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

Percentage Accurate: 99.7% → 99.7%

Time: 5.8s

Alternatives: 3

Speedup: 1.0×

• 26.2% 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

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

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(y * Float64(3.0 * Float64(x * y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 88.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*l* 89.5%

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

   2. associate-*l* 89.5%

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

3. Simplified 89.5%

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

   1. add-sqr-sqrt 89.3%

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

   2. sqrt-unprod 74.4%

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

   3. pow1/2 74.4%

      \[\leadsto x \cdot \color{blue}{{\left(\left(3 \cdot \left(y \cdot y\right)\right) \cdot \left(3 \cdot \left(y \cdot y\right)\right)\right)}^{0.5}} \]

   4. *-commutative 74.4%

      \[\leadsto x \cdot {\left(\color{blue}{\left(\left(y \cdot y\right) \cdot 3\right)} \cdot \left(3 \cdot \left(y \cdot y\right)\right)\right)}^{0.5} \]

   5. *-commutative 74.4%

      \[\leadsto x \cdot {\left(\left(\left(y \cdot y\right) \cdot 3\right) \cdot \color{blue}{\left(\left(y \cdot y\right) \cdot 3\right)}\right)}^{0.5} \]

   6. swap-sqr 74.4%

      \[\leadsto x \cdot {\color{blue}{\left(\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left(3 \cdot 3\right)\right)}}^{0.5} \]

   7. pow2 74.4%

      \[\leadsto x \cdot {\left(\left(\color{blue}{{y}^{2}} \cdot \left(y \cdot y\right)\right) \cdot \left(3 \cdot 3\right)\right)}^{0.5} \]

   8. pow2 74.4%

      \[\leadsto x \cdot {\left(\left({y}^{2} \cdot \color{blue}{{y}^{2}}\right) \cdot \left(3 \cdot 3\right)\right)}^{0.5} \]

   9. pow-prod-up 74.5%

      \[\leadsto x \cdot {\left(\color{blue}{{y}^{\left(2 + 2\right)}} \cdot \left(3 \cdot 3\right)\right)}^{0.5} \]

   10. metadata-eval 74.5%

       \[\leadsto x \cdot {\left({y}^{\color{blue}{4}} \cdot \left(3 \cdot 3\right)\right)}^{0.5} \]

   11. metadata-eval 74.5%

       \[\leadsto x \cdot {\left({y}^{4} \cdot \color{blue}{9}\right)}^{0.5} \]

6. Applied egg-rr 74.5%

   \[\leadsto x \cdot \color{blue}{{\left({y}^{4} \cdot 9\right)}^{0.5}} \]
7. Step-by-step derivation

   1. unpow1/2 74.5%

      \[\leadsto x \cdot \color{blue}{\sqrt{{y}^{4} \cdot 9}} \]

8. Simplified 74.5%

   \[\leadsto x \cdot \color{blue}{\sqrt{{y}^{4} \cdot 9}} \]
9. Step-by-step derivation

   1. *-commutative 74.5%

      \[\leadsto x \cdot \sqrt{\color{blue}{9 \cdot {y}^{4}}} \]

   2. sqrt-prod 74.4%

      \[\leadsto x \cdot \color{blue}{\left(\sqrt{9} \cdot \sqrt{{y}^{4}}\right)} \]

   3. metadata-eval 74.4%

      \[\leadsto x \cdot \left(\color{blue}{3} \cdot \sqrt{{y}^{4}}\right) \]

   4. sqrt-pow1 89.5%

      \[\leadsto x \cdot \left(3 \cdot \color{blue}{{y}^{\left(\frac{4}{2}\right)}}\right) \]

   5. metadata-eval 89.5%

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

   6. pow2 89.5%

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

   7. associate-*l* 89.5%

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

   8. *-commutative 89.5%

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

10. Applied egg-rr 89.5%

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

11. Final simplification 89.5%

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

Alternative 3: 88.2% accurate, 1.0× speedup

Math

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

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(x * Float64(3.0 * Float64(y * y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*l* 89.5%

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

   2. associate-*l* 89.5%

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

3. Simplified 89.5%

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

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 2024110 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :alt
  (* (* x (* 3.0 y)) y)

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