
(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 5 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 (- y z))))
double code(double x, double y, double z) {
return x / (y / (y - z));
}
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 / (y - z))
end function
public static double code(double x, double y, double z) {
return x / (y / (y - z));
}
def code(x, y, z): return x / (y / (y - z))
function code(x, y, z) return Float64(x / Float64(y / Float64(y - z))) end
function tmp = code(x, y, z) tmp = x / (y / (y - z)); end
code[x_, y_, z_] := N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{\frac{y}{y - z}}
\end{array}
Initial program 85.3%
Applied rewrites96.6%
(FPCore (x y z) :precision binary64 (if (<= y -8.5e+155) (* 1.0 x) (if (<= y 4e+230) (* (/ x y) (- y z)) (* 1.0 x))))
double code(double x, double y, double z) {
double tmp;
if (y <= -8.5e+155) {
tmp = 1.0 * x;
} else if (y <= 4e+230) {
tmp = (x / y) * (y - z);
} else {
tmp = 1.0 * 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 (y <= (-8.5d+155)) then
tmp = 1.0d0 * x
else if (y <= 4d+230) then
tmp = (x / y) * (y - z)
else
tmp = 1.0d0 * x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= -8.5e+155) {
tmp = 1.0 * x;
} else if (y <= 4e+230) {
tmp = (x / y) * (y - z);
} else {
tmp = 1.0 * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -8.5e+155: tmp = 1.0 * x elif y <= 4e+230: tmp = (x / y) * (y - z) else: tmp = 1.0 * x return tmp
function code(x, y, z) tmp = 0.0 if (y <= -8.5e+155) tmp = Float64(1.0 * x); elseif (y <= 4e+230) tmp = Float64(Float64(x / y) * Float64(y - z)); else tmp = Float64(1.0 * x); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -8.5e+155) tmp = 1.0 * x; elseif (y <= 4e+230) tmp = (x / y) * (y - z); else tmp = 1.0 * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -8.5e+155], N[(1.0 * x), $MachinePrecision], If[LessEqual[y, 4e+230], N[(N[(x / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -8.5 \cdot 10^{+155}:\\
\;\;\;\;1 \cdot x\\
\mathbf{elif}\;y \leq 4 \cdot 10^{+230}:\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\
\mathbf{else}:\\
\;\;\;\;1 \cdot x\\
\end{array}
\end{array}
if y < -8.5000000000000002e155 or 4.0000000000000004e230 < y Initial program 67.1%
Applied rewrites100.0%
lift-/.f64N/A
lift--.f64N/A
div-subN/A
sub-negN/A
*-inversesN/A
+-commutativeN/A
distribute-frac-neg2N/A
div-invN/A
lower-fma.f64N/A
neg-mul-1N/A
associate-/r*N/A
metadata-evalN/A
lower-/.f64100.0
Applied rewrites100.0%
Taylor expanded in y around inf
Applied rewrites96.1%
if -8.5000000000000002e155 < y < 4.0000000000000004e230Initial program 90.5%
Applied rewrites91.3%
(FPCore (x y z) :precision binary64 (if (<= y -5.5e-28) (* 1.0 x) (if (<= y 1.18e-61) (* (/ (- x) y) z) (* 1.0 x))))
double code(double x, double y, double z) {
double tmp;
if (y <= -5.5e-28) {
tmp = 1.0 * x;
} else if (y <= 1.18e-61) {
tmp = (-x / y) * z;
} else {
tmp = 1.0 * 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 (y <= (-5.5d-28)) then
tmp = 1.0d0 * x
else if (y <= 1.18d-61) then
tmp = (-x / y) * z
else
tmp = 1.0d0 * x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= -5.5e-28) {
tmp = 1.0 * x;
} else if (y <= 1.18e-61) {
tmp = (-x / y) * z;
} else {
tmp = 1.0 * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -5.5e-28: tmp = 1.0 * x elif y <= 1.18e-61: tmp = (-x / y) * z else: tmp = 1.0 * x return tmp
function code(x, y, z) tmp = 0.0 if (y <= -5.5e-28) tmp = Float64(1.0 * x); elseif (y <= 1.18e-61) tmp = Float64(Float64(Float64(-x) / y) * z); else tmp = Float64(1.0 * x); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -5.5e-28) tmp = 1.0 * x; elseif (y <= 1.18e-61) tmp = (-x / y) * z; else tmp = 1.0 * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -5.5e-28], N[(1.0 * x), $MachinePrecision], If[LessEqual[y, 1.18e-61], N[(N[((-x) / y), $MachinePrecision] * z), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -5.5 \cdot 10^{-28}:\\
\;\;\;\;1 \cdot x\\
\mathbf{elif}\;y \leq 1.18 \cdot 10^{-61}:\\
\;\;\;\;\frac{-x}{y} \cdot z\\
\mathbf{else}:\\
\;\;\;\;1 \cdot x\\
\end{array}
\end{array}
if y < -5.49999999999999967e-28 or 1.1800000000000001e-61 < y Initial program 80.0%
Applied rewrites99.9%
lift-/.f64N/A
lift--.f64N/A
div-subN/A
sub-negN/A
*-inversesN/A
+-commutativeN/A
distribute-frac-neg2N/A
div-invN/A
lower-fma.f64N/A
neg-mul-1N/A
associate-/r*N/A
metadata-evalN/A
lower-/.f6499.9
Applied rewrites99.9%
Taylor expanded in y around inf
Applied rewrites80.4%
if -5.49999999999999967e-28 < y < 1.1800000000000001e-61Initial program 92.8%
Taylor expanded in y around 0
associate-*l/N/A
associate-*l*N/A
lower-*.f64N/A
associate-*r/N/A
lower-/.f64N/A
mul-1-negN/A
lower-neg.f6476.4
Applied rewrites76.4%
(FPCore (x y z) :precision binary64 (* (/ (- y z) y) x))
double code(double x, double y, double z) {
return ((y - z) / y) * x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = ((y - z) / y) * x
end function
public static double code(double x, double y, double z) {
return ((y - z) / y) * x;
}
def code(x, y, z): return ((y - z) / y) * x
function code(x, y, z) return Float64(Float64(Float64(y - z) / y) * x) end
function tmp = code(x, y, z) tmp = ((y - z) / y) * x; end
code[x_, y_, z_] := N[(N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]
\begin{array}{l}
\\
\frac{y - z}{y} \cdot x
\end{array}
Initial program 85.3%
Applied rewrites96.2%
(FPCore (x y z) :precision binary64 (* 1.0 x))
double code(double x, double y, double z) {
return 1.0 * x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = 1.0d0 * x
end function
public static double code(double x, double y, double z) {
return 1.0 * x;
}
def code(x, y, z): return 1.0 * x
function code(x, y, z) return Float64(1.0 * x) end
function tmp = code(x, y, z) tmp = 1.0 * x; end
code[x_, y_, z_] := N[(1.0 * x), $MachinePrecision]
\begin{array}{l}
\\
1 \cdot x
\end{array}
Initial program 85.3%
Applied rewrites96.2%
lift-/.f64N/A
lift--.f64N/A
div-subN/A
sub-negN/A
*-inversesN/A
+-commutativeN/A
distribute-frac-neg2N/A
div-invN/A
lower-fma.f64N/A
neg-mul-1N/A
associate-/r*N/A
metadata-evalN/A
lower-/.f6496.2
Applied rewrites96.2%
Taylor expanded in y around inf
Applied rewrites56.2%
(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 2024298
(FPCore (x y z)
:name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
:precision binary64
:alt
(! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))
(/ (* x (- y z)) y))