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

Percentage Accurate: 62.8% → 100.0%

Time: 4.1s

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: 62.8% 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 61.8%

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

   1. sqr-neg 61.8%

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

   2. cancel-sign-sub 61.8%

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

   3. +-commutative 61.8%

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

   4. +-commutative 61.8%

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

   5. *-commutative 61.8%

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

   6. *-commutative 61.8%

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

   7. associate--l+ 61.8%

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

   8. associate-+r+ 73.0%

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

   9. sqr-neg 73.0%

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

   10. distribute-lft-neg-out 73.0%

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

   11. sub-neg 73.0%

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

   12. +-inverses 98.0%

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

   13. +-lft-identity 98.0%

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

   14. *-commutative 98.0%

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

   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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+56} \lor \neg \left(x \leq 1.55 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e+56) (not (<= x 1.55e+22))) (* y x) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+56) || !(x <= 1.55e+22)) {
		tmp = y * x;
	} else {
		tmp = z * -y;
	}
	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 <= (-1.4d+56)) .or. (.not. (x <= 1.55d+22))) then
        tmp = y * x
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+56) || !(x <= 1.55e+22)) {
		tmp = y * x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e+56) or not (x <= 1.55e+22):
		tmp = y * x
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e+56) || !(x <= 1.55e+22))
		tmp = Float64(y * x);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4e+56) || ~((x <= 1.55e+22)))
		tmp = y * x;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e+56], N[Not[LessEqual[x, 1.55e+22]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000004e56 or 1.5500000000000001e22 < x

   1. Initial program 71.1%

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

      1. sqr-neg 71.1%

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

      2. cancel-sign-sub 71.1%

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

      3. +-commutative 71.1%

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

      4. +-commutative 71.1%

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

      5. *-commutative 71.1%

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

      6. *-commutative 71.1%

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

      7. associate--l+ 71.1%

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

      8. associate-+r+ 74.4%

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

      9. sqr-neg 74.4%

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

      10. distribute-lft-neg-out 74.4%

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

      11. sub-neg 74.4%

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

      12. +-inverses 96.0%

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

      13. +-lft-identity 96.0%

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

      14. *-commutative 96.0%

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

      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. Add Preprocessing

   5. Taylor expanded in x around inf 81.2%

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

      1. *-commutative 81.2%

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

   7. Simplified 81.2%

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

   if -1.40000000000000004e56 < x < 1.5500000000000001e22

   1. Initial program 52.8%

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

      1. sqr-neg 52.8%

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

      2. cancel-sign-sub 52.8%

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

      3. +-commutative 52.8%

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

      4. +-commutative 52.8%

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

      5. *-commutative 52.8%

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

      6. *-commutative 52.8%

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

      7. associate--l+ 52.8%

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

      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 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. Add Preprocessing

   5. Taylor expanded in x around 0 82.4%

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

      1. associate-*r* 82.4%

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

      2. *-commutative 82.4%

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

      3. mul-1-neg 82.4%

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

   7. Simplified 82.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+56} \lor \neg \left(x \leq 1.55 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.3% 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 61.8%

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

   1. sqr-neg 61.8%

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

   2. cancel-sign-sub 61.8%

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

   3. +-commutative 61.8%

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

   4. +-commutative 61.8%

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

   5. *-commutative 61.8%

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

   6. *-commutative 61.8%

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

   7. associate--l+ 61.8%

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

   8. associate-+r+ 73.0%

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

   9. sqr-neg 73.0%

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

   10. distribute-lft-neg-out 73.0%

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

   11. sub-neg 73.0%

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

   12. +-inverses 98.0%

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

   13. +-lft-identity 98.0%

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

   14. *-commutative 98.0%

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

   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. Add Preprocessing

5. Taylor expanded in x around inf 52.3%

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

   1. *-commutative 52.3%

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

7. Simplified 52.3%

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

8. Final simplification 52.3%

   \[\leadsto y \cdot x \]
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 2024029 
(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)))