
(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 (* (/ z y) x)))
double code(double x, double y, double z) {
return x - ((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 = x - ((z / y) * x)
end function
public static double code(double x, double y, double z) {
return x - ((z / y) * x);
}
def code(x, y, z): return x - ((z / y) * x)
function code(x, y, z) return Float64(x - Float64(Float64(z / y) * x)) end
function tmp = code(x, y, z) tmp = x - ((z / y) * x); end
code[x_, y_, z_] := N[(x - N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{z}{y} \cdot x
\end{array}
Initial program 83.0%
lift-/.f64N/A
lift-*.f64N/A
associate-/l*N/A
*-commutativeN/A
lower-*.f64N/A
lower-/.f6497.6
Applied rewrites97.6%
Applied rewrites97.6%
(FPCore (x y z) :precision binary64 (if (<= (/ (* (- y z) x) y) 5e+301) (- x (/ (* z x) y)) (* (/ x y) (- y z))))
double code(double x, double y, double z) {
double tmp;
if ((((y - z) * x) / y) <= 5e+301) {
tmp = x - ((z * x) / y);
} else {
tmp = (x / y) * (y - z);
}
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 - z) * x) / y) <= 5d+301) then
tmp = x - ((z * x) / y)
else
tmp = (x / y) * (y - z)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((((y - z) * x) / y) <= 5e+301) {
tmp = x - ((z * x) / y);
} else {
tmp = (x / y) * (y - z);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (((y - z) * x) / y) <= 5e+301: tmp = x - ((z * x) / y) else: tmp = (x / y) * (y - z) return tmp
function code(x, y, z) tmp = 0.0 if (Float64(Float64(Float64(y - z) * x) / y) <= 5e+301) tmp = Float64(x - Float64(Float64(z * x) / y)); else tmp = Float64(Float64(x / y) * Float64(y - z)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((((y - z) * x) / y) <= 5e+301) tmp = x - ((z * x) / y); else tmp = (x / y) * (y - z); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], 5e+301], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq 5 \cdot 10^{+301}:\\
\;\;\;\;x - \frac{z \cdot x}{y}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\
\end{array}
\end{array}
if (/.f64 (*.f64 x (-.f64 y z)) y) < 5.0000000000000004e301Initial program 87.2%
Taylor expanded in z around 0
mul-1-negN/A
unsub-negN/A
lower--.f64N/A
lower-/.f64N/A
*-commutativeN/A
lower-*.f6495.0
Applied rewrites95.0%
if 5.0000000000000004e301 < (/.f64 (*.f64 x (-.f64 y z)) y) Initial program 59.4%
lift-/.f64N/A
lift-*.f64N/A
*-commutativeN/A
associate-/l*N/A
*-commutativeN/A
lower-*.f64N/A
lower-/.f6499.8
Applied rewrites99.8%
Final simplification95.8%
(FPCore (x y z) :precision binary64 (if (<= (/ (* (- y z) x) y) -4e-243) (* (/ (- z) y) x) (* 1.0 x)))
double code(double x, double y, double z) {
double tmp;
if ((((y - z) * x) / y) <= -4e-243) {
tmp = (-z / y) * x;
} 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 - z) * x) / y) <= (-4d-243)) then
tmp = (-z / y) * x
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 - z) * x) / y) <= -4e-243) {
tmp = (-z / y) * x;
} else {
tmp = 1.0 * x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (((y - z) * x) / y) <= -4e-243: tmp = (-z / y) * x else: tmp = 1.0 * x return tmp
function code(x, y, z) tmp = 0.0 if (Float64(Float64(Float64(y - z) * x) / y) <= -4e-243) tmp = Float64(Float64(Float64(-z) / y) * x); else tmp = Float64(1.0 * x); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((((y - z) * x) / y) <= -4e-243) tmp = (-z / y) * x; else tmp = 1.0 * x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], -4e-243], N[(N[((-z) / y), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \leq -4 \cdot 10^{-243}:\\
\;\;\;\;\frac{-z}{y} \cdot x\\
\mathbf{else}:\\
\;\;\;\;1 \cdot x\\
\end{array}
\end{array}
if (/.f64 (*.f64 x (-.f64 y z)) y) < -3.99999999999999998e-243Initial program 84.8%
Taylor expanded in z around inf
associate-/l*N/A
*-commutativeN/A
associate-*r*N/A
lower-*.f64N/A
associate-*r/N/A
lower-/.f64N/A
mul-1-negN/A
lower-neg.f6450.7
Applied rewrites50.7%
if -3.99999999999999998e-243 < (/.f64 (*.f64 x (-.f64 y z)) y) Initial program 81.7%
lift-/.f64N/A
lift-*.f64N/A
associate-/l*N/A
*-commutativeN/A
lower-*.f64N/A
lower-/.f6497.9
Applied rewrites97.9%
Taylor expanded in z around 0
Applied rewrites58.8%
Final simplification55.5%
(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 83.0%
lift-/.f64N/A
lift-*.f64N/A
associate-/l*N/A
*-commutativeN/A
lower-*.f64N/A
lower-/.f6497.6
Applied rewrites97.6%
(FPCore (x y z) :precision binary64 (- x (/ (* z x) y)))
double code(double x, double y, double z) {
return x - ((z * x) / 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 - ((z * x) / y)
end function
public static double code(double x, double y, double z) {
return x - ((z * x) / y);
}
def code(x, y, z): return x - ((z * x) / y)
function code(x, y, z) return Float64(x - Float64(Float64(z * x) / y)) end
function tmp = code(x, y, z) tmp = x - ((z * x) / y); end
code[x_, y_, z_] := N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{z \cdot x}{y}
\end{array}
Initial program 83.0%
Taylor expanded in z around 0
mul-1-negN/A
unsub-negN/A
lower--.f64N/A
lower-/.f64N/A
*-commutativeN/A
lower-*.f6494.3
Applied rewrites94.3%
(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 83.0%
lift-/.f64N/A
lift-*.f64N/A
associate-/l*N/A
*-commutativeN/A
lower-*.f64N/A
lower-/.f6497.6
Applied rewrites97.6%
Taylor expanded in z around 0
Applied rewrites54.4%
(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 2024240
(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))