
(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
double code(double x, double y, double z) {
return (x * (y - z)) / y;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x * (y - z)) / y
end function
public static double code(double x, double y, double z) {
return (x * (y - z)) / y;
}
def code(x, y, z): return (x * (y - z)) / y
function code(x, y, z) return Float64(Float64(x * Float64(y - z)) / y) end
function tmp = code(x, y, z) tmp = (x * (y - z)) / y; end
code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]
\begin{array}{l}
\\
\frac{x \cdot \left(y - z\right)}{y}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 6 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
double code(double x, double y, double z) {
return (x * (y - z)) / y;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x * (y - z)) / y
end function
public static double code(double x, double y, double z) {
return (x * (y - z)) / y;
}
def code(x, y, z): return (x * (y - z)) / y
function code(x, y, z) return Float64(Float64(x * Float64(y - z)) / y) end
function tmp = code(x, y, z) tmp = (x * (y - z)) / y; end
code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]
\begin{array}{l}
\\
\frac{x \cdot \left(y - z\right)}{y}
\end{array}
(FPCore (x y z) :precision binary64 (* x (/ (- y z) y)))
double code(double x, double y, double z) {
return x * ((y - z) / y);
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = x * ((y - z) / y)
end function
public static double code(double x, double y, double z) {
return x * ((y - z) / y);
}
def code(x, y, z): return x * ((y - z) / y)
function code(x, y, z) return Float64(x * Float64(Float64(y - z) / y)) end
function tmp = code(x, y, z) tmp = x * ((y - z) / y); end
code[x_, y_, z_] := N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \frac{y - z}{y}
\end{array}
Initial program 84.6%
associate-*r/95.8%
Simplified95.8%
Final simplification95.8%
(FPCore (x y z)
:precision binary64
(let* ((t_0 (* (- x) (/ z y))))
(if (<= z -4.2e-14)
t_0
(if (<= z -7e-133)
(* y (/ x y))
(if (or (<= z -1.05e-188) (not (<= z 210000000.0))) t_0 x)))))
double code(double x, double y, double z) {
double t_0 = -x * (z / y);
double tmp;
if (z <= -4.2e-14) {
tmp = t_0;
} else if (z <= -7e-133) {
tmp = y * (x / y);
} else if ((z <= -1.05e-188) || !(z <= 210000000.0)) {
tmp = t_0;
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: t_0
real(8) :: tmp
t_0 = -x * (z / y)
if (z <= (-4.2d-14)) then
tmp = t_0
else if (z <= (-7d-133)) then
tmp = y * (x / y)
else if ((z <= (-1.05d-188)) .or. (.not. (z <= 210000000.0d0))) then
tmp = t_0
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = -x * (z / y);
double tmp;
if (z <= -4.2e-14) {
tmp = t_0;
} else if (z <= -7e-133) {
tmp = y * (x / y);
} else if ((z <= -1.05e-188) || !(z <= 210000000.0)) {
tmp = t_0;
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): t_0 = -x * (z / y) tmp = 0 if z <= -4.2e-14: tmp = t_0 elif z <= -7e-133: tmp = y * (x / y) elif (z <= -1.05e-188) or not (z <= 210000000.0): tmp = t_0 else: tmp = x return tmp
function code(x, y, z) t_0 = Float64(Float64(-x) * Float64(z / y)) tmp = 0.0 if (z <= -4.2e-14) tmp = t_0; elseif (z <= -7e-133) tmp = Float64(y * Float64(x / y)); elseif ((z <= -1.05e-188) || !(z <= 210000000.0)) tmp = t_0; else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) t_0 = -x * (z / y); tmp = 0.0; if (z <= -4.2e-14) tmp = t_0; elseif (z <= -7e-133) tmp = y * (x / y); elseif ((z <= -1.05e-188) || ~((z <= 210000000.0))) tmp = t_0; else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-14], t$95$0, If[LessEqual[z, -7e-133], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.05e-188], N[Not[LessEqual[z, 210000000.0]], $MachinePrecision]], t$95$0, x]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \left(-x\right) \cdot \frac{z}{y}\\
