
(FPCore (x y z t) :precision binary64 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
double code(double x, double y, double z, double t) {
return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function
public static double code(double x, double y, double z, double t) {
return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
def code(x, y, z, t): return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
function code(x, y, z, t) return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) end
function tmp = code(x, y, z, t) tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0); end
code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
double code(double x, double y, double z, double t) {
return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function
public static double code(double x, double y, double z, double t) {
return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
def code(x, y, z, t): return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
function code(x, y, z, t) return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) end
function tmp = code(x, y, z, t) tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0); end
code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
\end{array}
(FPCore (x y z t) :precision binary64 (/ (+ x (fma y (/ z (- (* z t) x)) (/ x (- x (* z t))))) (+ x 1.0)))
double code(double x, double y, double z, double t) {
return (x + fma(y, (z / ((z * t) - x)), (x / (x - (z * t))))) / (x + 1.0);
}
function code(x, y, z, t) return Float64(Float64(x + fma(y, Float64(z / Float64(Float64(z * t) - x)), Float64(x / Float64(x - Float64(z * t))))) / Float64(x + 1.0)) end
code[x_, y_, z_, t_] := N[(N[(x + N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + \mathsf{fma}\left(y, \frac{z}{z \cdot t - x}, \frac{x}{x - z \cdot t}\right)}{x + 1}
\end{array}
Initial program 92.6%
Applied egg-rr0
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
(if (<= t_1 1e+267)
t_1
(/
(+ x (- (/ z (- (* z (/ t y)) (/ x y))) (/ x (- (* z t) x))))
(+ x 1.0)))))
double code(double x, double y, double z, double t) {
double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
double tmp;
if (t_1 <= 1e+267) {
tmp = t_1;
} else {
tmp = (x + ((z / ((z * (t / y)) - (x / y))) - (x / ((z * t) - x)))) / (x + 1.0);
}
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) :: tmp
t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
if (t_1 <= 1d+267) then
tmp = t_1
else
tmp = (x + ((z / ((z * (t / y)) - (x / y))) - (x / ((z * t) - x)))) / (x + 1.0d0)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
double tmp;
if (t_1 <= 1e+267) {
tmp = t_1;
} else {
tmp = (x + ((z / ((z * (t / y)) - (x / y))) - (x / ((z * t) - x)))) / (x + 1.0);
}
return tmp;
}
def code(x, y, z, t): t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0) tmp = 0 if t_1 <= 1e+267: tmp = t_1 else: tmp = (x + ((z / ((z * (t / y)) - (x / y))) - (x / ((z * t) - x)))) / (x + 1.0) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) tmp = 0.0 if (t_1 <= 1e+267) tmp = t_1; else tmp = Float64(Float64(x + Float64(Float64(z / Float64(Float64(z * Float64(t / y)) - Float64(x / y))) - Float64(x / Float64(Float64(z * t) - x)))) / Float64(x + 1.0)); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0); tmp = 0.0; if (t_1 <= 1e+267) tmp = t_1; else tmp = (x + ((z / ((z * (t / y)) - (x / y))) - (x / ((z * t) - x)))) / (x + 1.0); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+267], t$95$1, N[(N[(x + N[(N[(z / N[(N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\
\mathbf{if}\;t\_1 \leq 10^{+267}:\\
\;\;\;\;t\_1\\
\mathbf{else}:\\
\;\;\;\;\frac{x + \left(\frac{z}{z \cdot \frac{t}{y} - \frac{x}{y}} - \frac{x}{z \cdot t - x}\right)}{x + 1}\\
\end{array}
\end{array}
if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999997e266Initial program 97.9%
if 9.9999999999999997e266 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) Initial program 13.7%
Applied egg-rr0
Applied egg-rr0
Applied egg-rr0
Applied egg-rr0
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
(t_2 (- (* z t) x)))
(if (<= t_1 1e+267) t_1 (/ (+ x (- (/ z (/ t_2 y)) (/ x t_2))) (+ x 1.0)))))
double code(double x, double y, double z, double t) {
double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
double t_2 = (z * t) - x;
double tmp;
if (t_1 <= 1e+267) {
tmp = t_1;
} else {
tmp = (x + ((z / (t_2 / y)) - (x / t_2))) / (x + 1.0);
}
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) :: tmp
t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
t_2 = (z * t) - x
if (t_1 <= 1d+267) then
tmp = t_1
else
tmp = (x + ((z / (t_2 / y)) - (x / t_2))) / (x + 1.0d0)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
double t_2 = (z * t) - x;
double tmp;
if (t_1 <= 1e+267) {
tmp = t_1;
} else {
tmp = (x + ((z / (t_2 / y)) - (x / t_2))) / (x + 1.0);
}
return tmp;
}
