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

Percentage Accurate: 99.6% → 99.7%

Time: 5.9s

Alternatives: 2

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. add-cube-cbrt 98.9%

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

   2. pow3 98.9%

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

   3. *-commutative 98.9%

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

   4. associate-*l* 98.9%

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

3. Applied egg-rr 98.9%

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

   1. rem-cube-cbrt 99.7%

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

   2. *-commutative 99.7%

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

   3. associate-*r* 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-*l* 99.7%

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

   2. associate-*l* 90.5%

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

3. Simplified 90.5%

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

4. Taylor expanded in x around 0 90.5%

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

   1. unpow2 90.5%

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

   2. associate-*l* 99.7%

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

6. Simplified 99.7%

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

7. Final simplification 99.7%

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

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023278 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

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

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