\mathbf{if}\;z \leq -4.2 \cdot 10^{-14}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq -7 \cdot 10^{-133}:\\
\;\;\;\;y \cdot \frac{x}{y}\\
\mathbf{elif}\;z \leq -1.05 \cdot 10^{-188} \lor \neg \left(z \leq 210000000\right):\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if z < -4.1999999999999998e-14 or -7.00000000000000006e-133 < z < -1.05e-188 or 2.1e8 < z Initial program 88.2%
associate-*r/92.4%
Simplified92.4%
Taylor expanded in y around 0 71.9%
neg-mul-171.9%
distribute-neg-frac71.9%
Simplified71.9%
if -4.1999999999999998e-14 < z < -7.00000000000000006e-133Initial program 90.9%
Taylor expanded in y around inf 53.5%
associate-/l*62.5%
associate-/r/75.8%
Applied egg-rr75.8%
if -1.05e-188 < z < 2.1e8Initial program 78.2%
associate-*r/99.9%
Simplified99.9%
Taylor expanded in y around inf 78.9%
Final simplification74.9%
(FPCore (x y z) :precision binary64 (if (or (<= z -3.5e-14) (not (<= z 63000.0))) (* z (/ (- x) y)) x))
double code(double x, double y, double z) {
double tmp;
if ((z <= -3.5e-14) || !(z <= 63000.0)) {
tmp = z * (-x / y);
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if ((z <= (-3.5d-14)) .or. (.not. (z <= 63000.0d0))) then
tmp = z * (-x / y)
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((z <= -3.5e-14) || !(z <= 63000.0)) {
tmp = z * (-x / y);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (z <= -3.5e-14) or not (z <= 63000.0): tmp = z * (-x / y) else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if ((z <= -3.5e-14) || !(z <= 63000.0)) tmp = Float64(z * Float64(Float64(-x) / y)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((z <= -3.5e-14) || ~((z <= 63000.0))) tmp = z * (-x / y); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e-14], N[Not[LessEqual[z, 63000.0]], $MachinePrecision]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -3.5 \cdot 10^{-14} \lor \neg \left(z \leq 63000\right):\\
\;\;\;\;z \cdot \frac{-x}{y}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if z < -3.5000000000000002e-14 or 63000 < z Initial program 88.2%
associate-*r/91.9%
Simplified91.9%
Taylor expanded in y around 0 77.3%
mul-1-neg77.3%
associate-*l/75.9%
distribute-lft-neg-in75.9%
*-commutative75.9%
distribute-neg-frac75.9%
Simplified75.9%
if -3.5000000000000002e-14 < z < 63000Initial program 80.9%
associate-*r/99.9%
Simplified99.9%
Taylor expanded in y around inf 73.7%
Final simplification74.8%
(FPCore (x y z) :precision binary64 (if (or (<= z -1.9e-14) (not (<= z 250000000.0))) (/ (* x (- z)) y) x))
double code(double x, double y, double z) {
double tmp;
if ((z <= -1.9e-14) || !(z <= 250000000.0)) {
tmp = (x * -z) / y;
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if ((z <= (-1.9d-14)) .or. (.not. (z <= 250000000.0d0))) then
tmp = (x * -z) / y
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((z <= -1.9e-14) || !(z <= 250000000.0)) {
tmp = (x * -z) / y;
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (z <= -1.9e-14) or not (z <= 250000000.0): tmp = (x * -z) / y else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if ((z <= -1.9e-14) || !(z <= 250000000.0)) tmp = Float64(Float64(x * Float64(-z)) / y); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((z <= -1.9e-14) || ~((z <= 250000000.0))) tmp = (x * -z) / y; else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e-14], N[Not[LessEqual[z, 250000000.0]], $MachinePrecision]], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -1.9 \cdot 10^{-14} \lor \neg \left(z \leq 250000000\right):\\
\;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if z < -1.9000000000000001e-14 or 2.5e8 < z Initial program 88.2%
associate-*r/91.9%
Simplified91.9%
Taylor expanded in y around 0 77.3%
