, t) return Float64(t * Float64(1.0 - Float64(x / y))) end
function tmp = code(x, y, z, t) tmp = t * (1.0 - (x / y)); end
code[x_, y_, z_, t_] := N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
t \cdot \left(1 - \frac{x}{y}\right)
\end{array}
(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}
(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$1]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\
\mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
\end{array}
herbie shell --seed 2023347
(FPCore (x y z t)
:name "Numeric.Signal.Multichannel:$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))