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

Percentage Accurate: 62.6% → 100.0%

Time: 3.7s

Alternatives: 3

Speedup: 3.0×

• 20.7% 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: 62.6% 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 63.6%

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

   1. sqr-neg 63.6%

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

   2. cancel-sign-sub 63.6%

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

   3. +-commutative 63.6%

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

   4. +-commutative 63.6%

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

   5. *-commutative 63.6%

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

   6. *-commutative 63.6%

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

   7. associate--l+ 63.6%

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

   8. associate-+r+ 74.2%

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

   9. sqr-neg 74.2%

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

   10. distribute-lft-neg-out 74.2%

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

   11. sub-neg 74.2%

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

   12. +-inverses 94.9%

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

   13. +-lft-identity 94.9%

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

   14. *-commutative 94.9%

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

   15. 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: 78.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32} \lor \neg \left(z \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+32) (not (<= z 2e+28))) (* z (- y)) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+32) || !(z <= 2e+28)) {
		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 <= (-1.5d+32)) .or. (.not. (z <= 2d+28))) 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 <= -1.5e+32) || !(z <= 2e+28)) {
		tmp = z * -y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e+32) or not (z <= 2e+28):
		tmp = z * -y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e+32) || !(z <= 2e+28))
		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 <= -1.5e+32) || ~((z <= 2e+28)))
		tmp = z * -y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e+32], N[Not[LessEqual[z, 2e+28]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e32 or 1.99999999999999992e28 < z

   1. Initial program 70.8%

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

      1. sqr-neg 70.8%

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

      2. cancel-sign-sub 70.8%

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

      3. +-commutative 70.8%

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

      4. +-commutative 70.8%

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

      5. *-commutative 70.8%

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

      6. *-commutative 70.8%

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

      7. associate--l+ 70.8%

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

      8. associate-+r+ 71.7%

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

      9. sqr-neg 71.7%

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

      10. distribute-lft-neg-out 71.7%

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

      11. sub-neg 71.7%

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

      12. +-inverses 89.2%

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

      13. +-lft-identity 89.2%

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

      14. *-commutative 89.2%

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

      15. 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 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-rgt-neg-out 80.4%

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

   6. Simplified 80.4%

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

   if -1.5e32 < z < 1.99999999999999992e28

   1. Initial program 57.3%

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

      1. sqr-neg 57.3%

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

      2. cancel-sign-sub 57.3%

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

      3. +-commutative 57.3%

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

      4. +-commutative 57.3%

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

      5. *-commutative 57.3%

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

      6. *-commutative 57.3%

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

      7. associate--l+ 57.3%

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

      8. associate-+r+ 76.5%

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

      9. sqr-neg 76.5%

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

      10. distribute-lft-neg-out 76.5%

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

      11. sub-neg 76.5%

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

      12. +-inverses 100.0%

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

      13. +-lft-identity 100.0%

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

      14. *-commutative 100.0%

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

      15. 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 79.9%

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

      1. *-commutative 79.9%

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

   6. Simplified 79.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32} \lor \neg \left(z \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 53.0% 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 63.6%

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

   1. sqr-neg 63.6%

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

   2. cancel-sign-sub 63.6%

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

   3. +-commutative 63.6%

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

   4. +-commutative 63.6%

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

   5. *-commutative 63.6%

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

   6. *-commutative 63.6%

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

   7. associate--l+ 63.6%

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

   8. associate-+r+ 74.2%

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

   9. sqr-neg 74.2%

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

   10. distribute-lft-neg-out 74.2%

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

   11. sub-neg 74.2%

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

   12. +-inverses 94.9%

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

   13. +-lft-identity 94.9%

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

   14. *-commutative 94.9%

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

   15. 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 53.9%

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

   1. *-commutative 53.9%

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

6. Simplified 53.9%

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

7. Final simplification 53.9%

   \[\leadsto y \cdot x \]

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 2023308 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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