
(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 98.4%
fma-def98.4%
Simplified98.4%
Final simplification98.4%
(FPCore (x y z t) :precision binary64 (if (<= z -1.05e-25) (+ t (* (/ x y) z)) (if (<= z 4.8e-125) (- t (* (/ x y) t)) (+ t (/ z (/ y x))))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -1.05e-25) {
tmp = t + ((x / y) * z);
} else if (z <= 4.8e-125) {
tmp = t - ((x / y) * t);
} 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 (z <= (-1.05d-25)) then
tmp = t + ((x / y) * z)
else if (z <= 4.8d-125) then
tmp = t - ((x / y) * t)
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 (z <= -1.05e-25) {
tmp = t + ((x / y) * z);
} else if (z <= 4.8e-125) {
tmp = t - ((x / y) * t);
} else {
tmp = t + (z / (y / x));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -1.05e-25: tmp = t + ((x / y) * z) elif z <= 4.8e-125: tmp = t - ((x / y) * t) else: tmp = t + (z / (y / x)) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -1.05e-25) tmp = Float64(t + Float64(Float64(x / y) * z)); elseif (z <= 4.8e-125) tmp = Float64(t - Float64(Float64(x / y) * t)); 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 (z <= -1.05e-25) tmp = t + ((x / y) * z); elseif (z <= 4.8e-125) tmp = t - ((x / y) * t); else tmp = t + (z / (y / x)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e-25], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-125], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -1.05 \cdot 10^{-25}:\\
\;\;\;\;t + \frac{x}{y} \cdot z\\
\mathbf{elif}\;z \leq 4.8 \cdot 10^{-125}:\\
\;\;\;\;t - \frac{x}{y} \cdot t\\
\mathbf{else}:\\
\;\;\;\;t + \frac{z}{\frac{y}{x}}\\
\end{array}
\end{array}
if z < -1.05000000000000001e-25Initial program 98.4%
Taylor expanded in z around inf 85.0%
associate-*r/90.6%
Simplified90.6%
if -1.05000000000000001e-25 < z < 4.8000000000000003e-125Initial program 98.0%
Taylor expanded in z around 0 88.9%
mul-1-neg88.9%
unsub-neg88.9%
associate-*r/91.2%
Simplified91.2%
if 4.8000000000000003e-125 < z Initial program 98.9%
Taylor expanded in z around inf 86.0%
associate-/l*90.3%
Simplified90.3%
Final simplification90.7%
(FPCore (x y z t) :precision binary64 (if (<= z -1.25e-25) (+ t (* (/ x y) z)) (if (<= z 2e-122) (- t (/ t (/ y x))) (+ t (/ z (/ y x))))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -1.25e-25) {
tmp = t + ((x / y) * z);
} else if (z <= 2e-122) {
tmp = t - (t / (y / x));
} 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 (z <= (-1.25d-25)) then
tmp = t + ((x / y) * z)
else if (z <= 2d-122) then
tmp = t - (t / (y / x))
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 (z <= -1.25e-25) {
tmp = t + ((x / y) * z);
} else if (z <= 2e-122) {
tmp = t - (t / (y / x));
} else {
tmp = t + (z / (y / x));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -1.25e-25: tmp = t + ((x / y) * z) elif z <= 2e-122: tmp = t - (t / (y / x)) else: tmp = t + (z / (y / x)) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -1.25e-25) tmp = Float64(t + Float64(Float64(x / y) * z)); elseif (z <= 2e-122) tmp = Float64(t - Float64(t / Float64(y / x))); 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 (z <= -1.25e-25) tmp = t + ((x / y) * z); elseif (z <= 2e-122) tmp = t - (t / (y / x)); else tmp = t + (z / (y / x)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e-25], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-122], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -1.25 \cdot 10^{-25}:\\
\;\;\;\;t + \frac{x}{y} \cdot z\\
\mathbf{elif}\;z \leq 2 \cdot 10^{-122}:\\
\;\;\;\;t - \frac{t}{\frac{y}{x}}\\
\mathbf{else}:\\
\;\;\;\;t + \frac{z}{\frac{y}{x}}\\
\end{array}
\end{array}
if z < -1.2499999999999999e-25Initial program 98.4%
Taylor expanded in z around inf 85.0%
associate-*r/90.6%
Simplified90.6%
if -1.2499999999999999e-25 < z < 2.00000000000000012e-122Initial program 98.0%
Taylor expanded in z around 0 88.9%
mul-1-neg88.9%
unsub-neg88.9%
associate-/l*91.3%
associate-/r/87.6%
Simplified87.6%
associate-*l/88.9%
associate-/l*91.3%
Applied egg-rr91.3%
if 2.00000000000000012e-122 < z Initial program 98.9%
Taylor expanded in z around inf 86.0%
associate-/l*90.3%
Simplified90.3%
Final simplification90.8%
(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 98.4%
Final simplification98.4%
(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 98.4%
Taylor expanded in z around inf 73.6%
associate-*r/78.4%
Simplified78.4%
Final simplification78.4%
(FPCore (x y z t) :precision binary64 (+ t (/ z (/ y x))))
double code(double x, double y, double z, double t) {
return t + (z / (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 / (y / x))
end function
public static double code(double x, double y, double z, double t) {
return t + (z / (y / x));
}
def code(x, y, z, t): return t + (z / (y / x))
function code(x, y, z, t) return Float64(t + Float64(z / Float64(y / x))) end
function tmp = code(x, y, z, t) tmp = t + (z / (y / x)); end
code[x_, y_, z_, t_] := N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
t + \frac{z}{\frac{y}{x}}
\end{array}
Initial program 98.4%
Taylor expanded in z around inf 73.6%
associate-/l*78.4%
Simplified78.4%
Final simplification78.4%
(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 98.4%
Taylor expanded in x around 0 37.8%
Final simplification37.8%
(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$1]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\
\mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
\end{array}
herbie shell --seed 2023268
(FPCore (x y z t)
:name "Numeric.Signal.Multichannel:$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))