
(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(Float64(y * y) / z)) end
function tmp = code(x, y, z) tmp = x + ((y * y) / z); end
code[x_, y_, z_] := N[(x + N[(N[(y * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y \cdot y}{z}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 4 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(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(Float64(y * y) / z)) end
function tmp = code(x, y, z) tmp = x + ((y * y) / z); end
code[x_, y_, z_] := N[(x + N[(N[(y * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y \cdot y}{z}
\end{array}
(FPCore (x y z) :precision binary64 (fma (/ y z) y x))
double code(double x, double y, double z) {
return fma((y / z), y, x);
}
function code(x, y, z) return fma(Float64(y / z), y, x) end
code[x_, y_, z_] := N[(N[(y / z), $MachinePrecision] * y + x), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(\frac{y}{z}, y, x\right)
\end{array}
Initial program 92.6%
lift-+.f64N/A
+-commutativeN/A
lift-/.f64N/A
lift-*.f64N/A
associate-*l/N/A
lower-fma.f64N/A
lower-/.f6499.9
Applied rewrites99.9%
(FPCore (x y z)
:precision binary64
(let* ((t_0 (/ (* y y) z)))
(if (or (<= t_0 -2e+134) (not (<= t_0 2e-46)))
(* (/ y z) y)
(* -1.0 (- x)))))
double code(double x, double y, double z) {
double t_0 = (y * y) / z;
double tmp;
if ((t_0 <= -2e+134) || !(t_0 <= 2e-46)) {
tmp = (y / z) * y;
} 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) :: t_0
real(8) :: tmp
t_0 = (y * y) / z
if ((t_0 <= (-2d+134)) .or. (.not. (t_0 <= 2d-46))) then
tmp = (y / z) * y
else
tmp = (-1.0d0) * -x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double t_0 = (y * y) / z;
double tmp;
if ((t_0 <= -2e+134) || !(t_0 <= 2e-46)) {
tmp = (y / z) * y;
} else {
tmp = -1.0 * -x;
}
return tmp;
}
def code(x, y, z): t_0 = (y * y) / z tmp = 0 if (t_0 <= -2e+134) or not (t_0 <= 2e-46): tmp = (y / z) * y else: tmp = -1.0 * -x return tmp
function code(x, y, z) t_0 = Float64(Float64(y * y) / z) tmp = 0.0 if ((t_0 <= -2e+134) || !(t_0 <= 2e-46)) tmp = Float64(Float64(y / z) * y); else tmp = Float64(-1.0 * Float64(-x)); end return tmp end
function tmp_2 = code(x, y, z) t_0 = (y * y) / z; tmp = 0.0; if ((t_0 <= -2e+134) || ~((t_0 <= 2e-46))) tmp = (y / z) * y; else tmp = -1.0 * -x; end tmp_2 = tmp; end
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] / z), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e+134], N[Not[LessEqual[t$95$0, 2e-46]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * y), $MachinePrecision], N[(-1.0 * (-x)), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{y \cdot y}{z}\\
\mathbf{if}\;t\_0 \leq -2 \cdot 10^{+134} \lor \neg \left(t\_0 \leq 2 \cdot 10^{-46}\right):\\
\;\;\;\;\frac{y}{z} \cdot y\\
\mathbf{else}:\\
\;\;\;\;-1 \cdot \left(-x\right)\\
\end{array}
\end{array}
if (/.f64 (*.f64 y y) z) < -1.99999999999999984e134 or 2.00000000000000005e-46 < (/.f64 (*.f64 y y) z) Initial program 87.5%
Taylor expanded in x around 0
lower-/.f64N/A
unpow2N/A
lower-*.f6480.3
Applied rewrites80.3%
Applied rewrites91.9%
if -1.99999999999999984e134 < (/.f64 (*.f64 y y) z) < 2.00000000000000005e-46Initial program 97.7%
Taylor expanded in x around 0
lower-/.f64N/A
unpow2N/A
lower-*.f6415.5
Applied rewrites15.5%
Applied rewrites17.7%
Taylor expanded in x around -inf
associate-*r*N/A
*-commutativeN/A
lower-*.f64N/A
*-commutativeN/A
associate-/r*N/A
associate-/l*N/A
lower--.f64N/A
mul-1-negN/A
distribute-frac-negN/A
associate-/r*N/A
*-commutativeN/A
unpow2N/A
associate-/l*N/A
distribute-lft-neg-inN/A
lower-*.f64N/A
lower-neg.f64N/A
lower-/.f64N/A
lower-*.f64N/A
mul-1-negN/A
lower-neg.f6495.1
Applied rewrites95.1%
Taylor expanded in x around inf
Applied rewrites85.1%
Final simplification88.5%
(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 * Float64(-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 \left(-x\right)
\end{array}
Initial program 92.6%
Taylor expanded in x around 0
lower-/.f64N/A
unpow2N/A
lower-*.f6448.2
Applied rewrites48.2%
Applied rewrites55.1%
Taylor expanded in x around -inf
associate-*r*N/A
*-commutativeN/A
lower-*.f64N/A
*-commutativeN/A
associate-/r*N/A
associate-/l*N/A
lower--.f64N/A
mul-1-negN/A
distribute-frac-negN/A
associate-/r*N/A
*-commutativeN/A
unpow2N/A
associate-/l*N/A
distribute-lft-neg-inN/A
lower-*.f64N/A
lower-neg.f64N/A
lower-/.f64N/A
lower-*.f64N/A
mul-1-negN/A
lower-neg.f6488.2
Applied rewrites88.2%
Taylor expanded in x around inf
Applied rewrites47.0%
(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 Float64(-x) end
function tmp = code(x, y, z) tmp = -x; end
code[x_, y_, z_] := (-x)
\begin{array}{l}
\\
-x
\end{array}
Initial program 92.6%
Applied rewrites9.7%
Taylor expanded in x around inf
mul-1-negN/A
lower-neg.f642.4
Applied rewrites2.4%
(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}
\\
x + y \cdot \frac{y}{z}
\end{array}
herbie shell --seed 2024338
(FPCore (x y z)
:name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
:precision binary64
:alt
(! :herbie-platform default (+ x (* y (/ y z))))
(+ x (/ (* y y) z)))