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

Percentage Accurate: 68.0% → 100.0%

Time: 13.6s

Alternatives: 3

Speedup: 3.0×

• 21.0% 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: 68.0% 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: 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 73.4%

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

   1. +-commutative N/A

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

   2. distribute-rgt-out-- N/A

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

   3. distribute-lft-out N/A

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

   4. distribute-lft-out-- N/A

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

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(y + \left(x - y\right)\right) - z\right)}\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\left(x - y\right) + y\right) - z\right)\right) \]

   7. associate-+r- N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(\left(x - y\right) + \color{blue}{\left(y - z\right)}\right)\right) \]

   8. associate-+l- N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(x - \color{blue}{\left(y - \left(y - z\right)\right)}\right)\right) \]

   9. associate--r- N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(\left(y - y\right) + \color{blue}{z}\right)\right)\right) \]

   10. +-inverses N/A

       \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(0 + z\right)\right)\right) \]

   11. +-lft-identity N/A

       \[\leadsto \mathsf{*.f64}\left(y, \left(x - z\right)\right) \]

   12. --lowering--.f64 100.0%

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{y \cdot \left(x - z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(0 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.6e+22) (* y x) (if (<= x 5.3e-33) (* y (- 0.0 z)) (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.6e+22) {
		tmp = y * x;
	} else if (x <= 5.3e-33) {
		tmp = y * (0.0 - 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 (x <= (-1.6d+22)) then
        tmp = y * x
    else if (x <= 5.3d-33) then
        tmp = y * (0.0d0 - 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 (x <= -1.6e+22) {
		tmp = y * x;
	} else if (x <= 5.3e-33) {
		tmp = y * (0.0 - z);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.6e+22:
		tmp = y * x
	elif x <= 5.3e-33:
		tmp = y * (0.0 - z)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.6e+22)
		tmp = Float64(y * x);
	elseif (x <= 5.3e-33)
		tmp = Float64(y * Float64(0.0 - z));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.6e+22)
		tmp = y * x;
	elseif (x <= 5.3e-33)
		tmp = y * (0.0 - z);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.6e+22], N[(y * x), $MachinePrecision], If[LessEqual[x, 5.3e-33], N[(y * N[(0.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e22 or 5.29999999999999968e-33 < x

   1. Initial program 76.4%

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

      1. +-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out-- N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(y + \left(x - y\right)\right) - z\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\left(x - y\right) + y\right) - z\right)\right) \]

      7. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\left(x - y\right) + \color{blue}{\left(y - z\right)}\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x - \color{blue}{\left(y - \left(y - z\right)\right)}\right)\right) \]

      9. associate--r- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(\left(y - y\right) + \color{blue}{z}\right)\right)\right) \]

      10. +-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(0 + z\right)\right)\right) \]

      11. +-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x - z\right)\right) \]

      12. --lowering--.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   7. Simplified 79.4%

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

   if -1.6e22 < x < 5.29999999999999968e-33

   1. Initial program 70.5%

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

      1. +-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. distribute-lft-out N/A

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

      4. distribute-lft-out-- N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(y + \left(x - y\right)\right) - z\right)}\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\left(x - y\right) + y\right) - z\right)\right) \]

      7. associate-+r- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\left(x - y\right) + \color{blue}{\left(y - z\right)}\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x - \color{blue}{\left(y - \left(y - z\right)\right)}\right)\right) \]

      9. associate--r- N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(\left(y - y\right) + \color{blue}{z}\right)\right)\right) \]

      10. +-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(0 + z\right)\right)\right) \]

      11. +-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x - z\right)\right) \]

      12. --lowering--.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

      1. flip-- N/A

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

      2. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{x + z}{x \cdot x - z \cdot z}}} \]

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{x + z}{x \cdot x - z \cdot z}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{1}{\color{blue}{\frac{x \cdot x - z \cdot z}{x + z}}}\right)\right) \]

      6. flip-- N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{1}{x - \color{blue}{z}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \color{blue}{\left(x - z\right)}\right)\right) \]

      8. --lowering--.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{1}{x - z}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{-1}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 82.8%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right) \]

   9. Simplified 82.8%

      \[\leadsto \frac{y}{\color{blue}{\frac{-1}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{z}}{y}}} \]

       2. div-inv N/A

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

       3. associate-/r* N/A

          \[\leadsto \frac{\frac{1}{\frac{-1}{z}}}{\color{blue}{\frac{1}{y}}} \]

       4. frac-2neg N/A

          \[\leadsto \frac{\frac{1}{\frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(z\right)}}}{\frac{1}{y}} \]

       5. metadata-eval N/A

          \[\leadsto \frac{\frac{1}{\frac{1}{\mathsf{neg}\left(z\right)}}}{\frac{1}{y}} \]

       6. remove-double-div N/A

          \[\leadsto \frac{\mathsf{neg}\left(z\right)}{\frac{\color{blue}{1}}{y}} \]

       7. distribute-neg-frac N/A

          \[\leadsto \mathsf{neg}\left(\frac{z}{\frac{1}{y}}\right) \]

       8. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{z}{\frac{1}{y}}\right)\right) \]

       9. associate-/r/ N/A

          \[\leadsto \mathsf{neg.f64}\left(\left(\frac{z}{1} \cdot y\right)\right) \]

       10. /-rgt-identity N/A

           \[\leadsto \mathsf{neg.f64}\left(\left(z \cdot y\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{neg.f64}\left(\left(y \cdot z\right)\right) \]

       12. *-lowering-*.f64 83.0%

           \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(y, z\right)\right) \]

   11. Applied egg-rr 83.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(0 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.7% 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 73.4%

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

   1. +-commutative N/A

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

   2. distribute-rgt-out-- N/A

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

   3. distribute-lft-out N/A

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

   4. distribute-lft-out-- N/A

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

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(y + \left(x - y\right)\right) - z\right)}\right) \]

   6. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(\left(\left(x - y\right) + y\right) - z\right)\right) \]

   7. associate-+r- N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(\left(x - y\right) + \color{blue}{\left(y - z\right)}\right)\right) \]

   8. associate-+l- N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(x - \color{blue}{\left(y - \left(y - z\right)\right)}\right)\right) \]

   9. associate--r- N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(\left(y - y\right) + \color{blue}{z}\right)\right)\right) \]

   10. +-inverses N/A

       \[\leadsto \mathsf{*.f64}\left(y, \left(x - \left(0 + z\right)\right)\right) \]

   11. +-lft-identity N/A

       \[\leadsto \mathsf{*.f64}\left(y, \left(x - z\right)\right) \]

   12. --lowering--.f64 100.0%

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(x, \color{blue}{z}\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 52.6%

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

7. Simplified 52.6%

   \[\leadsto \color{blue}{y \cdot x} \]
8. Add Preprocessing

Developer Target 1: 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 2024141 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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