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

Percentage Accurate: 88.5% → 99.7%

Time: 3.1s

Alternatives: 3

Speedup: 1.0×

• 25.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. *-commutative 91.7%

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

   2. associate-*l* 91.6%

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

3. Simplified 91.6%

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

   1. associate-*r* 91.7%

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

   2. *-commutative 91.7%

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

   3. associate-*r* 99.7%

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

   4. expm1-log1p-u 76.6%

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

   5. expm1-udef 52.1%

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

   6. log1p-udef 52.1%

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

   7. add-exp-log 75.2%

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

   8. *-commutative 75.2%

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

   9. associate-*l* 75.3%

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

5. Applied egg-rr 75.3%

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

   1. add-exp-log 51.8%

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

   2. associate--l+ 51.8%

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

   3. log1p-def 51.8%

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

   4. associate-*r* 50.8%

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

   5. *-commutative 50.8%

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

   6. associate-*r* 50.8%

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

   7. *-commutative 50.8%

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

   8. add-exp-log 49.4%

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

   9. expm1-def 49.4%

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

   10. log1p-expm1-u 57.7%

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

   11. associate-*r* 57.7%

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

   12. log-prod 38.1%

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

   13. add-sqr-sqrt 38.1%

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

   14. swap-sqr 38.1%

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

   15. unpow2 38.1%

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

   16. log-prod 57.7%

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

   17. add-exp-log 91.4%

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

7. Applied egg-rr 99.8%

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

8. Final simplification 99.8%

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

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 91.7%

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

   1. *-commutative 91.7%

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

   2. associate-*l* 91.6%

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

3. Simplified 91.6%

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

4. Taylor expanded in x around 0 91.7%

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

   1. unpow2 91.7%

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

6. Simplified 91.7%

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

7. Final simplification 91.7%

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

Alternative 3: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

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

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 2023199 
(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))