
(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}
(FPCore (x y z t)
:precision binary64
(if (or (<= (/ y z) -5e+304)
(and (not (<= (/ y z) -1e-186)) (<= (/ y z) 5e-179)))
(* y (/ x z))
(/ x (/ z y))))
double code(double x, double y, double z, double t) {
double tmp;
if (((y / z) <= -5e+304) || (!((y / z) <= -1e-186) && ((y / z) <= 5e-179))) {
tmp = y * (x / z);
} else {
tmp = x / (z / y);
}
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) :: tmp
if (((y / z) <= (-5d+304)) .or. (.not. ((y / z) <= (-1d-186))) .and. ((y / z) <= 5d-179)) then
tmp = y * (x / z)
else
tmp = x / (z / y)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (((y / z) <= -5e+304) || (!((y / z) <= -1e-186) && ((y / z) <= 5e-179))) {
tmp = y * (x / z);
} else {
tmp = x / (z / y);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if ((y / z) <= -5e+304) or (not ((y / z) <= -1e-186) and ((y / z) <= 5e-179)): tmp = y * (x / z) else: tmp = x / (z / y) return tmp
function code(x, y, z, t) tmp = 0.0 if ((Float64(y / z) <= -5e+304) || (!(Float64(y / z) <= -1e-186) && (Float64(y / z) <= 5e-179))) tmp = Float64(y * Float64(x / z)); else tmp = Float64(x / Float64(z / y)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (((y / z) <= -5e+304) || (~(((y / z) <= -1e-186)) && ((y / z) <= 5e-179))) tmp = y * (x / z); else tmp = x / (z / y); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y / z), $MachinePrecision], -5e+304], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], -1e-186]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 5e-179]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+304} \lor \neg \left(\frac{y}{z} \leq -1 \cdot 10^{-186}\right) \land \frac{y}{z} \leq 5 \cdot 10^{-179}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\
\end{array}
\end{array}
if (/.f64 y z) < -4.9999999999999997e304 or -9.9999999999999991e-187 < (/.f64 y z) < 4.9999999999999998e-179Initial program 75.6%
*-commutative75.6%
associate-/l*80.7%
*-inverses80.7%
/-rgt-identity80.7%
associate-*l/99.9%
associate-*r/99.9%
Simplified99.9%
if -4.9999999999999997e304 < (/.f64 y z) < -9.9999999999999991e-187 or 4.9999999999999998e-179 < (/.f64 y z) Initial program 85.1%
associate-/l*98.1%
*-inverses98.1%
/-rgt-identity98.1%
Simplified98.1%
clear-num98.0%
un-div-inv98.8%
Applied egg-rr98.8%
Final simplification99.1%
(FPCore (x y z t)
:precision binary64
(if (or (<= (/ y z) -5e+256)
(and (not (<= (/ y z) -1e-186)) (<= (/ y z) 5e-237)))
(* y (/ x z))
(* x (/ y z))))
double code(double x, double y, double z, double t) {
double tmp;
if (((y / z) <= -5e+256) || (!((y / z) <= -1e-186) && ((y / z) <= 5e-237))) {
tmp = y * (x / z);
} else {
tmp = x * (y / 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) :: tmp
if (((y / z) <= (-5d+256)) .or. (.not. ((y / z) <= (-1d-186))) .and. ((y / z) <= 5d-237)) then
tmp = y * (x / z)
else
tmp = x * (y / z)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (((y / z) <= -5e+256) || (!((y / z) <= -1e-186) && ((y / z) <= 5e-237))) {
tmp = y * (x / z);
} else {
tmp = x * (y / z);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if ((y / z) <= -5e+256) or (not ((y / z) <= -1e-186) and ((y / z) <= 5e-237)): tmp = y * (x / z) else: tmp = x * (y / z) return tmp
function code(x, y, z, t) tmp = 0.0 if ((Float64(y / z) <= -5e+256) || (!(Float64(y / z) <= -1e-186) && (Float64(y / z) <= 5e-237))) tmp = Float64(y * Float64(x / z)); else tmp = Float64(x * Float64(y / z)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (((y / z) <= -5e+256) || (~(((y / z) <= -1e-186)) && ((y / z) <= 5e-237))) tmp = y * (x / z); else tmp = x * (y / z); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y / z), $MachinePrecision], -5e+256], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], -1e-186]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 5e-237]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+256} \lor \neg \left(\frac{y}{z} \leq -1 \cdot 10^{-186}\right) \land \frac{y}{z} \leq 5 \cdot 10^{-237}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y}{z}\\
\end{array}
\end{array}
if (/.f64 y z) < -5.00000000000000015e256 or -9.9999999999999991e-187 < (/.f64 y z) < 5.0000000000000002e-237Initial program 73.1%
*-commutative73.1%
associate-/l*81.0%
*-inverses81.0%
/-rgt-identity81.0%
associate-*l/99.9%
associate-*r/99.9%
Simplified99.9%
if -5.00000000000000015e256 < (/.f64 y z) < -9.9999999999999991e-187 or 5.0000000000000002e-237 < (/.f64 y z) Initial program 86.1%
associate-/l*98.1%
*-inverses98.1%
/-rgt-identity98.1%
Simplified98.1%
Final simplification98.6%
(FPCore (x y z t) :precision binary64 (if (<= x 1.15e-96) (/ (* x y) z) (* y (/ x z))))
double code(double x, double y, double z, double t) {
double tmp;
if (x <= 1.15e-96) {
tmp = (x * y) / z;
} 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) :: tmp
if (x <= 1.15d-96) then
tmp = (x * y) / z
else
tmp = y * (x / z)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (x <= 1.15e-96) {
tmp = (x * y) / z;
} else {
tmp = y * (x / z);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if x <= 1.15e-96: tmp = (x * y) / z else: tmp = y * (x / z) return tmp
function code(x, y, z, t) tmp = 0.0 if (x <= 1.15e-96) tmp = Float64(Float64(x * y) / z); else tmp = Float64(y * Float64(x / z)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (x <= 1.15e-96) tmp = (x * y) / z; else tmp = y * (x / z); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[x, 1.15e-96], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq 1.15 \cdot 10^{-96}:\\
\;\;\;\;\frac{x \cdot y}{z}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\end{array}
\end{array}
if x < 1.15e-96Initial program 83.7%
associate-/l*94.1%
*-inverses94.1%
/-rgt-identity94.1%
Simplified94.1%
Taylor expanded in x around 0 95.4%
if 1.15e-96 < x Initial program 80.5%
*-commutative80.5%
associate-/l*92.4%
*-inverses92.4%
/-rgt-identity92.4%
associate-*l/93.8%
associate-*r/89.4%
Simplified89.4%
Final simplification93.6%
(FPCore (x y z t) :precision binary64 (* x (/ y z)))
double code(double x, double y, double z, double t) {
return x * (y / z);
}
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
public static double code(double x, double y, double z, double t) {
return x * (y / z);
}
def code(x, y, z, t): return x * (y / z)
function code(x, y, z, t) return Float64(x * Float64(y / z)) end
function tmp = code(x, y, z, t) tmp = x * (y / z); end
code[x_, y_, z_, t_] := N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \frac{y}{z}
\end{array}
Initial program 82.7%
associate-/l*93.6%
*-inverses93.6%
/-rgt-identity93.6%
Simplified93.6%
Final simplification93.6%
(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 2023181
(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)))