
(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))
double code(double x, double y, double z, double t) {
return x * (((y / z) * t) / t);
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x * (((y / z) * t) / t)
end function
public static double code(double x, double y, double z, double t) {
return x * (((y / z) * t) / t);
}
def code(x, y, z, t): return x * (((y / z) * t) / t)
function code(x, y, z, t) return Float64(x * Float64(Float64(Float64(y / z) * t) / t)) end
function tmp = code(x, y, z, t) tmp = x * (((y / z) * t) / t); end
code[x_, y_, z_, t_] := N[(x * N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \frac{\frac{y}{z} \cdot t}{t}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 4 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))
double code(double x, double y, double z, double t) {
return x * (((y / z) * t) / t);
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x * (((y / z) * t) / t)
end function
public static double code(double x, double y, double z, double t) {
return x * (((y / z) * t) / t);
}
def code(x, y, z, t): return x * (((y / z) * t) / t)
function code(x, y, z, t) return Float64(x * Float64(Float64(Float64(y / z) * t) / t)) end
function tmp = code(x, y, z, t) tmp = x * (((y / z) * t) / t); end
code[x_, y_, z_, t_] := N[(x * N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \frac{\frac{y}{z} \cdot t}{t}
\end{array}
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y z t) :precision binary64 (if (<= (* x (/ (* (/ y z) t) t)) 2e-269) (/ y (/ z x)) (/ x (/ z y))))
assert(x < y);
double code(double x, double y, double z, double t) {
double tmp;
if ((x * (((y / z) * t) / t)) <= 2e-269) {
tmp = y / (z / x);
} else {
tmp = x / (z / y);
}
return tmp;
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if ((x * (((y / z) * t) / t)) <= 2d-269) then
tmp = y / (z / x)
else
tmp = x / (z / y)
end if
code = tmp
end function
assert x < y;
public static double code(double x, double y, double z, double t) {
double tmp;
if ((x * (((y / z) * t) / t)) <= 2e-269) {
tmp = y / (z / x);
} else {
tmp = x / (z / y);
}
return tmp;
}
[x, y] = sort([x, y]) def code(x, y, z, t): tmp = 0 if (x * (((y / z) * t) / t)) <= 2e-269: tmp = y / (z / x) else: tmp = x / (z / y) return tmp
x, y = sort([x, y]) function code(x, y, z, t) tmp = 0.0 if (Float64(x * Float64(Float64(Float64(y / z) * t) / t)) <= 2e-269) tmp = Float64(y / Float64(z / x)); else tmp = Float64(x / Float64(z / y)); end return tmp end
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
tmp = 0.0;
if ((x * (((y / z) * t) / t)) <= 2e-269)
tmp = y / (z / x);
else
tmp = x / (z / y);
end
tmp_2 = tmp;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_, z_, t_] := If[LessEqual[N[(x * N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], 2e-269], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\frac{y}{z} \cdot t}{t} \leq 2 \cdot 10^{-269}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\
\end{array}
\end{array}
if (*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t)) < 1.9999999999999999e-269Initial program 78.1%
associate-/l*91.7%
*-inverses91.7%
/-rgt-identity91.7%
Simplified91.7%
*-commutative91.7%
associate-*l/91.3%
associate-/l*94.2%
Applied egg-rr94.2%
if 1.9999999999999999e-269 < (*.f64 x (/.f64 (*.f64 (/.f64 y z) t) t)) Initial program 87.8%
associate-/l*96.5%
*-inverses96.5%
/-rgt-identity96.5%
Simplified96.5%
clear-num96.3%
un-div-inv97.8%
Applied egg-rr97.8%
Final simplification95.4%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y z t) :precision binary64 (if (<= t 1.9e-195) (* x (/ y z)) (* y (/ x z))))
assert(x < y);
double code(double x, double y, double z, double t) {
double tmp;
if (t <= 1.9e-195) {
tmp = x * (y / z);
} else {
tmp = y * (x / z);
}
return tmp;
