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

Percentage Accurate: 88.2% → 99.6%

Time: 4.6s

Alternatives: 4

Speedup: 1.0×

• 24.3% 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: 88.2% 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: 99.6% accurate, 1.0× speedup

Math

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
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* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around 0 89.2%

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

   1. unpow2 89.2%

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

   2. *-commutative 89.2%

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

   3. rem-exp-log 40.9%

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

   4. *-rgt-identity 40.9%

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

   5. associate-*l* 45.6%

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

   6. *-rgt-identity 45.6%

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

   7. rem-exp-log 99.7%

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

6. Simplified 99.7%

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

   1. add-cube-cbrt 99.0%

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

   2. pow3 99.0%

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

8. Applied egg-rr 99.0%

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

   1. add-log-exp 60.1%

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

   2. *-un-lft-identity 60.1%

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

   3. log-prod 60.1%

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

   4. metadata-eval 60.1%

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

   5. add-log-exp 99.0%

      \[\leadsto 0 + \color{blue}{3 \cdot {\left(\sqrt[3]{x \cdot \left(x \cdot y\right)}\right)}^{3}} \]

   6. *-commutative 99.0%

      \[\leadsto 0 + \color{blue}{{\left(\sqrt[3]{x \cdot \left(x \cdot y\right)}\right)}^{3} \cdot 3} \]

   7. unpow3 99.0%

      \[\leadsto 0 + \color{blue}{\left(\left(\sqrt[3]{x \cdot \left(x \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(x \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(x \cdot y\right)}\right)} \cdot 3 \]

   8. add-cube-cbrt 99.7%

      \[\leadsto 0 + \color{blue}{\left(x \cdot \left(x \cdot y\right)\right)} \cdot 3 \]

   9. associate-*l* 99.8%

      \[\leadsto 0 + \color{blue}{x \cdot \left(\left(x \cdot y\right) \cdot 3\right)} \]

   10. associate-*l* 99.8%

       \[\leadsto 0 + x \cdot \color{blue}{\left(x \cdot \left(y \cdot 3\right)\right)} \]

10. Applied egg-rr 99.8%

    \[\leadsto \color{blue}{0 + x \cdot \left(x \cdot \left(y \cdot 3\right)\right)} \]

11. Final simplification 99.8%

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

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 89.3%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
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* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around 0 89.2%

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

   1. unpow2 89.2%

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

   2. *-commutative 89.2%

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

   3. rem-exp-log 40.9%

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

   4. *-rgt-identity 40.9%

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

   5. associate-*l* 45.6%

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

   6. *-rgt-identity 45.6%

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

   7. rem-exp-log 99.7%

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

6. Simplified 99.7%

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

7. Final simplification 99.7%

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

Alternative 3: 99.7% accurate, 1.0× speedup

Math

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
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* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 4: 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 89.3%

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

   1. *-commutative 89.3%

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

   2. associate-*l* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

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 2023266 
(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))