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

Percentage Accurate: 68.7% → 100.0%

Time: 3.8s

Alternatives: 3

Speedup: 3.0×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 68.7% 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: 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 66.6%

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

   1. associate-+l- 73.8%

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

   2. *-commutative 73.8%

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

   3. +-inverses 97.7%

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

   4. --rgt-identity 97.7%

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

   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. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto y \cdot \left(x - z\right) \]
6. Add Preprocessing

Alternative 2: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2500000000000 \lor \neg \left(z \leq 4.9 \cdot 10^{+82}\right) \land \left(z \leq 9.5 \cdot 10^{+142} \lor \neg \left(z \leq 1.25 \cdot 10^{+200}\right)\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2500000000000.0)
         (and (not (<= z 4.9e+82))
              (or (<= z 9.5e+142) (not (<= z 1.25e+200)))))
   (* z (- y))
   (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2500000000000.0) || (!(z <= 4.9e+82) && ((z <= 9.5e+142) || !(z <= 1.25e+200)))) {
		tmp = z * -y;
	} 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 <= (-2500000000000.0d0)) .or. (.not. (z <= 4.9d+82)) .and. (z <= 9.5d+142) .or. (.not. (z <= 1.25d+200))) then
        tmp = z * -y
    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 <= -2500000000000.0) || (!(z <= 4.9e+82) && ((z <= 9.5e+142) || !(z <= 1.25e+200)))) {
		tmp = z * -y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2500000000000.0) or (not (z <= 4.9e+82) and ((z <= 9.5e+142) or not (z <= 1.25e+200))):
		tmp = z * -y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2500000000000.0) || (!(z <= 4.9e+82) && ((z <= 9.5e+142) || !(z <= 1.25e+200))))
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2500000000000.0) || (~((z <= 4.9e+82)) && ((z <= 9.5e+142) || ~((z <= 1.25e+200)))))
		tmp = z * -y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2500000000000.0], And[N[Not[LessEqual[z, 4.9e+82]], $MachinePrecision], Or[LessEqual[z, 9.5e+142], N[Not[LessEqual[z, 1.25e+200]], $MachinePrecision]]]], N[(z * (-y)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e12 or 4.9000000000000001e82 < z < 9.50000000000000001e142 or 1.25000000000000005e200 < z

   1. Initial program 68.9%

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

      1. associate-+l- 68.9%

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

      2. *-commutative 68.9%

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

      3. +-inverses 96.2%

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

      4. --rgt-identity 96.2%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 84.3%

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

      1. associate-*r* 84.3%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. *-commutative 84.3%

         \[\leadsto \color{blue}{z \cdot \left(-1 \cdot y\right)} \]

      3. mul-1-neg 84.3%

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

   7. Simplified 84.3%

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

   if -2.5e12 < z < 4.9000000000000001e82 or 9.50000000000000001e142 < z < 1.25000000000000005e200

   1. Initial program 64.9%

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

      1. associate-+l- 77.3%

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

      2. *-commutative 77.3%

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

      3. +-inverses 98.7%

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

      4. --rgt-identity 98.7%

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

      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. Add Preprocessing

   5. Taylor expanded in x around inf 84.5%

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

      1. *-commutative 84.5%

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

   7. Simplified 84.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2500000000000 \lor \neg \left(z \leq 4.9 \cdot 10^{+82}\right) \land \left(z \leq 9.5 \cdot 10^{+142} \lor \neg \left(z \leq 1.25 \cdot 10^{+200}\right)\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.0% 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 66.6%

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

   1. associate-+l- 73.8%

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

   2. *-commutative 73.8%

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

   3. +-inverses 97.7%

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

   4. --rgt-identity 97.7%

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

   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. Add Preprocessing

5. Taylor expanded in x around inf 58.6%

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

   1. *-commutative 58.6%

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

7. Simplified 58.6%

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

8. Final simplification 58.6%

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

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 2024011 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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