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

Percentage Accurate: 99.7% → 99.7%

Time: 5.4s

Alternatives: 3

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. add-cbrt-cube 83.2%

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

   2. pow3 83.2%

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

   3. *-commutative 83.2%

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

   4. associate-*l* 83.2%

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

3. Applied egg-rr 83.2%

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

   1. rem-cbrt-cube 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%

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

   4. *-commutative 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

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 99.3%

   \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y \]
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* 86.1%

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

3. Simplified 86.1%

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

4. Taylor expanded in x around 0 86.5%

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

   1. unpow2 86.5%

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

   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%

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

Alternative 3: 99.7% accurate, 1.0× speedup

Math

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

   \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y \]
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* 86.1%

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

3. Simplified 86.1%

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

   1. associate-*l* 86.1%

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

   2. associate-*l* 86.2%

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

   3. add-sqr-sqrt 55.9%

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

   4. sqrt-unprod 50.3%

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

   5. pow2 50.3%

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

   6. add-sqr-sqrt 49.8%

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

   7. pow2 49.8%

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

   8. pow-pow 49.8%

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

   9. *-commutative 49.8%

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

   10. sqrt-prod 38.2%

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

   11. sqrt-prod 17.1%

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

   12. add-sqr-sqrt 41.5%

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

   13. metadata-eval 41.5%

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

5. Applied egg-rr 41.5%

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

   1. sqrt-pow1 51.7%

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

   2. metadata-eval 51.7%

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

   3. unpow2 51.7%

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

   4. swap-sqr 44.3%

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

   5. add-sqr-sqrt 86.2%

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

   6. associate-*l* 86.5%

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

   7. associate-*r* 99.7%

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

   8. *-commutative 99.7%

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

   9. *-commutative 99.7%

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

   10. associate-*l* 99.7%

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

   11. *-commutative 99.7%

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

7. Applied egg-rr 99.7%

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

8. Final simplification 99.7%

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

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 2023196 
(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))