Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, C

Percentage Accurate: 99.7% → 99.7%

Time: 2.5s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot 3} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot 3} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{3}}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[\frac{x}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-lft-identity 99.7%

      \[\leadsto \color{blue}{1 \cdot \frac{x}{y \cdot 3}} \]

   2. metadata-eval 99.7%

      \[\leadsto \color{blue}{\frac{-1}{-1}} \cdot \frac{x}{y \cdot 3} \]

   3. times-frac 99.7%

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

   4. *-commutative 99.7%

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

   5. neg-mul-1 99.7%

      \[\leadsto \frac{x \cdot -1}{\color{blue}{-y \cdot 3}} \]

   6. distribute-rgt-neg-in 99.7%

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

   7. times-frac 99.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{-1}{-3}} \]

   8. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{-1}{-3}}{y}} \]

   9. associate-*r/ 99.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{-1}{-3}}{y}} \]

   10. metadata-eval 99.6%

       \[\leadsto x \cdot \frac{\frac{-1}{\color{blue}{-3}}}{y} \]

   11. metadata-eval 99.6%

       \[\leadsto x \cdot \frac{\color{blue}{0.3333333333333333}}{y} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x \cdot \frac{0.3333333333333333}{y}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{3}}}{y} \]

   2. associate-/r* 99.6%

      \[\leadsto x \cdot \color{blue}{\frac{1}{3 \cdot y}} \]

   3. *-commutative 99.6%

      \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot 3}} \]

   4. div-inv 99.7%

      \[\leadsto \color{blue}{\frac{x}{y \cdot 3}} \]

   5. *-commutative 99.7%

      \[\leadsto \frac{x}{\color{blue}{3 \cdot y}} \]

   6. associate-/r* 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{3}}{y}} \]

6. Applied egg-rr 99.7%

   \[\leadsto \color{blue}{\frac{\frac{x}{3}}{y}} \]

7. Final simplification 99.7%

   \[\leadsto \frac{\frac{x}{3}}{y} \]
8. Add Preprocessing

Alternative 2: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{0.3333333333333333}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ 0.3333333333333333 y)))

C

double code(double x, double y) {
	return x * (0.3333333333333333 / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (0.3333333333333333d0 / y)
end function

Java

public static double code(double x, double y) {
	return x * (0.3333333333333333 / y);
}

Python

def code(x, y):
	return x * (0.3333333333333333 / y)

Julia

function code(x, y)
	return Float64(x * Float64(0.3333333333333333 / y))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (0.3333333333333333 / y);
end

Wolfram

code[x_, y_] := N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\frac{x}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-lft-identity 99.7%

      \[\leadsto \color{blue}{1 \cdot \frac{x}{y \cdot 3}} \]

   2. metadata-eval 99.7%

      \[\leadsto \color{blue}{\frac{-1}{-1}} \cdot \frac{x}{y \cdot 3} \]

   3. times-frac 99.7%

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

   4. *-commutative 99.7%

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

   5. neg-mul-1 99.7%

      \[\leadsto \frac{x \cdot -1}{\color{blue}{-y \cdot 3}} \]

   6. distribute-rgt-neg-in 99.7%

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

   7. times-frac 99.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{-1}{-3}} \]

   8. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{-1}{-3}}{y}} \]

   9. associate-*r/ 99.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{-1}{-3}}{y}} \]

   10. metadata-eval 99.6%

       \[\leadsto x \cdot \frac{\frac{-1}{\color{blue}{-3}}}{y} \]

   11. metadata-eval 99.6%

       \[\leadsto x \cdot \frac{\color{blue}{0.3333333333333333}}{y} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x \cdot \frac{0.3333333333333333}{y}} \]
4. Add Preprocessing

5. Final simplification 99.6%

   \[\leadsto x \cdot \frac{0.3333333333333333}{y} \]
6. Add Preprocessing

Alternative 3: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{3 \cdot y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[\frac{x}{y \cdot 3} \]
2. Add Preprocessing

3. Final simplification 99.7%

   \[\leadsto \frac{x}{3 \cdot y} \]
4. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y}}{3} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024047 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :alt
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))