Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, F

Percentage Accurate: 99.7% → 99.7%

Time: 1.1s

Alternatives: 2

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 27\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x 27.0) y))

C

double code(double x, double y) {
	return (x * 27.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 27.0d0) * y
end function

Java

public static double code(double x, double y) {
	return (x * 27.0) * y;
}

Python

def code(x, y):
	return (x * 27.0) * y

Julia

function code(x, y)
	return Float64(Float64(x * 27.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 27.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(x * 27.0), $MachinePrecision] * y), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 27\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x 27.0) y))

C

double code(double x, double y) {
	return (x * 27.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 27.0d0) * y
end function

Java

public static double code(double x, double y) {
	return (x * 27.0) * y;
}

Python

def code(x, y):
	return (x * 27.0) * y

Julia

function code(x, y)
	return Float64(Float64(x * 27.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 27.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(x * 27.0), $MachinePrecision] * y), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x_m, y_m] = \mathsf{sort}([x_m, y_m])\\ \\ y\_s \cdot \left(x\_s \cdot \left(\left(x\_m \cdot 27\right) \cdot y\_m\right)\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
(FPCore (y_s x_s x_m y_m)
 :precision binary64
 (* y_s (* x_s (* (* x_m 27.0) y_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
y\_m = fabs(y);
y\_s = copysign(1.0, y);
assert(x_m < y_m);
double code(double y_s, double x_s, double x_m, double y_m) {
	return y_s * (x_s * ((x_m * 27.0) * y_m));
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
y\_m = abs(y)
y\_s = copysign(1.0d0, y)
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
real(8) function code(y_s, x_s, x_m, y_m)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    code = y_s * (x_s * ((x_m * 27.0d0) * y_m))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
assert x_m < y_m;
public static double code(double y_s, double x_s, double x_m, double y_m) {
	return y_s * (x_s * ((x_m * 27.0) * y_m));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
[x_m, y_m] = sort([x_m, y_m])
def code(y_s, x_s, x_m, y_m):
	return y_s * (x_s * ((x_m * 27.0) * y_m))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
y\_m = abs(y)
y\_s = copysign(1.0, y)
x_m, y_m = sort([x_m, y_m])
function code(y_s, x_s, x_m, y_m)
	return Float64(y_s * Float64(x_s * Float64(Float64(x_m * 27.0) * y_m)))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
x_m, y_m = num2cell(sort([x_m, y_m])){:}
function tmp = code(y_s, x_s, x_m, y_m)
	tmp = y_s * (x_s * ((x_m * 27.0) * y_m));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_] := N[(y$95$s * N[(x$95$s * N[(N[(x$95$m * 27.0), $MachinePrecision] * y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

   \[\left(x \cdot 27\right) \cdot y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ y\_m = \left|y\right| \\ y\_s = \mathsf{copysign}\left(1, y\right) \\ [x_m, y_m] = \mathsf{sort}([x_m, y_m])\\ \\ y\_s \cdot \left(x\_s \cdot \left(x\_m \cdot \left(27 \cdot y\_m\right)\right)\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
y\_m = (fabs.f64 y)
y\_s = (copysign.f64 #s(literal 1 binary64) y)
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
(FPCore (y_s x_s x_m y_m)
 :precision binary64
 (* y_s (* x_s (* x_m (* 27.0 y_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
y\_m = fabs(y);
y\_s = copysign(1.0, y);
assert(x_m < y_m);
double code(double y_s, double x_s, double x_m, double y_m) {
	return y_s * (x_s * (x_m * (27.0 * y_m)));
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
y\_m = abs(y)
y\_s = copysign(1.0d0, y)
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
real(8) function code(y_s, x_s, x_m, y_m)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    code = y_s * (x_s * (x_m * (27.0d0 * y_m)))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
y\_m = Math.abs(y);
y\_s = Math.copySign(1.0, y);
assert x_m < y_m;
public static double code(double y_s, double x_s, double x_m, double y_m) {
	return y_s * (x_s * (x_m * (27.0 * y_m)));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
y\_m = math.fabs(y)
y\_s = math.copysign(1.0, y)
[x_m, y_m] = sort([x_m, y_m])
def code(y_s, x_s, x_m, y_m):
	return y_s * (x_s * (x_m * (27.0 * y_m)))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
y\_m = abs(y)
y\_s = copysign(1.0, y)
x_m, y_m = sort([x_m, y_m])
function code(y_s, x_s, x_m, y_m)
	return Float64(y_s * Float64(x_s * Float64(x_m * Float64(27.0 * y_m))))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
y\_m = abs(y);
y\_s = sign(y) * abs(1.0);
x_m, y_m = num2cell(sort([x_m, y_m])){:}
function tmp = code(y_s, x_s, x_m, y_m)
	tmp = y_s * (x_s * (x_m * (27.0 * y_m)));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
y\_m = N[Abs[y], $MachinePrecision]
y\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
code[y$95$s_, x$95$s_, x$95$m_, y$95$m_] := N[(y$95$s * N[(x$95$s * N[(x$95$m * N[(27.0 * y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

   \[\left(x \cdot 27\right) \cdot y \]
2. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto x \cdot \color{blue}{\left(27 \cdot y\right)} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(27 \cdot y\right)}\right) \]

   3. *-lowering-*.f64 99.7%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(27, \color{blue}{y}\right)\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{x \cdot \left(27 \cdot y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27.0) y))