
(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 82.7%
remove-double-neg82.7%
distribute-frac-neg282.7%
distribute-frac-neg82.7%
distribute-rgt-neg-in82.7%
associate-/l*96.6%
distribute-frac-neg96.6%
distribute-frac-neg296.6%
remove-double-neg96.6%
div-sub96.6%
*-inverses96.6%
Simplified96.6%
*-inverses96.6%
div-sub96.6%
clear-num96.5%
un-div-inv97.3%
Applied egg-rr97.3%
(FPCore (x y z) :precision binary64 (if (<= y -6.8e-61) x (if (<= y 9.5e-93) (* z (/ x (- y))) x)))
double code(double x, double y, double z) {
double tmp;
if (y <= -6.8e-61) {
tmp = x;
} else if (y <= 9.5e-93) {
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 (y <= (-6.8d-61)) then
tmp = x
else if (y <= 9.5d-93) 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 (y <= -6.8e-61) {
tmp = x;
} else if (y <= 9.5e-93) {
tmp = z * (x / -y);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -6.8e-61: tmp = x elif y <= 9.5e-93: tmp = z * (x / -y) else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if (y <= -6.8e-61) tmp = x; elseif (y <= 9.5e-93) tmp = Float64(z * Float64(x / Float64(-y))); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -6.8e-61) tmp = x; elseif (y <= 9.5e-93) tmp = z * (x / -y); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -6.8e-61], x, If[LessEqual[y, 9.5e-93], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], x]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -6.8 \cdot 10^{-61}:\\
\;\;\;\;x\\
\mathbf{elif}\;y \leq 9.5 \cdot 10^{-93}:\\
\;\;\;\;z \cdot \frac{x}{-y}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if y < -6.7999999999999996e-61 or 9.5000000000000001e-93 < y Initial program 76.6%
remove-double-neg76.6%
distribute-frac-neg276.6%
distribute-frac-neg76.6%
distribute-rgt-neg-in76.6%
associate-/l*99.9%
distribute-frac-neg99.9%
distribute-frac-neg299.9%
remove-double-neg99.9%
div-sub99.9%
*-inverses99.9%
Simplified99.9%
Taylor expanded in z around 0 75.9%
if -6.7999999999999996e-61 < y < 9.5000000000000001e-93Initial program 93.6%
remove-double-neg93.6%
distribute-frac-neg293.6%
distribute-frac-neg93.6%
distribute-rgt-neg-in93.6%
associate-/l*90.7%
distribute-frac-neg90.7%
distribute-frac-neg290.7%
remove-double-neg90.7%
div-sub90.7%
*-inverses90.7%
Simplified90.7%
Taylor expanded in z around inf 76.2%
mul-1-neg76.2%
distribute-frac-neg276.2%
*-commutative76.2%
associate-/l*77.0%
Simplified77.0%
(FPCore (x y z) :precision binary64 (if (<= y -9.5e-124) x (if (<= y 2.8e-92) (* x (/ (- z) y)) x)))
double code(double x, double y, double z) {
double tmp;
if (y <= -9.5e-124) {
tmp = x;
} else if (y <= 2.8e-92) {
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 (y <= (-9.5d-124)) then
tmp = x
else if (y <= 2.8d-92) 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 (y <= -9.5e-124) {
tmp = x;
} else if (y <= 2.8e-92) {
tmp = x * (-z / y);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -9.5e-124: tmp = x elif y <= 2.8e-92: tmp = x * (-z / y) else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if (y <= -9.5e-124) tmp = x; elseif (y <= 2.8e-92) tmp = Float64(x * Float64(Float64(-z) / y)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -9.5e-124) tmp = x; elseif (y <= 2.8e-92) tmp = x * (-z / y); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -9.5e-124], x, If[LessEqual[y, 2.8e-92], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -9.5 \cdot 10^{-124}:\\
\;\;\;\;x\\
\mathbf{elif}\;y \leq 2.8 \cdot 10^{-92}:\\
\;\;\;\;x \cdot \frac{-z}{y}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if y < -9.49999999999999989e-124 or 2.8e-92 < y Initial program 77.8%
remove-double-neg77.8%
distribute-frac-neg277.8%
distribute-frac-neg77.8%
distribute-rgt-neg-in77.8%
associate-/l*99.3%
distribute-frac-neg99.3%
distribute-frac-neg299.3%
remove-double-neg99.3%
div-sub99.3%
*-inverses99.3%
Simplified99.3%
Taylor expanded in z around 0 74.1%
if -9.49999999999999989e-124 < y < 2.8e-92Initial program 93.3%
associate-/l*90.6%
Simplified90.6%
Taylor expanded in y around 0 75.0%
neg-mul-175.0%
Simplified75.0%
(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 82.7%
remove-double-neg82.7%
distribute-frac-neg282.7%
distribute-frac-neg82.7%
distribute-rgt-neg-in82.7%
associate-/l*96.6%
distribute-frac-neg96.6%
distribute-frac-neg296.6%
remove-double-neg96.6%
div-sub96.6%
*-inverses96.6%
Simplified96.6%
(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 82.7%
remove-double-neg82.7%
distribute-frac-neg282.7%
distribute-frac-neg82.7%
distribute-rgt-neg-in82.7%
associate-/l*96.6%
distribute-frac-neg96.6%
distribute-frac-neg296.6%
remove-double-neg96.6%
div-sub96.6%
*-inverses96.6%
Simplified96.6%
Taylor expanded in z around 0 56.0%
(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 2024130
(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))