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if (t <= 1.9d-195) then
tmp = x * (y / z)
else
tmp = y * (x / z)
end if
code = tmp
end function
assert x < y;
public static double code(double x, double y, double z, double t) {
double tmp;
if (t <= 1.9e-195) {
tmp = x * (y / z);
} else {
tmp = y * (x / z);
}
return tmp;
}
[x, y] = sort([x, y]) def code(x, y, z, t): tmp = 0 if t <= 1.9e-195: tmp = x * (y / z) else: tmp = y * (x / z) return tmp
x, y = sort([x, y]) function code(x, y, z, t) tmp = 0.0 if (t <= 1.9e-195) tmp = Float64(x * Float64(y / z)); else tmp = Float64(y * Float64(x / z)); end return tmp end
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
tmp = 0.0;
if (t <= 1.9e-195)
tmp = x * (y / z);
else
tmp = y * (x / z);
end
tmp_2 = tmp;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_, z_, t_] := If[LessEqual[t, 1.9e-195], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\begin{array}{l}
\mathbf{if}\;t \leq 1.9 \cdot 10^{-195}:\\
\;\;\;\;x \cdot \frac{y}{z}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\end{array}
\end{array}
if t < 1.90000000000000006e-195Initial program 80.2%
associate-/l*93.9%
*-inverses93.9%
/-rgt-identity93.9%
Simplified93.9%
if 1.90000000000000006e-195 < t Initial program 82.9%
*-commutative82.9%
associate-/l*92.4%
*-inverses92.4%
/-rgt-identity92.4%
associate-*l/92.1%
associate-*r/91.7%
Simplified91.7%
Final simplification93.0%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y z t) :precision binary64 (if (<= y 2.5e-304) (* y (/ x z)) (/ x (/ z y))))
assert(x < y);
double code(double x, double y, double z, double t) {
double tmp;
if (y <= 2.5e-304) {
tmp = y * (x / z);
} else {
tmp = x / (z / y);
}
return tmp;
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if (y <= 2.5d-304) then
tmp = y * (x / z)
else
tmp = x / (z / y)
end if
code = tmp
end function
assert x < y;
public static double code(double x, double y, double z, double t) {
double tmp;
if (y <= 2.5e-304) {
tmp = y * (x / z);
} else {
tmp = x / (z / y);
}
return tmp;
}
[x, y] = sort([x, y]) def code(x, y, z, t): tmp = 0 if y <= 2.5e-304: tmp = y * (x / z) else: tmp = x / (z / y) return tmp
x, y = sort([x, y]) function code(x, y, z, t) tmp = 0.0 if (y <= 2.5e-304) tmp = Float64(y * Float64(x / z)); else tmp = Float64(x / Float64(z / y)); end return tmp end
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
tmp = 0.0;
if (y <= 2.5e-304)
tmp = y * (x / z);
else
tmp = x / (z / y);
end
tmp_2 = tmp;
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_, z_, t_] := If[LessEqual[y, 2.5e-304], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
\begin{array}{l}
\mathbf{if}\;y \leq 2.5 \cdot 10^{-304}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\
\end{array}
\end{array}
if y < 2.49999999999999983e-304Initial program 83.5%
*-commutative83.5%
associate-/l*94.2%
*-inverses94.2%
/-rgt-identity94.2%
associate-*l/92.1%
associate-*r/92.8%
Simplified92.8%
if 2.49999999999999983e-304 < y Initial program 79.0%
associate-/l*92.3%
*-inverses92.3%
/-rgt-identity92.3%
Simplified92.3%
clear-num91.5%
un-div-inv92.8%
Applied egg-rr92.8%
Final simplification92.8%
NOTE: x and y should be sorted in increasing order before calling this function. (FPCore (x y z t) :precision binary64 (* x (/ y z)))
assert(x < y);
double code(double x, double y, double z, double t) {
return x * (y / z);
}
NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x * (y / z)
end function
assert x < y;
public static double code(double x, double y, double z, double t) {
return x * (y / z);
}
[x, y] = sort([x, y]) def code(x, y, z, t): return x * (y / z)
x, y = sort([x, y]) function code(x, y, z, t) return Float64(x * Float64(y / z)) end
x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t)
tmp = x * (y / z);
end
