Linear.Quaternion:$c/ from linear-1.19.1.3, D

Percentage Accurate: 68.0% → 98.0%

Time: 1.4s

Alternatives: 3

Speedup: 2.1×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x \cdot y - y \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x y) (* y z)))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x * y) - (y * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * y) - Float64(y * z))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot y} - y \cdot z \]

5. Applied rewrites 66.3%

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

6. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \color{blue}{{y}^{2}} - y \cdot z \]

8. Applied rewrites 97.7%

   \[\leadsto x \cdot \color{blue}{y} - y \cdot z \]
9. Add Preprocessing

Alternative 2: 53.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-17}:\\ \;\;\;\;x \cdot y + y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.2e-17) (+ (* x y) (* y y)) (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e-17) {
		tmp = (x * y) + (y * y);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6.2d-17)) then
        tmp = (x * y) + (y * y)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e-17) {
		tmp = (x * y) + (y * y);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.2e-17:
		tmp = (x * y) + (y * y)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.2e-17)
		tmp = Float64(Float64(x * y) + Float64(y * y));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.2e-17)
		tmp = (x * y) + (y * y);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.2e-17], N[(N[(x * y), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999997e-17

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot y - y \cdot z} \]

   5. Applied rewrites 17.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto -1 \cdot {y}^{2} + \color{blue}{y} \cdot y \]

   8. Applied rewrites 31.4%

      \[\leadsto x \cdot y + \color{blue}{y} \cdot y \]

   if -6.1999999999999997e-17 < z

   1. Initial program 66.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot y - y \cdot z} \]

   5. Applied rewrites 41.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 44.3%

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

   9. Taylor expanded in x around 0

      \[\leadsto -1 \cdot {y}^{\color{blue}{2}} \]

   11. Applied rewrites 64.6%

       \[\leadsto x \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 53.2% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot y - y \cdot z} \]

5. Applied rewrites 35.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 39.6%

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

9. Taylor expanded in x around 0

   \[\leadsto -1 \cdot {y}^{\color{blue}{2}} \]

11. Applied rewrites 54.5%

    \[\leadsto x \cdot y \]
12. Add Preprocessing

Developer Target 1: 100.0% accurate, 3.3× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (- x z) y))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x - z) * y

Julia

function code(x, y, z)
	return Float64(Float64(x - z) * y)
end

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (* (- x z) y))

  (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))