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

Percentage Accurate: 88.2% → 99.8%

Time: 4.3s

Alternatives: 3

Speedup: 1.0×

• 24.4% 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: 88.2% 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: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ x \cdot \mathsf{fma}\left(x, y, y \cdot \left(x \cdot 2\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (fma x y (* y (* x 2.0)))))

C

double code(double x, double y) {
	return x * fma(x, y, (y * (x * 2.0)));
}

Julia

function code(x, y)
	return Float64(x * fma(x, y, Float64(y * Float64(x * 2.0))))
end

Wolfram

code[x_, y_] := N[(x * N[(x * y + N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

   1. associate-*l* 99.7%

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

   2. associate-*l* 99.7%

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

3. Simplified 99.7%

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

   1. associate-*r* 99.7%

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

   2. *-commutative 99.7%

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

   3. associate-*r* 99.7%

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

   4. add-log-exp 56.0%

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

   5. add-cube-cbrt 55.9%

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

   6. log-prod 55.9%

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

   7. pow2 55.9%

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

   8. associate-*r* 55.9%

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

   9. *-commutative 55.9%

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

   10. associate-*r* 55.9%

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

   11. *-commutative 55.9%

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

   12. exp-prod 55.9%

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

   13. pow3 55.9%

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

   14. add-cbrt-cube 55.9%

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

   15. exp-prod 54.1%

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

   16. associate-*r* 54.1%

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

6. Applied egg-rr 56.8%

   \[\leadsto x \cdot \color{blue}{\left(\log \left({\left({\left(e^{x}\right)}^{y}\right)}^{2}\right) + x \cdot y\right)} \]
7. Step-by-step derivation

   1. +-commutative 56.8%

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

   2. fma-define 56.8%

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

   3. exp-prod 58.8%

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

   4. unpow2 58.8%

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

   5. prod-exp 58.9%

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

   6. rem-log-exp 99.8%

      \[\leadsto x \cdot \mathsf{fma}\left(x, y, \color{blue}{x \cdot y + x \cdot y}\right) \]

   7. distribute-rgt-out 99.8%

      \[\leadsto x \cdot \mathsf{fma}\left(x, y, \color{blue}{y \cdot \left(x + x\right)}\right) \]

   8. count-2 99.8%

      \[\leadsto x \cdot \mathsf{fma}\left(x, y, y \cdot \color{blue}{\left(2 \cdot x\right)}\right) \]

   9. *-commutative 99.8%

      \[\leadsto x \cdot \mathsf{fma}\left(x, y, y \cdot \color{blue}{\left(x \cdot 2\right)}\right) \]

8. Simplified 99.8%

   \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(x, y, y \cdot \left(x \cdot 2\right)\right)} \]

9. Final simplification 99.8%

   \[\leadsto x \cdot \mathsf{fma}\left(x, y, y \cdot \left(x \cdot 2\right)\right) \]
10. Add Preprocessing

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-*l* 99.7%

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

   2. associate-*l* 99.7%

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

3. Simplified 99.7%

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

   1. add-sqr-sqrt 68.9%

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

   2. pow2 68.9%

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

   3. associate-*r* 68.9%

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

   4. *-commutative 68.9%

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

   5. associate-*r* 68.8%

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

   6. associate-*r* 61.1%

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

   7. sqrt-prod 48.5%

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

   8. sqrt-unprod 31.8%

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

   9. add-sqr-sqrt 56.3%

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

6. Applied egg-rr 56.3%

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

   1. unpow2 56.3%

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

   2. swap-sqr 48.5%

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

   3. add-sqr-sqrt 86.0%

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

   4. associate-*l* 99.7%

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

   5. associate-*l* 99.7%

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

   6. *-commutative 99.7%

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

   7. *-commutative 99.7%

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

   8. associate-*l* 99.7%

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

   9. associate-*l* 99.7%

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

8. Applied egg-rr 99.7%

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

9. Final simplification 99.7%

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

Alternative 3: 99.7% accurate, 1.0× speedup

Math

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. *-commutative 86.1%

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

   2. associate-*l* 99.7%

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

   3. associate-*r* 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in x around 0 99.7%

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

   1. associate-*r* 99.7%

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

7. Simplified 99.7%

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

8. Final simplification 99.7%

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

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 2024044 
(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))