
(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 6 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 97.6%
fma-def97.6%
Simplified97.6%
Final simplification97.6%
(FPCore (x y z t) :precision binary64 (if (or (<= z -0.001) (not (<= z 4e-58))) (+ t (* (/ x y) z)) (* t (- 1.0 (/ x y)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -0.001) || !(z <= 4e-58)) {
tmp = t + ((x / y) * z);
} 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 <= (-0.001d0)) .or. (.not. (z <= 4d-58))) then
tmp = t + ((x / y) * z)
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 <= -0.001) || !(z <= 4e-58)) {
tmp = t + ((x / y) * z);
} else {
tmp = t * (1.0 - (x / y));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -0.001) or not (z <= 4e-58): tmp = t + ((x / y) * z) else: tmp = t * (1.0 - (x / y)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -0.001) || !(z <= 4e-58)) tmp = Float64(t + Float64(Float64(x / y) * z)); 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 <= -0.001) || ~((z <= 4e-58))) tmp = t + ((x / y) * z); else tmp = t * (1.0 - (x / y)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.001], N[Not[LessEqual[z, 4e-58]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.001 \lor \neg \left(z \leq 4 \cdot 10^{-58}\right):\\
\;\;\;\;t + \frac{x}{y} \cdot z\\
\mathbf{else}:\\
\;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\
\end{array}
\end{array}
if z < -1e-3 or 4.0000000000000001e-58 < z Initial program 99.0%
Taylor expanded in z around inf 86.8%
associate-/l*87.2%
associate-/r/91.0%
Applied egg-rr91.0%
if -1e-3 < z < 4.0000000000000001e-58Initial program 96.2%
fma-def96.2%
Simplified96.2%
Taylor expanded in z around 0 86.4%
mul-1-neg86.4%
unsub-neg86.4%
*-rgt-identity86.4%
associate-*r/88.2%
distribute-lft-out--88.2%
Simplified88.2%
Final simplification89.6%
(FPCore (x y z t) :precision binary64 (if (<= z -0.395) (+ t (/ z (/ y x))) (if (<= z 4.1e-58) (* t (- 1.0 (/ x y))) (+ t (* (/ x y) z)))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -0.395) {
tmp = t + (z / (y / x));
} else if (z <= 4.1e-58) {
tmp = t * (1.0 - (x / y));
} else {
tmp = t + ((x / y) * z);
}
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 <= (-0.395d0)) then
tmp = t + (z / (y / x))
else if (z <= 4.1d-58) then
tmp = t * (1.0d0 - (x / y))
else
tmp = t + ((x / y) * z)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (z <= -0.395) {
tmp = t + (z / (y / x));
} else if (z <= 4.1e-58) {
tmp = t * (1.0 - (x / y));
} else {
tmp = t + ((x / y) * z);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -0.395: tmp = t + (z / (y / x)) elif z <= 4.1e-58: tmp = t * (1.0 - (x / y)) else: tmp = t + ((x / y) * z) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -0.395) tmp = Float64(t + Float64(z / Float64(y / x))); elseif (z <= 4.1e-58) tmp = Float64(t * Float64(1.0 - Float64(x / y))); else tmp = Float64(t + Float64(Float64(x / y) * z)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (z <= -0.395) tmp = t + (z / (y / x)); elseif (z <= 4.1e-58) tmp = t * (1.0 - (x / y)); else tmp = t + ((x / y) * z); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -0.395], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-58], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.395:\\
\;\;\;\;t + \frac{z}{\frac{y}{x}}\\
\mathbf{elif}\;z \leq 4.1 \cdot 10^{-58}:\\
\;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\
\mathbf{else}:\\
\;\;\;\;t + \frac{x}{y} \cdot z\\
\end{array}
\end{array}
if z < -0.39500000000000002Initial program 98.1%
Taylor expanded in z around inf 90.1%
*-commutative90.1%
associate-*l/91.7%
Simplified91.7%
associate-/r/94.9%
Applied egg-rr94.9%
if -0.39500000000000002 < z < 4.10000000000000028e-58Initial program 96.2%
fma-def96.2%
Simplified96.2%
Taylor expanded in z around 0 86.4%
mul-1-neg86.4%
unsub-neg86.4%
*-rgt-identity86.4%
associate-*r/88.2%
distribute-lft-out--88.2%
Simplified88.2%
if 4.10000000000000028e-58 < z Initial program 99.7%
Taylor expanded in z around inf 84.3%
associate-/l*85.0%
associate-/r/87.9%
Applied egg-rr87.9%
Final simplification89.6%
(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 97.6%
Final simplification97.6%
(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}
Initial program 97.6%
fma-def97.6%
Simplified97.6%
Taylor expanded in z around 0 64.7%
mul-1-neg64.7%
unsub-neg64.7%
*-rgt-identity64.7%
associate-*r/67.8%
distribute-lft-out--67.8%
Simplified67.8%
Final simplification67.8%
(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 97.6%
fma-def97.6%
Simplified97.6%
Taylor expanded in x around 0 38.9%
Final simplification38.9%
(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$1]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\
\mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
\end{array}
herbie shell --seed 2024024
(FPCore (x y z t)
:name "Numeric.Signal.Multichannel:$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))