Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 88.5% → 99.7%

Time: 6.2s

Alternatives: 4

Speedup: 1.0×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (* x 3.0) x) y))

C

double code(double x, double y) {
	return ((x * 3.0) * x) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 3.0d0) * x) * y
end function

Java

public static double code(double x, double y) {
	return ((x * 3.0) * x) * y;
}

Python

def code(x, y):
	return ((x * 3.0) * x) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 3.0) * x) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 3.0) * x) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision]

Initial Program: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (* x 3.0) x) y))

C

double code(double x, double y) {
	return ((x * 3.0) * x) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 3.0d0) * x) * y
end function

Java

public static double code(double x, double y) {
	return ((x * 3.0) * x) * y;
}

Python

def code(x, y):
	return ((x * 3.0) * x) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 3.0) * x) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 3.0) * x) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 3.0), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot \left(x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x 3.0) (* x y)))

C

double code(double x, double y) {
	return (x * 3.0) * (x * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 3.0d0) * (x * y)
end function

Java

public static double code(double x, double y) {
	return (x * 3.0) * (x * y);
}

Python

def code(x, y):
	return (x * 3.0) * (x * y)

Julia

function code(x, y)
	return Float64(Float64(x * 3.0) * Float64(x * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 3.0) * (x * y);
end

Wolfram

code[x_, y_] := N[(N[(x * 3.0), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.7%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. associate-*l* 99.7%

      \[\leadsto \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)} \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)} \]

4. Final simplification 99.7%

   \[\leadsto \left(x \cdot 3\right) \cdot \left(x \cdot y\right) \]

Alternative 2: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(y \cdot \left(x \cdot x\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 3.0 (* y (* x x))))

C

double code(double x, double y) {
	return 3.0 * (y * (x * x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 3.0d0 * (y * (x * x))
end function

Java

public static double code(double x, double y) {
	return 3.0 * (y * (x * x));
}

Python

def code(x, y):
	return 3.0 * (y * (x * x))

Julia

function code(x, y)
	return Float64(3.0 * Float64(y * Float64(x * x)))
end

MATLAB

function tmp = code(x, y)
	tmp = 3.0 * (y * (x * x));
end

Wolfram

code[x_, y_] := N[(3.0 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.7%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. *-commutative 88.7%

      \[\leadsto \left(\color{blue}{\left(3 \cdot x\right)} \cdot x\right) \cdot y \]

   2. associate-*l* 88.6%

      \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right)} \cdot y \]

3. Simplified 88.6%

   \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right) \cdot y} \]

4. Taylor expanded in x around 0 88.6%

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot {x}^{2}\right)} \]
5. Step-by-step derivation

   1. unpow2 88.6%

      \[\leadsto 3 \cdot \left(y \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

6. Simplified 88.6%

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot \left(x \cdot x\right)\right)} \]

7. Final simplification 88.6%

   \[\leadsto 3 \cdot \left(y \cdot \left(x \cdot x\right)\right) \]

Alternative 3: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(3 \cdot \left(x \cdot x\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y (* 3.0 (* x x))))

C

double code(double x, double y) {
	return y * (3.0 * (x * x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (3.0d0 * (x * x))
end function

Java

public static double code(double x, double y) {
	return y * (3.0 * (x * x));
}

Python

def code(x, y):
	return y * (3.0 * (x * x))

Julia

function code(x, y)
	return Float64(y * Float64(3.0 * Float64(x * x)))
end

MATLAB

function tmp = code(x, y)
	tmp = y * (3.0 * (x * x));
end

Wolfram

code[x_, y_] := N[(y * N[(3.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.7%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. *-commutative 88.7%

      \[\leadsto \left(\color{blue}{\left(3 \cdot x\right)} \cdot x\right) \cdot y \]

   2. associate-*l* 88.6%

      \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right)} \cdot y \]

3. Simplified 88.6%

   \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right) \cdot y} \]

4. Final simplification 88.6%

   \[\leadsto y \cdot \left(3 \cdot \left(x \cdot x\right)\right) \]

Alternative 4: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(3 \cdot \left(x \cdot y\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (* 3.0 (* x y))))

C

double code(double x, double y) {
	return x * (3.0 * (x * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (3.0d0 * (x * y))
end function

Java

public static double code(double x, double y) {
	return x * (3.0 * (x * y));
}

Python

def code(x, y):
	return x * (3.0 * (x * y))

Julia

function code(x, y)
	return Float64(x * Float64(3.0 * Float64(x * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (3.0 * (x * y));
end

Wolfram

code[x_, y_] := N[(x * N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.7%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. *-commutative 88.7%

      \[\leadsto \left(\color{blue}{\left(3 \cdot x\right)} \cdot x\right) \cdot y \]

   2. associate-*l* 88.6%

      \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right)} \cdot y \]

3. Simplified 88.6%

   \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot x\right)\right) \cdot y} \]
4. Step-by-step derivation

   1. associate-*r* 88.7%

      \[\leadsto \color{blue}{\left(\left(3 \cdot x\right) \cdot x\right)} \cdot y \]

   2. *-commutative 88.7%

      \[\leadsto \left(\color{blue}{\left(x \cdot 3\right)} \cdot x\right) \cdot y \]

   3. associate-*r* 99.7%

      \[\leadsto \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)} \]

   4. expm1-log1p-u 75.5%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)\right)} \]

   5. expm1-udef 50.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)} - 1} \]

   6. log1p-udef 50.5%

      \[\leadsto e^{\color{blue}{\log \left(1 + \left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)}} - 1 \]

   7. add-exp-log 74.7%

      \[\leadsto \color{blue}{\left(1 + \left(x \cdot 3\right) \cdot \left(x \cdot y\right)\right)} - 1 \]

   8. *-commutative 74.7%

      \[\leadsto \left(1 + \color{blue}{\left(3 \cdot x\right)} \cdot \left(x \cdot y\right)\right) - 1 \]

   9. associate-*l* 74.7%

      \[\leadsto \left(1 + \color{blue}{3 \cdot \left(x \cdot \left(x \cdot y\right)\right)}\right) - 1 \]

5. Applied egg-rr 74.7%

   \[\leadsto \color{blue}{\left(1 + 3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\right) - 1} \]
6. Step-by-step derivation

   1. add-exp-log 50.5%

      \[\leadsto \color{blue}{e^{\log \left(1 + 3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\right)}} - 1 \]

   2. log1p-udef 50.5%

      \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\right)}} - 1 \]

   3. expm1-udef 75.5%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\right)\right)} \]

   4. expm1-log1p-u 99.7%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot \left(x \cdot y\right)\right)} \]

   5. *-commutative 99.7%

      \[\leadsto 3 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot x\right)} \]

   6. associate-*r* 99.7%

      \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot y\right)\right) \cdot x} \]

7. Applied egg-rr 99.7%

   \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot y\right)\right) \cdot x} \]

8. Final simplification 99.7%

   \[\leadsto x \cdot \left(3 \cdot \left(x \cdot y\right)\right) \]

Developer target: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot \left(x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x 3.0) (* x y)))

C

double code(double x, double y) {
	return (x * 3.0) * (x * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 3.0d0) * (x * y)
end function

Java

public static double code(double x, double y) {
	return (x * 3.0) * (x * y);
}

Python

def code(x, y):
	return (x * 3.0) * (x * y)

Julia

function code(x, y)
	return Float64(Float64(x * 3.0) * Float64(x * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 3.0) * (x * y);
end

Wolfram

code[x_, y_] := N[(N[(x * 3.0), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023255 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* (* x 3.0) (* x y))

  (* (* (* x 3.0) x) y))