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

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 3

Speedup: 1.4×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ 1.0 2.0) (+ x y)))

C

double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 / 2.0d0) * (x + y)
end function

Java

public static double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Python

def code(x, y):
	return (1.0 / 2.0) * (x + y)

Julia

function code(x, y)
	return Float64(Float64(1.0 / 2.0) * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 / 2.0) * (x + y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ 1.0 2.0) (+ x y)))

C

double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 / 2.0d0) * (x + y)
end function

Java

public static double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Python

def code(x, y):
	return (1.0 / 2.0) * (x + y)

Julia

function code(x, y)
	return Float64(Float64(1.0 / 2.0) * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 / 2.0) * (x + y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (+ x y)))

C

double code(double x, double y) {
	return 0.5 * (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * (x + y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * (x + y);
}

Python

def code(x, y):
	return 0.5 * (x + y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * (x + y);
end

Wolfram

code[x_, y_] := N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{1}{2} \cdot \left(x + y\right) \]
2. Step-by-step derivation

   1. metadata-eval 100.0%

      \[\leadsto \color{blue}{0.5} \cdot \left(x + y\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-93} \lor \neg \left(y \leq 9 \cdot 10^{-72}\right) \land y \leq 7.2 \cdot 10^{-33}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y 5.2e-93) (and (not (<= y 9e-72)) (<= y 7.2e-33)))
   (* 0.5 x)
   (* 0.5 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= 5.2e-93) || (!(y <= 9e-72) && (y <= 7.2e-33))) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= 5.2d-93) .or. (.not. (y <= 9d-72)) .and. (y <= 7.2d-33)) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= 5.2e-93) || (!(y <= 9e-72) && (y <= 7.2e-33))) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= 5.2e-93) or (not (y <= 9e-72) and (y <= 7.2e-33)):
		tmp = 0.5 * x
	else:
		tmp = 0.5 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= 5.2e-93) || (!(y <= 9e-72) && (y <= 7.2e-33)))
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= 5.2e-93) || (~((y <= 9e-72)) && (y <= 7.2e-33)))
		tmp = 0.5 * x;
	else
		tmp = 0.5 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, 5.2e-93], And[N[Not[LessEqual[y, 9e-72]], $MachinePrecision], LessEqual[y, 7.2e-33]]], N[(0.5 * x), $MachinePrecision], N[(0.5 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.1999999999999997e-93 or 9e-72 < y < 7.20000000000000068e-33

   1. Initial program 100.0%

      \[\frac{1}{2} \cdot \left(x + y\right) \]
   2. Step-by-step derivation

      1. metadata-eval 100.0%

         \[\leadsto \color{blue}{0.5} \cdot \left(x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 62.2%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if 5.1999999999999997e-93 < y < 9e-72 or 7.20000000000000068e-33 < y

   1. Initial program 100.0%

      \[\frac{1}{2} \cdot \left(x + y\right) \]
   2. Step-by-step derivation

      1. metadata-eval 100.0%

         \[\leadsto \color{blue}{0.5} \cdot \left(x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.0%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-93} \lor \neg \left(y \leq 9 \cdot 10^{-72}\right) \land y \leq 7.2 \cdot 10^{-33}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 x))

C

double code(double x, double y) {
	return 0.5 * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * x
end function

Java

public static double code(double x, double y) {
	return 0.5 * x;
}

Python

def code(x, y):
	return 0.5 * x

Julia

function code(x, y)
	return Float64(0.5 * x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * x;
end

Wolfram

code[x_, y_] := N[(0.5 * x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{1}{2} \cdot \left(x + y\right) \]
2. Step-by-step derivation

   1. metadata-eval 100.0%

      \[\leadsto \color{blue}{0.5} \cdot \left(x + y\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{0.5 \cdot \left(x + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 52.7%

   \[\leadsto \color{blue}{0.5 \cdot x} \]
6. Add Preprocessing

Developer target: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) 2.0))

C

double code(double x, double y) {
	return (x + y) / 2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / 2.0d0
end function

Java

public static double code(double x, double y) {
	return (x + y) / 2.0;
}

Python

def code(x, y):
	return (x + y) / 2.0

Julia

function code(x, y)
	return Float64(Float64(x + y) / 2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / 2.0;
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / 2.0), $MachinePrecision]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, G"
  :precision binary64

  :alt
  (/ (+ x y) 2.0)

  (* (/ 1.0 2.0) (+ x y)))