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

Percentage Accurate: 99.7% → 99.7%

Time: 3.1s

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. /-rgt-identity 99.7%

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

   2. metadata-eval 99.7%

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

   3. associate-/l* 99.7%

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

   4. times-frac 99.2%

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

   5. metadata-eval 99.2%

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

   6. metadata-eval 99.2%

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

3. Simplified 99.2%

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

   1. metadata-eval 99.2%

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

   2. div-inv 99.4%

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

   3. associate-/l/ 99.7%

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

   4. 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. Add Preprocessing

Alternative 2: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. clear-num 99.4%

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

   2. associate-/r/ 99.6%

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

   3. *-commutative 99.6%

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

   4. associate-/r* 99.6%

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

   5. metadata-eval 99.6%

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

4. Applied egg-rr 99.6%

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

Alternative 3: 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]

Derivation

1. Initial program 99.7%

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

Developer target: 99.6% 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 2024034 -o generate:simplify
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3.0)

  (/ x (* y 3.0)))