
(FPCore (x y z t) :precision binary64 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))
double code(double x, double y, double z, double t) {
return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function
public static double code(double x, double y, double z, double t) {
return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}
def code(x, y, z, t): return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t
function code(x, y, z, t) return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t) end
function tmp = code(x, y, z, t) tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t; end
code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))
double code(double x, double y, double z, double t) {
return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function
public static double code(double x, double y, double z, double t) {
return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}
def code(x, y, z, t): return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t
function code(x, y, z, t) return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t) end
function tmp = code(x, y, z, t) tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t; end
code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t
\end{array}
(FPCore (x y z t) :precision binary64 (+ (- (* 0.125 x) (* y (/ z 2.0))) t))
double code(double x, double y, double z, double t) {
return ((0.125 * x) - (y * (z / 2.0))) + 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 = ((0.125d0 * x) - (y * (z / 2.0d0))) + t
end function
public static double code(double x, double y, double z, double t) {
return ((0.125 * x) - (y * (z / 2.0))) + t;
}
def code(x, y, z, t): return ((0.125 * x) - (y * (z / 2.0))) + t
function code(x, y, z, t) return Float64(Float64(Float64(0.125 * x) - Float64(y * Float64(z / 2.0))) + t) end
function tmp = code(x, y, z, t) tmp = ((0.125 * x) - (y * (z / 2.0))) + t; end
code[x_, y_, z_, t_] := N[(N[(N[(0.125 * x), $MachinePrecision] - N[(y * N[(z / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t
\end{array}
Initial program 100.0%
associate-+l-100.0%
*-commutative100.0%
associate-+l-100.0%
metadata-eval100.0%
*-commutative100.0%
associate-/l*100.0%
Simplified100.0%
(FPCore (x y z t) :precision binary64 (if (or (<= (* y z) -1.4e+84) (not (<= (* y z) 1.7e+80))) (- t (* (* y z) 0.5)) (+ (* 0.125 x) t)))
double code(double x, double y, double z, double t) {
double tmp;
if (((y * z) <= -1.4e+84) || !((y * z) <= 1.7e+80)) {
tmp = t - ((y * z) * 0.5);
} else {
tmp = (0.125 * x) + t;
}
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) <= (-1.4d+84)) .or. (.not. ((y * z) <= 1.7d+80))) then
tmp = t - ((y * z) * 0.5d0)
else
tmp = (0.125d0 * x) + t
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (((y * z) <= -1.4e+84) || !((y * z) <= 1.7e+80)) {
tmp = t - ((y * z) * 0.5);
} else {
tmp = (0.125 * x) + t;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if ((y * z) <= -1.4e+84) or not ((y * z) <= 1.7e+80): tmp = t - ((y * z) * 0.5) else: tmp = (0.125 * x) + t return tmp
function code(x, y, z, t) tmp = 0.0 if ((Float64(y * z) <= -1.4e+84) || !(Float64(y * z) <= 1.7e+80)) tmp = Float64(t - Float64(Float64(y * z) * 0.5)); else tmp = Float64(Float64(0.125 * x) + t); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (((y * z) <= -1.4e+84) || ~(((y * z) <= 1.7e+80))) tmp = t - ((y * z) * 0.5); else tmp = (0.125 * x) + t; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -1.4e+84], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1.7e+80]], $MachinePrecision]], N[(t - N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \cdot z \leq -1.4 \cdot 10^{+84} \lor \neg \left(y \cdot z \leq 1.7 \cdot 10^{+80}\right):\\
\;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\
\mathbf{else}:\\
\;\;\;\;0.125 \cdot x + t\\
\end{array}
\end{array}
if (*.f64 y z) < -1.39999999999999991e84 or 1.69999999999999996e80 < (*.f64 y z) Initial program 100.0%
associate-+l-100.0%
*-commutative100.0%
associate-+l-100.0%
metadata-eval100.0%
*-commutative100.0%
associate-/l*100.0%
Simplified100.0%
Taylor expanded in x around 0 91.9%
if -1.39999999999999991e84 < (*.f64 y z) < 1.69999999999999996e80Initial program 100.0%
associate-+l-100.0%
*-commutative100.0%
associate-+l-100.0%
metadata-eval100.0%
*-commutative100.0%
associate-/l*100.0%
