
(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 (+ (* (/ 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}
Initial program 96.6%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (* (/ x y) (- z t))))
(if (<= (/ x y) -8.8e-14)
t_1
(if (<= (/ x y) 3.8e-105) (+ (/ x y) t) t_1))))
double code(double x, double y, double z, double t) {
double t_1 = (x / y) * (z - t);
double tmp;
if ((x / y) <= -8.8e-14) {
tmp = t_1;
} else if ((x / y) <= 3.8e-105) {
tmp = (x / 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)
if ((x / y) <= (-8.8d-14)) then
tmp = t_1
else if ((x / y) <= 3.8d-105) then
tmp = (x / 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);
double tmp;
if ((x / y) <= -8.8e-14) {
tmp = t_1;
} else if ((x / y) <= 3.8e-105) {
tmp = (x / y) + t;
} else {
tmp = t_1;
}
return tmp;
}
def code(x, y, z, t): t_1 = (x / y) * (z - t) tmp = 0 if (x / y) <= -8.8e-14: tmp = t_1 elif (x / y) <= 3.8e-105: tmp = (x / y) + t else: tmp = t_1 return tmp
function code(x, y, z, t) t_1 = Float64(Float64(x / y) * Float64(z - t)) tmp = 0.0 if (Float64(x / y) <= -8.8e-14) tmp = t_1; elseif (Float64(x / y) <= 3.8e-105) tmp = Float64(Float64(x / y) + t); else tmp = t_1; end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (x / y) * (z - t); tmp = 0.0; if ((x / y) <= -8.8e-14) tmp = t_1; elseif ((x / y) <= 3.8e-105) tmp = (x / y) + t; else tmp = t_1; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -8.8e-14], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 3.8e-105], N[(N[(x / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x}{y} \cdot \left(z - t\right)\\
\mathbf{if}\;\frac{x}{y} \leq -8.8 \cdot 10^{-14}:\\
\;\;\;\;t\_1\\
\mathbf{elif}\;\frac{x}{y} \leq 3.8 \cdot 10^{-105}:\\
\;\;\;\;\frac{x}{y} + t\\
\mathbf{else}:\\
\;\;\;\;t\_1\\
\end{array}
\end{array}
if (/.f64 x y) < -8.8000000000000004e-14 or 3.7999999999999998e-105 < (/.f64 x y) Initial program 95.5%
Taylor expanded in x around 0
Applied rewrites89.8%
if -8.8000000000000004e-14 < (/.f64 x y) < 3.7999999999999998e-105Initial program 98.2%
Taylor expanded in x around 0
Applied rewrites82.1%
(FPCore (x y z t) :precision binary64 (if (<= (+ (* (/ x y) (- z t)) t) 5e+301) (+ (/ x y) t) (+ (* (- z t) (- z t)) t)))
double code(double x, double y, double z, double t) {
double tmp;
if ((((x / y) * (z - t)) + t) <= 5e+301) {
tmp = (x / y) + t;
} else {
tmp = ((z - t) * (z - t)) + 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 / y) * (z - t)) + t) <= 5d+301) then
tmp = (x / y) + t
else
tmp = ((z - t) * (z - t)) + t
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((((x / y) * (z - t)) + t) <= 5e+301) {
tmp = (x / y) + t;
} else {
tmp = ((z - t) * (z - t)) + t;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (((x / y) * (z - t)) + t) <= 5e+301: tmp = (x / y) + t else: tmp = ((z - t) * (z - t)) + t return tmp
function code(x, y, z, t) tmp = 0.0 if (Float64(Float64(Float64(x / y) * Float64(z - t)) + t) <= 5e+301) tmp = Float64(Float64(x / y) + t); else tmp = Float64(Float64(Float64(z - t) * Float64(z - t)) + t); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((((x / y) * (z - t)) + t) <= 5e+301) tmp = (x / y) + t; else tmp = ((z - t) * (z - t)) + t; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], 5e+301], N[(N[(x / y), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \cdot \left(z - t\right) + t \leq 5 \cdot 10^{+301}:\\
\;\;\;\;\frac{x}{y} + t\\
\mathbf{else}:\\
\;\;\;\;\left(z - t\right) \cdot \left(z - t\right) + t\\
\end{array}
\end{array}
if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 5.0000000000000004e301Initial program 96.8%
Taylor expanded in x around 0
Applied rewrites47.6%
if 5.0000000000000004e301 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) Initial program 95.8%
Taylor expanded in x around 0
Applied rewrites58.1%
(FPCore (x y z t) :precision binary64 (if (<= (+ (* (/ x y) (- z t)) t) 5e+301) (+ (/ x y) t) (* (- z t) (- z t))))
double code(double x, double y, double z, double t) {
double tmp;
if ((((x / y) * (z - t)) + t) <= 5e+301) {
tmp = (x / y) + t;
} else {
tmp = (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) :: tmp
if ((((x / y) * (z - t)) + t) <= 5d+301) then
tmp = (x / y) + t
else
tmp = (z - t) * (z - t)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((((x / y) * (z - t)) + t) <= 5e+301) {
tmp = (x / y) + t;
} else {
tmp = (z - t) * (z - t);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (((x / y) * (z - t)) + t) <= 5e+301: tmp = (x / y) + t else: tmp = (z - t) * (z - t) return tmp