associate-*r/77.3%
mul-1-neg77.3%
distribute-rgt-neg-out77.3%
Simplified77.3%
if -1.9000000000000001e-14 < z < 2.5e8Initial program 80.9%
associate-*r/99.9%
Simplified99.9%
Taylor expanded in y around inf 73.7%
Final simplification75.5%
(FPCore (x y z) :precision binary64 (if (<= x -2.4e+107) (* y (/ x y)) x))
double code(double x, double y, double z) {
double tmp;
if (x <= -2.4e+107) {
tmp = y * (x / y);
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (x <= (-2.4d+107)) then
tmp = y * (x / y)
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -2.4e+107) {
tmp = y * (x / y);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -2.4e+107: tmp = y * (x / y) else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if (x <= -2.4e+107) tmp = Float64(y * Float64(x / y)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -2.4e+107) tmp = y * (x / y); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -2.4e+107], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.4 \cdot 10^{+107}:\\
\;\;\;\;y \cdot \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if x < -2.4000000000000001e107Initial program 80.6%
Taylor expanded in y around inf 23.8%
associate-/l*36.8%
associate-/r/54.5%
Applied egg-rr54.5%
if -2.4000000000000001e107 < x Initial program 85.6%
associate-*r/94.9%
Simplified94.9%
Taylor expanded in y around inf 48.5%
Final simplification49.6%
(FPCore (x y z) :precision binary64 x)
double code(double x, double y, double z) {
return x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = x
end function
public static double code(double x, double y, double z) {
return x;
}
def code(x, y, z): return x
function code(x, y, z) return x end
function tmp = code(x, y, z) tmp = x; end
code[x_, y_, z_] := x
\begin{array}{l}
\\
x
\end{array}
Initial program 84.6%
associate-*r/95.8%
Simplified95.8%
Taylor expanded in y around inf 46.3%
Final simplification46.3%
(FPCore (x y z) :precision binary64 (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))
double code(double x, double y, double z) {
double tmp;
if (z < -2.060202331921739e+104) {
tmp = x - ((z * x) / y);
} else if (z < 1.6939766013828526e+213) {
tmp = x / (y / (y - z));
} else {
tmp = (y - z) * (x / y);
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (z < (-2.060202331921739d+104)) then
tmp = x - ((z * x) / y)
else if (z < 1.6939766013828526d+213) then
tmp = x / (y / (y - z))
else
tmp = (y - z) * (x / y)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (z < -2.060202331921739e+104) {
tmp = x - ((z * x) / y);
} else if (z < 1.6939766013828526e+213) {
tmp = x / (y / (y - z));
} else {
tmp = (y - z) * (x / y);
}
return tmp;
}
def code(x, y, z): tmp = 0 if z < -2.060202331921739e+104: tmp = x - ((z * x) / y) elif z < 1.6939766013828526e+213: tmp = x / (y / (y - z)) else: tmp = (y - z) * (x / y) return tmp
function code(x, y, z) tmp = 0.0 if (z < -2.060202331921739e+104) tmp = Float64(x - Float64(Float64(z * x) / y)); elseif (z < 1.6939766013828526e+213) tmp = Float64(x / Float64(y / Float64(y - z))); else tmp = Float64(Float64(y - z) * Float64(x / y)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (z < -2.060202331921739e+104) tmp = x - ((z * x) / y); elseif (z < 1.6939766013828526e+213) tmp = x / (y / (y - z)); else tmp = (y - z) * (x / y); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\
\;\;\;\;x - \frac{z \cdot x}{y}\\
\mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\
\mathbf{else}:\\
\;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\
\end{array}
\end{array}
herbie shell --seed 2023297
(FPCore (x y z)
:name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
:precision binary64
:herbie-target
(if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))
(/ (* x (- y z)) y))