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

Percentage Accurate: 62.1% → 98.0%

Time: 1.4s

Alternatives: 4

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 62.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(y * y), $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 62.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 69.3%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 97.7%

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

Alternative 2: 70.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot y - y \cdot z\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+130}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y y) (* y z))))
   (if (<= z -8.5e-17) t_0 (if (<= z 2.05e+130) (* x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * y) - (y * z);
	double tmp;
	if (z <= -8.5e-17) {
		tmp = t_0;
	} else if (z <= 2.05e+130) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (y * y) - (y * z)
    if (z <= (-8.5d-17)) then
        tmp = t_0
    else if (z <= 2.05d+130) then
        tmp = x * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * y) - (y * z);
	double tmp;
	if (z <= -8.5e-17) {
		tmp = t_0;
	} else if (z <= 2.05e+130) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * y) - (y * z)
	tmp = 0
	if z <= -8.5e-17:
		tmp = t_0
	elif z <= 2.05e+130:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * y) - Float64(y * z))
	tmp = 0.0
	if (z <= -8.5e-17)
		tmp = t_0;
	elseif (z <= 2.05e+130)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * y) - (y * z);
	tmp = 0.0;
	if (z <= -8.5e-17)
		tmp = t_0;
	elseif (z <= 2.05e+130)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-17], t$95$0, If[LessEqual[z, 2.05e+130], N[(x * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e-17 or 2.04999999999999989e130 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 93.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 72.5%

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

   if -8.5e-17 < z < 2.04999999999999989e130

   1. Initial program 58.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.7%

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

Alternative 3: 53.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.4 \cdot 10^{+162}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 5.4e+162) (* x y) (* y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5.4e+162) {
		tmp = x * y;
	} else {
		tmp = y * 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 <= 5.4d+162) then
        tmp = x * y
    else
        tmp = y * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 5.4e+162) {
		tmp = x * y;
	} else {
		tmp = y * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5.4e+162:
		tmp = x * y
	else:
		tmp = y * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5.4e+162)
		tmp = Float64(x * y);
	else
		tmp = Float64(y * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 5.4e+162)
		tmp = x * y;
	else
		tmp = y * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5.4e+162], N[(x * y), $MachinePrecision], N[(y * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.4000000000000003e162

   1. Initial program 61.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.8%

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

   if 5.4000000000000003e162 < z

   1. Initial program 71.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 92.9%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 87.7%

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

   12. Taylor expanded in x around 0

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

   14. Applied rewrites 20.3%

       \[\leadsto y \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 14.5% accurate, 5.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return y * 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 = y * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 69.3%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 97.7%

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

9. Taylor expanded in x around inf

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

11. Applied rewrites 40.4%

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

12. Taylor expanded in x around 0

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

14. Applied rewrites 13.9%

    \[\leadsto y \cdot \color{blue}{y} \]
15. 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, C"
  :precision binary64
  :pre (TRUE)

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

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