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

Percentage Accurate: 64.1% → 100.0%

Time: 6.3s

Alternatives: 2

Speedup: 3.0×

• 20.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 64.1% 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: 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 64.3%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. associate-+r- N/A

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

   4. +-commutative N/A

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

   5. associate-+l+ N/A

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

   6. sub-neg N/A

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

   7. +-inverses N/A

      \[\leadsto \left(x \cdot y + 0\right) - y \cdot z \]

   8. +-rgt-identity N/A

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

   9. *-commutative N/A

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

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

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

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

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

   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: 54.8% 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 64.3%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. associate-+r- N/A

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

   4. +-commutative N/A

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

   5. associate-+l+ N/A

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

   6. sub-neg N/A

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

   7. +-inverses N/A

      \[\leadsto \left(x \cdot y + 0\right) - y \cdot z \]

   8. +-rgt-identity N/A

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

   9. *-commutative N/A

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

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

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

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

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

   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 49.0%

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

7. Simplified 49.0%

   \[\leadsto \color{blue}{y \cdot x} \]
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 2024163 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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