NOTE: x and y should be sorted in increasing order before calling this function. code[x_, y_, z_, t_] := N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
[x, y] = \mathsf{sort}([x, y])\\
\\
x \cdot \frac{y}{z}
\end{array}
Initial program 81.3%
associate-/l*93.3%
*-inverses93.3%
/-rgt-identity93.3%
Simplified93.3%
Final simplification93.3%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (* x (/ y z))) (t_2 (/ (* (/ y z) t) t)) (t_3 (/ y (/ z x))))
(if (< t_2 -1.20672205123045e+245)
t_3
(if (< t_2 -5.907522236933906e-275)
t_1
(if (< t_2 5.658954423153415e-65)
t_3
(if (< t_2 2.0087180502407133e+217) t_1 (/ (* y x) z)))))))
double code(double x, double y, double z, double t) {
double t_1 = x * (y / z);
double t_2 = ((y / z) * t) / t;
double t_3 = y / (z / x);
double tmp;
if (t_2 < -1.20672205123045e+245) {
tmp = t_3;
} else if (t_2 < -5.907522236933906e-275) {
tmp = t_1;
} else if (t_2 < 5.658954423153415e-65) {
tmp = t_3;
} else if (t_2 < 2.0087180502407133e+217) {
tmp = t_1;
} else {
tmp = (y * x) / z;
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: t_1
real(8) :: t_2
real(8) :: t_3
real(8) :: tmp
t_1 = x * (y / z)
t_2 = ((y / z) * t) / t
t_3 = y / (z / x)
if (t_2 < (-1.20672205123045d+245)) then
tmp = t_3
else if (t_2 < (-5.907522236933906d-275)) then
tmp = t_1
else if (t_2 < 5.658954423153415d-65) then
tmp = t_3
else if (t_2 < 2.0087180502407133d+217) then
tmp = t_1
else
tmp = (y * x) / z
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = x * (y / z);
double t_2 = ((y / z) * t) / t;
double t_3 = y / (z / x);
double tmp;
if (t_2 < -1.20672205123045e+245) {
tmp = t_3;
} else if (t_2 < -5.907522236933906e-275) {
tmp = t_1;
} else if (t_2 < 5.658954423153415e-65) {
tmp = t_3;
} else if (t_2 < 2.0087180502407133e+217) {
tmp = t_1;
} else {
tmp = (y * x) / z;
}
return tmp;
}
def code(x, y, z, t): t_1 = x * (y / z) t_2 = ((y / z) * t) / t t_3 = y / (z / x) tmp = 0 if t_2 < -1.20672205123045e+245: tmp = t_3 elif t_2 < -5.907522236933906e-275: tmp = t_1 elif t_2 < 5.658954423153415e-65: tmp = t_3 elif t_2 < 2.0087180502407133e+217: tmp = t_1 else: tmp = (y * x) / z return tmp
function code(x, y, z, t) t_1 = Float64(x * Float64(y / z)) t_2 = Float64(Float64(Float64(y / z) * t) / t) t_3 = Float64(y / Float64(z / x)) tmp = 0.0 if (t_2 < -1.20672205123045e+245) tmp = t_3; elseif (t_2 < -5.907522236933906e-275) tmp = t_1; elseif (t_2 < 5.658954423153415e-65) tmp = t_3; elseif (t_2 < 2.0087180502407133e+217) tmp = t_1; else tmp = Float64(Float64(y * x) / z); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = x * (y / z); t_2 = ((y / z) * t) / t; t_3 = y / (z / x); tmp = 0.0; if (t_2 < -1.20672205123045e+245) tmp = t_3; elseif (t_2 < -5.907522236933906e-275) tmp = t_1; elseif (t_2 < 5.658954423153415e-65) tmp = t_3; elseif (t_2 < 2.0087180502407133e+217) tmp = t_1; else tmp = (y * x) / z; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.20672205123045e+245], t$95$3, If[Less[t$95$2, -5.907522236933906e-275], t$95$1, If[Less[t$95$2, 5.658954423153415e-65], t$95$3, If[Less[t$95$2, 2.0087180502407133e+217], t$95$1, N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := x \cdot \frac{y}{z}\\
t_2 := \frac{\frac{y}{z} \cdot t}{t}\\
t_3 := \frac{y}{\frac{z}{x}}\\
\mathbf{if}\;t_2 < -1.20672205123045 \cdot 10^{+245}:\\
\;\;\;\;t_3\\
\mathbf{elif}\;t_2 < -5.907522236933906 \cdot 10^{-275}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;t_2 < 5.658954423153415 \cdot 10^{-65}:\\
\;\;\;\;t_3\\
\mathbf{elif}\;t_2 < 2.0087180502407133 \cdot 10^{+217}:\\
\;\;\;\;t_1\\
\mathbf{else}:\\
\;\;\;\;\frac{y \cdot x}{z}\\
\end{array}
\end{array}
herbie shell --seed 2023214
(FPCore (x y z t)
:name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
:precision binary64
:herbie-target
(if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))
(* x (/ (* (/ y z) t) t)))