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

Percentage Accurate: 63.4% → 100.0%

Time: 4.6s

Alternatives: 3

Speedup: 3.0×

• 20.1% 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: 63.4% 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 65.9%

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

   1. sqr-neg 65.9%

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

   2. cancel-sign-sub 65.9%

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

   3. +-commutative 65.9%

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

   4. cancel-sign-sub-inv 65.9%

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

   5. +-commutative 65.9%

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

   6. *-commutative 65.9%

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

   7. associate-+l+ 65.9%

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

   8. associate-+r+ 75.8%

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

   9. sqr-neg 75.8%

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

   10. distribute-lft-neg-out 75.8%

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

   11. sub-neg 75.8%

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

   12. +-inverses 99.2%

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

   13. +-lft-identity 99.2%

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

   14. cancel-sign-sub-inv 99.2%

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

   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: 77.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+53} \lor \neg \left(z \leq 4.4 \cdot 10^{-49}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e+53) (not (<= z 4.4e-49))) (* z (- y)) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e+53) || !(z <= 4.4e-49)) {
		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 <= (-3d+53)) .or. (.not. (z <= 4.4d-49))) 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 <= -3e+53) || !(z <= 4.4e-49)) {
		tmp = z * -y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e+53) or not (z <= 4.4e-49):
		tmp = z * -y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e+53) || !(z <= 4.4e-49))
		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 <= -3e+53) || ~((z <= 4.4e-49)))
		tmp = z * -y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e+53], N[Not[LessEqual[z, 4.4e-49]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999998e53 or 4.3999999999999998e-49 < z

   1. Initial program 76.5%

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

      1. sqr-neg 76.5%

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

      2. cancel-sign-sub 76.5%

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

      3. +-commutative 76.5%

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

      4. cancel-sign-sub-inv 76.5%

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

      5. +-commutative 76.5%

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

      6. *-commutative 76.5%

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

      7. associate-+l+ 76.5%

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

      8. associate-+r+ 79.5%

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

      9. sqr-neg 79.5%

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

      10. distribute-lft-neg-out 79.5%

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

      11. sub-neg 79.5%

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

      12. +-inverses 98.2%

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

      13. +-lft-identity 98.2%

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

      14. cancel-sign-sub-inv 98.2%

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

      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 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-lft-neg-in 86.1%

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

      3. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   if -2.99999999999999998e53 < z < 4.3999999999999998e-49

   1. Initial program 57.7%

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

      1. sqr-neg 57.7%

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

      2. cancel-sign-sub 57.7%

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

      3. +-commutative 57.7%

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

      4. cancel-sign-sub-inv 57.7%

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

      5. +-commutative 57.7%

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

      6. *-commutative 57.7%

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

      7. associate-+l+ 57.7%

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

      8. associate-+r+ 72.9%

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

      9. sqr-neg 72.9%

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

      10. distribute-lft-neg-out 72.9%

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

      11. sub-neg 72.9%

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

      12. +-inverses 100.0%

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

      13. +-lft-identity 100.0%

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

      14. cancel-sign-sub-inv 100.0%

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

      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 83.7%

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

      1. *-commutative 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+53} \lor \neg \left(z \leq 4.4 \cdot 10^{-49}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.8% 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 65.9%

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

   1. sqr-neg 65.9%

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

   2. cancel-sign-sub 65.9%

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

   3. +-commutative 65.9%

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

   4. cancel-sign-sub-inv 65.9%

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

   5. +-commutative 65.9%

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

   6. *-commutative 65.9%

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

   7. associate-+l+ 65.9%

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

   8. associate-+r+ 75.8%

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

   9. sqr-neg 75.8%

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

   10. distribute-lft-neg-out 75.8%

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

   11. sub-neg 75.8%

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

   12. +-inverses 99.2%

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

   13. +-lft-identity 99.2%

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

   14. cancel-sign-sub-inv 99.2%

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

   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 56.6%

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

   1. *-commutative 56.6%

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

7. Simplified 56.6%

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

8. Final simplification 56.6%

   \[\leadsto y \cdot x \]
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 2024034 
(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)))