def code(x, y, z, t): t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0) t_2 = (z * t) - x tmp = 0 if t_1 <= 1e+267: tmp = t_1 else: tmp = (x + ((z / (t_2 / y)) - (x / t_2))) / (x + 1.0) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) t_2 = Float64(Float64(z * t) - x) tmp = 0.0 if (t_1 <= 1e+267) tmp = t_1; else tmp = Float64(Float64(x + Float64(Float64(z / Float64(t_2 / y)) - Float64(x / t_2))) / Float64(x + 1.0)); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0); t_2 = (z * t) - x; tmp = 0.0; if (t_1 <= 1e+267) tmp = t_1; else tmp = (x + ((z / (t_2 / y)) - (x / t_2))) / (x + 1.0); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+267], t$95$1, N[(N[(x + N[(N[(z / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\
t_2 := z \cdot t - x\\
\mathbf{if}\;t\_1 \leq 10^{+267}:\\
\;\;\;\;t\_1\\
\mathbf{else}:\\
\;\;\;\;\frac{x + \left(\frac{z}{\frac{t\_2}{y}} - \frac{x}{t\_2}\right)}{x + 1}\\
\end{array}
\end{array}
if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999997e266Initial program 97.9%
if 9.9999999999999997e266 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) Initial program 13.7%
Applied egg-rr0
Applied egg-rr0
Applied egg-rr0
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
(t_2 (- (* z t) x)))
(if (<= t_1 1e+155) t_1 (/ (+ x (- (* z (/ y t_2)) (/ x t_2))) (+ x 1.0)))))
double code(double x, double y, double z, double t) {
double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
double t_2 = (z * t) - x;
double tmp;
if (t_1 <= 1e+155) {
tmp = t_1;
} else {
tmp = (x + ((z * (y / t_2)) - (x / t_2))) / (x + 1.0);
}
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) :: tmp
t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
t_2 = (z * t) - x
if (t_1 <= 1d+155) then
tmp = t_1
else
tmp = (x + ((z * (y / t_2)) - (x / t_2))) / (x + 1.0d0)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
double t_2 = (z * t) - x;
double tmp;
if (t_1 <= 1e+155) {
tmp = t_1;
} else {
tmp = (x + ((z * (y / t_2)) - (x / t_2))) / (x + 1.0);
}
return tmp;
}
def code(x, y, z, t): t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0) t_2 = (z * t) - x tmp = 0 if t_1 <= 1e+155: tmp = t_1 else: tmp = (x + ((z * (y / t_2)) - (x / t_2))) / (x + 1.0) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) t_2 = Float64(Float64(z * t) - x) tmp = 0.0 if (t_1 <= 1e+155) tmp = t_1; else tmp = Float64(Float64(x + Float64(Float64(z * Float64(y / t_2)) - Float64(x / t_2))) / Float64(x + 1.0)); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0); t_2 = (z * t) - x; tmp = 0.0; if (t_1 <= 1e+155) tmp = t_1; else tmp = (x + ((z * (y / t_2)) - (x / t_2))) / (x + 1.0); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+155], t$95$1, N[(N[(x + N[(N[(z * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\
t_2 := z \cdot t - x\\
\mathbf{if}\;t\_1 \leq 10^{+155}:\\
\;\;\;\;t\_1\\
\mathbf{else}:\\
\;\;\;\;\frac{x + \left(z \cdot \frac{y}{t\_2} - \frac{x}{t\_2}\right)}{x + 1}\\
\end{array}
\end{array}
if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000001e155Initial program 97.9%
if 1.00000000000000001e155 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) Initial program 23.2%
Applied egg-rr0
Applied egg-rr0
(FPCore (x y z t) :precision binary64 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
double code(double x, double y, double z, double t) {
return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function
public static double code(double x, double y, double z, double t) {
return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
def code(x, y, z, t): return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
function code(x, y, z, t) return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) end
function tmp = code(x, y, z, t) tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0); end
code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
\end{array}
Initial program 92.6%
(FPCore (x y z t) :precision binary64 (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0)))
double code(double x, double y, double z, double t) {
return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}
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 / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function
public static double code(double x, double y, double z, double t) {
return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}
def code(x, y, z, t): return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0)
function code(x, y, z, t) return Float64(Float64(x + Float64(Float64(y / Float64(t - Float64(x / z))) - Float64(x / Float64(Float64(t * z) - x)))) / Float64(x + 1.0)) end
function tmp = code(x, y, z, t) tmp = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0); end
code[x_, y_, z_, t_] := N[(N[(x + N[(N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}
\end{array}
herbie shell --seed 2024107
(FPCore (x y z t)
:name "Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A"
:precision binary64
:alt
(/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))
(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))