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

Percentage Accurate: 62.3% → 100.0%

Time: 2.8s

Alternatives: 3

Speedup: 3.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 62.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.7%

   \[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y \]
2. Step-by-step derivation

   1. associate-+l- 71.9%

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

   2. +-inverses 98.8%

      \[\leadsto \left(x \cdot y - y \cdot z\right) - \color{blue}{0} \]

   3. --rgt-identity 98.8%

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

   4. *-commutative 98.8%

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

   5. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto y \cdot \left(x - z\right) \]

Alternative 2: 76.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+70} \lor \neg \left(z \leq -6.6 \cdot 10^{+31}\right) \land \left(z \leq -7 \cdot 10^{-45} \lor \neg \left(z \leq 9.8 \cdot 10^{+33}\right)\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.65e+70)
         (and (not (<= z -6.6e+31)) (or (<= z -7e-45) (not (<= z 9.8e+33)))))
   (* y (- z))
   (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e+70) || (!(z <= -6.6e+31) && ((z <= -7e-45) || !(z <= 9.8e+33)))) {
		tmp = y * -z;
	} else {
		tmp = y * x;
	}
	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 <= (-2.65d+70)) .or. (.not. (z <= (-6.6d+31))) .and. (z <= (-7d-45)) .or. (.not. (z <= 9.8d+33))) then
        tmp = y * -z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e+70) || (!(z <= -6.6e+31) && ((z <= -7e-45) || !(z <= 9.8e+33)))) {
		tmp = y * -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.65e+70) or (not (z <= -6.6e+31) and ((z <= -7e-45) or not (z <= 9.8e+33))):
		tmp = y * -z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.65e+70) || (!(z <= -6.6e+31) && ((z <= -7e-45) || !(z <= 9.8e+33))))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.65e+70) || (~((z <= -6.6e+31)) && ((z <= -7e-45) || ~((z <= 9.8e+33)))))
		tmp = y * -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.65e+70], And[N[Not[LessEqual[z, -6.6e+31]], $MachinePrecision], Or[LessEqual[z, -7e-45], N[Not[LessEqual[z, 9.8e+33]], $MachinePrecision]]]], N[(y * (-z)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e70 or -6.59999999999999985e31 < z < -7e-45 or 9.80000000000000027e33 < z

   1. Initial program 61.9%

      \[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y \]
   2. Step-by-step derivation

      1. associate-+l- 71.0%

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

      2. +-inverses 98.1%

         \[\leadsto \left(x \cdot y - y \cdot z\right) - \color{blue}{0} \]

      3. --rgt-identity 98.1%

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

      4. *-commutative 98.1%

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

      5. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 84.6%

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

      2. distribute-rgt-neg-out 84.6%

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

   6. Simplified 84.6%

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

   if -2.65e70 < z < -6.59999999999999985e31 or -7e-45 < z < 9.80000000000000027e33

   1. Initial program 54.6%

      \[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y \]
   2. Step-by-step derivation

      1. associate-+l- 72.5%

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

      2. +-inverses 99.3%

         \[\leadsto \left(x \cdot y - y \cdot z\right) - \color{blue}{0} \]

      3. --rgt-identity 99.3%

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

      4. *-commutative 99.3%

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

      5. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 83.5%

      \[\leadsto \color{blue}{x \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 83.5%

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

   6. Simplified 83.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+70} \lor \neg \left(z \leq -6.6 \cdot 10^{+31}\right) \land \left(z \leq -7 \cdot 10^{-45} \lor \neg \left(z \leq 9.8 \cdot 10^{+33}\right)\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 52.9% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

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 * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.7%

   \[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y \]
2. Step-by-step derivation

   1. associate-+l- 71.9%

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

   2. +-inverses 98.8%

      \[\leadsto \left(x \cdot y - y \cdot z\right) - \color{blue}{0} \]

   3. --rgt-identity 98.8%

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

   4. *-commutative 98.8%

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

   5. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 58.2%

   \[\leadsto \color{blue}{x \cdot y} \]
5. Step-by-step derivation

   1. *-commutative 58.2%

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

6. Simplified 58.2%

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

7. Final simplification 58.2%

   \[\leadsto y \cdot x \]

Developer target: 100.0% accurate, 3.0× 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 2023331 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (- x z) y)

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