
(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 (* x (/ z y))))
double code(double x, double y, double z) {
return x - (x * (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 - (x * (z / y))
end function
public static double code(double x, double y, double z) {
return x - (x * (z / y));
}
def code(x, y, z): return x - (x * (z / y))
function code(x, y, z) return Float64(x - Float64(x * Float64(z / y))) end
function tmp = code(x, y, z) tmp = x - (x * (z / y)); end
code[x_, y_, z_] := N[(x - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - x \cdot \frac{z}{y}
\end{array}
Initial program 84.6%
associate-*r/96.6%
div-sub96.6%
*-inverses96.6%
Simplified96.6%
sub-neg96.6%
distribute-rgt-in96.6%
*-un-lft-identity96.6%
+-commutative96.6%
distribute-neg-frac96.6%
Applied egg-rr96.6%
Taylor expanded in z around 0 94.2%
metadata-eval94.2%
associate-*l/94.8%
*-commutative94.8%
cancel-sign-sub-inv94.8%
*-lft-identity94.8%
*-commutative94.8%
associate-*l/94.2%
associate-*r/96.6%
Simplified96.6%
Final simplification96.6%
(FPCore (x y z) :precision binary64 (if (or (<= z -2.2e-17) (not (<= z 4.2e+25))) (* (- z) (/ x y)) x))
double code(double x, double y, double z) {
double tmp;
if ((z <= -2.2e-17) || !(z <= 4.2e+25)) {
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 <= (-2.2d-17)) .or. (.not. (z <= 4.2d+25))) 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 <= -2.2e-17) || !(z <= 4.2e+25)) {
tmp = -z * (x / y);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (z <= -2.2e-17) or not (z <= 4.2e+25): tmp = -z * (x / y) else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if ((z <= -2.2e-17) || !(z <= 4.2e+25)) tmp = Float64(Float64(-z) * Float64(x / y)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((z <= -2.2e-17) || ~((z <= 4.2e+25))) tmp = -z * (x / y); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e-17], N[Not[LessEqual[z, 4.2e+25]], $MachinePrecision]], N[((-z) * N[(x / y), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -2.2 \cdot 10^{-17} \lor \neg \left(z \leq 4.2 \cdot 10^{+25}\right):\\
\;\;\;\;\left(-z\right) \cdot \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if z < -2.2e-17 or 4.1999999999999998e25 < z Initial program 86.5%
associate-*r/93.2%
div-sub93.2%
*-inverses93.2%
Simplified93.2%
Taylor expanded in z around inf 72.0%
*-commutative72.0%
associate-*r/72.7%
mul-1-neg72.7%
distribute-lft-neg-in72.7%
Simplified72.7%
if -2.2e-17 < z < 4.1999999999999998e25Initial program 82.8%
associate-*r/99.8%
div-sub99.9%
*-inverses99.9%
Simplified99.9%
Taylor expanded in z around 0 82.6%
Final simplification77.7%
(FPCore (x y z) :precision binary64 (if (<= x 2e+67) x (* y (/ x y))))
double code(double x, double y, double z) {
double tmp;
if (x <= 2e+67) {
tmp = x;
} else {
tmp = y * (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 (x <= 2d+67) then
tmp = x
else
tmp = y * (x / y)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= 2e+67) {
tmp = x;
} else {
tmp = y * (x / y);
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= 2e+67: tmp = x else: tmp = y * (x / y) return tmp
function code(x, y, z) tmp = 0.0 if (x <= 2e+67) tmp = x; else tmp = Float64(y * Float64(x / y)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= 2e+67) tmp = x; else tmp = y * (x / y); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, 2e+67], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq 2 \cdot 10^{+67}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{y}\\
\end{array}
\end{array}
if x < 1.99999999999999997e67Initial program 87.4%
associate-*r/95.7%
div-sub95.7%
*-inverses95.7%
Simplified95.7%
Taylor expanded in z around 0 55.4%
if 1.99999999999999997e67 < x Initial program 74.7%
Taylor expanded in y around inf 26.6%
associate-/l*46.9%
associate-/r/55.7%
Applied egg-rr55.7%
Final simplification55.5%
(FPCore (x y z) :precision binary64 (if (<= x 1.2e+66) x (/ y (/ y x))))
double code(double x, double y, double z) {
double tmp;
if (x <= 1.2e+66) {
tmp = x;
} else {
tmp = y / (y / 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 <= 1.2d+66) then
tmp = x
else
tmp = y / (y / x)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= 1.2e+66) {
tmp = x;
} else {
tmp = y / (y / x);
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= 1.2e+66: tmp = x else: tmp = y / (y / x) return tmp
function code(x, y, z) tmp = 0.0 if (x <= 1.2e+66) tmp = x; else tmp = Float64(y / Float64(y / x)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= 1.2e+66) tmp = x; else tmp = y / (y / x); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, 1.2e+66], x, N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq 1.2 \cdot 10^{+66}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{y}{x}}\\
\end{array}
\end{array}
if x < 1.2000000000000001e66Initial program 87.4%
associate-*r/95.7%
div-sub95.7%
*-inverses95.7%
Simplified95.7%
Taylor expanded in z around 0 55.4%
if 1.2000000000000001e66 < x Initial program 74.7%
Taylor expanded in y around inf 26.6%
associate-/l*46.9%
associate-/r/55.7%
Applied egg-rr55.7%
*-commutative55.7%
clear-num55.6%
un-div-inv55.7%
Applied egg-rr55.7%
Final simplification55.5%
(FPCore (x y z) :precision binary64 (* x (- 1.0 (/ z y))))
double code(double x, double y, double z) {
return x * (1.0 - (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 * (1.0d0 - (z / y))
end function
public static double code(double x, double y, double z) {
return x * (1.0 - (z / y));
}
def code(x, y, z): return x * (1.0 - (z / y))
function code(x, y, z) return Float64(x * Float64(1.0 - Float64(z / y))) end
function tmp = code(x, y, z) tmp = x * (1.0 - (z / y)); end
code[x_, y_, z_] := N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(1 - \frac{z}{y}\right)
\end{array}
Initial program 84.6%
associate-*r/96.6%
div-sub96.6%
*-inverses96.6%
Simplified96.6%
Final simplification96.6%
(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/96.6%
div-sub96.6%
*-inverses96.6%
Simplified96.6%
Taylor expanded in z around 0 53.5%
Final simplification53.5%
(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 2023301
(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))