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

Percentage Accurate: 99.7% → 99.7%

Time: 4.1s

Alternatives: 6

Speedup: 1.0×

• 24.2% 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: 99.7% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Final simplification 99.7%

   \[\leadsto \left(y \cdot \left(3 \cdot x\right)\right) \cdot y \]
4. Add Preprocessing

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 99.6

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

5. Applied rewrites 99.6%

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

Alternative 3: 87.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(x \cdot {y}^{2}\right) \cdot 3} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot {y}^{2}\right) \cdot 3} \]

   3. *-commutative N/A

      \[\leadsto \color{blue}{\left({y}^{2} \cdot x\right)} \cdot 3 \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left({y}^{2} \cdot x\right)} \cdot 3 \]

   5. unpow2 N/A

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

   6. lower-*.f64 88.2

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

5. Applied rewrites 88.2%

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

Alternative 4: 20.7% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. pow2 N/A

      \[\leadsto \left(x \cdot 3\right) \cdot \color{blue}{{y}^{2}} \]

   5. pow-to-exp N/A

      \[\leadsto \left(x \cdot 3\right) \cdot \color{blue}{e^{\log y \cdot 2}} \]

   6. *-commutative N/A

      \[\leadsto \left(x \cdot 3\right) \cdot e^{\color{blue}{2 \cdot \log y}} \]

   7. count-2 N/A

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

   8. flip-+ N/A

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

   9. +-inverses N/A

      \[\leadsto \left(x \cdot 3\right) \cdot e^{\frac{\color{blue}{0}}{\log y - \log y}} \]

   10. +-inverses N/A

       \[\leadsto \left(x \cdot 3\right) \cdot e^{\frac{\color{blue}{\log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}}{\log y - \log y}} \]

   11. +-inverses N/A

       \[\leadsto \left(x \cdot 3\right) \cdot e^{\frac{\log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}{\color{blue}{0}}} \]

   12. +-inverses N/A

       \[\leadsto \left(x \cdot 3\right) \cdot e^{\frac{\log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}{\color{blue}{\log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}}} \]

   13. flip-+ N/A

       \[\leadsto \left(x \cdot 3\right) \cdot e^{\color{blue}{\log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) + \log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}} \]

   14. log-prod N/A

       \[\leadsto \left(x \cdot 3\right) \cdot e^{\color{blue}{\log \left({y}^{\left(\frac{\frac{2}{2}}{2}\right)} \cdot {y}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}} \]

   15. sqr-pow N/A

       \[\leadsto \left(x \cdot 3\right) \cdot e^{\log \color{blue}{\left({y}^{\left(\frac{2}{2}\right)}\right)}} \]

   16. metadata-eval N/A

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

   17. unpow1 N/A

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

   18. rem-exp-log N/A

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

   19. lift-*.f64 21.7

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

4. Applied rewrites 21.7%

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

5. Final simplification 21.7%

   \[\leadsto y \cdot \left(3 \cdot x\right) \]
6. Add Preprocessing

Alternative 5: 20.7% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(x \cdot {y}^{2}\right) \cdot 3} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot {y}^{2}\right) \cdot 3} \]

   3. *-commutative N/A

      \[\leadsto \color{blue}{\left({y}^{2} \cdot x\right)} \cdot 3 \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left({y}^{2} \cdot x\right)} \cdot 3 \]

   5. unpow2 N/A

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

   6. lower-*.f64 88.2

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

5. Applied rewrites 88.2%

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

7. Applied rewrites 21.7%

   \[\leadsto \left(y \cdot x\right) \cdot 3 \]
8. Add Preprocessing

Alternative 6: 5.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ 3 \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

4. Applied rewrites 4.9%

   \[\leadsto \color{blue}{x \cdot 3} \]

5. Final simplification 4.9%

   \[\leadsto 3 \cdot x \]
6. Add Preprocessing

Developer Target 1: 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 2024277 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (* (* x (* 3 y)) y))

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