function code(x, y, z, t) tmp = 0.0 if (Float64(Float64(Float64(x / y) * Float64(z - t)) + t) <= 5e+301) tmp = Float64(Float64(x / y) + t); else tmp = Float64(Float64(z - t) * Float64(z - t)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((((x / y) * (z - t)) + t) <= 5e+301) tmp = (x / y) + t; else tmp = (z - t) * (z - t); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], 5e+301], N[(N[(x / y), $MachinePrecision] + t), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \cdot \left(z - t\right) + t \leq 5 \cdot 10^{+301}:\\
\;\;\;\;\frac{x}{y} + t\\
\mathbf{else}:\\
\;\;\;\;\left(z - t\right) \cdot \left(z - t\right)\\
\end{array}
\end{array}
if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 5.0000000000000004e301Initial program 96.8%
Taylor expanded in x around 0
Applied rewrites47.6%
if 5.0000000000000004e301 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) Initial program 95.8%
Taylor expanded in x around 0
Applied rewrites95.8%
Taylor expanded in x around 0
Applied rewrites58.0%
(FPCore (x y z t) :precision binary64 (if (<= (+ (* (/ x y) (- z t)) t) 1e-149) (/ x y) (* (- z t) (- z t))))
double code(double x, double y, double z, double t) {
double tmp;
if ((((x / y) * (z - t)) + t) <= 1e-149) {
tmp = x / y;
} else {
tmp = (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) :: tmp
if ((((x / y) * (z - t)) + t) <= 1d-149) then
tmp = x / y
else
tmp = (z - t) * (z - t)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((((x / y) * (z - t)) + t) <= 1e-149) {
tmp = x / y;
} else {
tmp = (z - t) * (z - t);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (((x / y) * (z - t)) + t) <= 1e-149: tmp = x / y else: tmp = (z - t) * (z - t) return tmp
function code(x, y, z, t) tmp = 0.0 if (Float64(Float64(Float64(x / y) * Float64(z - t)) + t) <= 1e-149) tmp = Float64(x / y); else tmp = Float64(Float64(z - t) * Float64(z - t)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((((x / y) * (z - t)) + t) <= 1e-149) tmp = x / y; else tmp = (z - t) * (z - t); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], 1e-149], N[(x / y), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \cdot \left(z - t\right) + t \leq 10^{-149}:\\
\;\;\;\;\frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;\left(z - t\right) \cdot \left(z - t\right)\\
\end{array}
\end{array}
if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 9.99999999999999979e-150Initial program 95.0%
Taylor expanded in x around 0
Applied rewrites56.8%
Taylor expanded in x around 0
Applied rewrites6.8%
if 9.99999999999999979e-150 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) Initial program 98.4%
Taylor expanded in x around 0
Applied rewrites61.5%
Taylor expanded in x around 0
Applied rewrites24.0%
(FPCore (x y z t) :precision binary64 (/ x y))
double code(double x, double y, double z, double t) {
return 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 = x / y
end function
public static double code(double x, double y, double z, double t) {
return x / y;
}
def code(x, y, z, t): return x / y
function code(x, y, z, t) return Float64(x / y) end
function tmp = code(x, y, z, t) tmp = x / y; end
code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{y}
\end{array}
Initial program 96.6%
Taylor expanded in x around 0
Applied rewrites59.1%
Taylor expanded in x around 0
Applied rewrites9.5%
(FPCore (x y z t) :precision binary64 (- z t))
double code(double x, double y, double z, double t) {
return 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 = z - t
end function
public static double code(double x, double y, double z, double t) {
return z - t;
}
def code(x, y, z, t): return z - t
function code(x, y, z, t) return Float64(z - t) end
function tmp = code(x, y, z, t) tmp = z - t; end
code[x_, y_, z_, t_] := N[(z - t), $MachinePrecision]
\begin{array}{l}
\\
z - t
\end{array}
Initial program 96.6%
Taylor expanded in x around 0
Applied rewrites59.1%
Taylor expanded in y around inf
Applied rewrites3.2%
(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$1]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\
\mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\
\;\;\;\;t\_1\\
\mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\
\mathbf{else}:\\
\;\;\;\;t\_1\\
\end{array}
\end{array}
herbie shell --seed 2024313
(FPCore (x y z t)
:name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
:precision binary64
:alt
(! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))
(+ (* (/ x y) (- z t)) t))