Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F

Percentage Accurate: 99.8% → 99.8%

Time: 2.1s

Alternatives: 4

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot x \]
2. Add Preprocessing

3. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{3 \cdot {x}^{2}} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{{x}^{2} \cdot 3} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{{x}^{2} \cdot 3} \]

   3. unpow2 N/A

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

   4. lower-*.f64 99.8

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

5. Applied rewrites 99.8%

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

Alternative 3: 4.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return 3.0 * x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{3 \cdot {x}^{2}} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{{x}^{2} \cdot 3} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{{x}^{2} \cdot 3} \]

   3. unpow2 N/A

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

   4. lower-*.f64 99.8

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

5. Applied rewrites 99.8%

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

7. Applied rewrites 4.8%

   \[\leadsto x \cdot 3 \]

8. Final simplification 4.8%

   \[\leadsto 3 \cdot x \]
9. Add Preprocessing

Alternative 4: 4.3% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 3 \end{array} \]

FPCore

(FPCore (x) :precision binary64 3.0)

C

double code(double x) {
	return 3.0;
}

Fortran

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

Java

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

Python

def code(x):
	return 3.0

Julia

function code(x)
	return 3.0
end

MATLAB

function tmp = code(x)
	tmp = 3.0;
end

Wolfram

code[x_] := 3.0

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot x \]
2. Add Preprocessing

4. Applied rewrites 4.3%

   \[\leadsto \color{blue}{3} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024332 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))