Examples.Basics.BasicTests:f3 from sbv-4.4

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 3

Speedup: 1.0×

• 44.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 57.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (y + (x * 2.0d0))
end function

Java

public static double code(double x, double y) {
	return y * (y + (x * 2.0));
}

Python

def code(x, y):
	return y * (y + (x * 2.0))

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = y * (y + (x * 2.0));
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 51.5%

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

   1. +-commutative 51.5%

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

   2. unpow2 51.5%

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

   3. associate-*r* 51.5%

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

   4. distribute-rgt-in 56.2%

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

5. Simplified 56.2%

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

6. Final simplification 56.2%

   \[\leadsto y \cdot \left(y + x \cdot 2\right) \]
7. Add Preprocessing

Alternative 3: 15.4% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (y * 2.0d0)
end function

Java

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

Python

def code(x, y):
	return x * (y * 2.0)

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = x * (y * 2.0);
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 51.5%

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

   1. +-commutative 51.5%

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

   2. unpow2 51.5%

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

   3. associate-*r* 51.5%

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

   4. distribute-rgt-in 56.2%

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

5. Simplified 56.2%

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

6. Taylor expanded in y around 0 12.9%

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

   1. associate-*r* 12.9%

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

   2. *-commutative 12.9%

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

   3. associate-*r* 12.9%

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

8. Simplified 12.9%

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

9. Final simplification 12.9%

   \[\leadsto x \cdot \left(y \cdot 2\right) \]
10. Add Preprocessing

Developer target: 93.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * x) + ((y * y) + (2.0d0 * (y * x)))
end function

Java

public static double code(double x, double y) {
	return (x * x) + ((y * y) + (2.0 * (y * x)));
}

Python

def code(x, y):
	return (x * x) + ((y * y) + (2.0 * (y * x)))

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = (x * x) + ((y * y) + (2.0 * (y * x)));
end

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

  :alt
  (+ (* x x) (+ (* y y) (* 2.0 (* y x))))

  (* (+ x y) (+ x y)))