Simplified100.0%
Taylor expanded in x around inf 89.3%
Final simplification90.3%
(FPCore (x y z t) :precision binary64 (if (or (<= x -1.4e-21) (not (<= x 1.25e+22))) (* 0.125 x) t))
double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -1.4e-21) || !(x <= 1.25e+22)) {
tmp = 0.125 * x;
} else {
tmp = t;
}
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 <= (-1.4d-21)) .or. (.not. (x <= 1.25d+22))) then
tmp = 0.125d0 * x
else
tmp = t
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -1.4e-21) || !(x <= 1.25e+22)) {
tmp = 0.125 * x;
} else {
tmp = t;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (x <= -1.4e-21) or not (x <= 1.25e+22): tmp = 0.125 * x else: tmp = t return tmp
function code(x, y, z, t) tmp = 0.0 if ((x <= -1.4e-21) || !(x <= 1.25e+22)) tmp = Float64(0.125 * x); else tmp = t; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((x <= -1.4e-21) || ~((x <= 1.25e+22))) tmp = 0.125 * x; else tmp = t; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.4e-21], N[Not[LessEqual[x, 1.25e+22]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.4 \cdot 10^{-21} \lor \neg \left(x \leq 1.25 \cdot 10^{+22}\right):\\
\;\;\;\;0.125 \cdot x\\
\mathbf{else}:\\
\;\;\;\;t\\
\end{array}
\end{array}
if x < -1.40000000000000002e-21 or 1.2499999999999999e22 < x Initial program 100.0%
associate-+l-100.0%
*-commutative100.0%
associate-+l-100.0%
metadata-eval100.0%
*-commutative100.0%
associate-/l*100.0%
Simplified100.0%
Taylor expanded in x around inf 66.2%
Taylor expanded in x around inf 55.6%
if -1.40000000000000002e-21 < x < 1.2499999999999999e22Initial program 100.0%
associate-+l-100.0%
*-commutative100.0%
associate-+l-100.0%
metadata-eval100.0%
*-commutative100.0%
associate-/l*100.0%
Simplified100.0%
Taylor expanded in t around inf 50.5%
Final simplification53.2%
(FPCore (x y z t) :precision binary64 (+ (* 0.125 x) t))
double code(double x, double y, double z, double t) {
return (0.125 * x) + 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 = (0.125d0 * x) + t
end function
public static double code(double x, double y, double z, double t) {
return (0.125 * x) + t;
}
def code(x, y, z, t): return (0.125 * x) + t
function code(x, y, z, t) return Float64(Float64(0.125 * x) + t) end
function tmp = code(x, y, z, t) tmp = (0.125 * x) + t; end
code[x_, y_, z_, t_] := N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]
\begin{array}{l}
\\
0.125 \cdot x + t
\end{array}
Initial program 100.0%
associate-+l-100.0%
*-commutative100.0%
associate-+l-100.0%
metadata-eval100.0%
*-commutative100.0%
associate-/l*100.0%
Simplified100.0%
Taylor expanded in x around inf 62.2%
(FPCore (x y z t) :precision binary64 t)
double code(double x, double y, double z, double t) {
return 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 = t
end function
public static double code(double x, double y, double z, double t) {
return t;
}
def code(x, y, z, t): return t
function code(x, y, z, t) return t end
function tmp = code(x, y, z, t) tmp = t; end
code[x_, y_, z_, t_] := t
\begin{array}{l}
\\
t
\end{array}
Initial program 100.0%
associate-+l-100.0%
*-commutative100.0%
associate-+l-100.0%
metadata-eval100.0%
*-commutative100.0%
associate-/l*100.0%
Simplified100.0%
Taylor expanded in t around inf 29.8%
(FPCore (x y z t) :precision binary64 (- (+ (/ x 8.0) t) (* (/ z 2.0) y)))
double code(double x, double y, double z, double t) {
return ((x / 8.0) + t) - ((z / 2.0) * y);
}
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 / 8.0d0) + t) - ((z / 2.0d0) * y)
end function
public static double code(double x, double y, double z, double t) {
return ((x / 8.0) + t) - ((z / 2.0) * y);
}
def code(x, y, z, t): return ((x / 8.0) + t) - ((z / 2.0) * y)
function code(x, y, z, t) return Float64(Float64(Float64(x / 8.0) + t) - Float64(Float64(z / 2.0) * y)) end
function tmp = code(x, y, z, t) tmp = ((x / 8.0) + t) - ((z / 2.0) * y); end
code[x_, y_, z_, t_] := N[(N[(N[(x / 8.0), $MachinePrecision] + t), $MachinePrecision] - N[(N[(z / 2.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y
\end{array}
herbie shell --seed 2024132
(FPCore (x y z t)
:name "Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B"
:precision binary64
:alt
(! :herbie-platform default (- (+ (/ x 8) t) (* (/ z 2) y)))
(+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))