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

Percentage Accurate: 63.6% → 100.0%

Time: 3.9s

Alternatives: 3

Speedup: 3.0×

• 20.9% 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: 63.6% 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 66.7%

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

   1. sqr-neg 66.7%

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

   2. cancel-sign-sub 66.7%

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

   3. +-commutative 66.7%

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

   4. +-commutative 66.7%

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

   5. *-commutative 66.7%

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

   6. associate--l+ 66.7%

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

   7. associate-+r+ 79.7%

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

   8. sqr-neg 79.7%

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

   9. distribute-lft-neg-out 79.7%

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

   10. sub-neg 79.7%

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

   11. +-inverses 98.0%

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

   12. +-lft-identity 98.0%

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

   13. 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: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-66}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138} \lor \neg \left(x \leq 3.3 \cdot 10^{-79}\right) \land x \leq 1.85 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.4e-66)
   (* y x)
   (if (or (<= x 1.55e-138) (and (not (<= x 3.3e-79)) (<= x 1.85e+24)))
     (* y (- z))
     (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.4e-66) {
		tmp = y * x;
	} else if ((x <= 1.55e-138) || (!(x <= 3.3e-79) && (x <= 1.85e+24))) {
		tmp = y * -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 <= (-8.4d-66)) then
        tmp = y * x
    else if ((x <= 1.55d-138) .or. (.not. (x <= 3.3d-79)) .and. (x <= 1.85d+24)) then
        tmp = y * -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 <= -8.4e-66) {
		tmp = y * x;
	} else if ((x <= 1.55e-138) || (!(x <= 3.3e-79) && (x <= 1.85e+24))) {
		tmp = y * -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.4e-66:
		tmp = y * x
	elif (x <= 1.55e-138) or (not (x <= 3.3e-79) and (x <= 1.85e+24)):
		tmp = y * -z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.4e-66)
		tmp = Float64(y * x);
	elseif ((x <= 1.55e-138) || (!(x <= 3.3e-79) && (x <= 1.85e+24)))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.4e-66)
		tmp = y * x;
	elseif ((x <= 1.55e-138) || (~((x <= 3.3e-79)) && (x <= 1.85e+24)))
		tmp = y * -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.4e-66], N[(y * x), $MachinePrecision], If[Or[LessEqual[x, 1.55e-138], And[N[Not[LessEqual[x, 3.3e-79]], $MachinePrecision], LessEqual[x, 1.85e+24]]], N[(y * (-z)), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4000000000000001e-66 or 1.5499999999999999e-138 < x < 3.2999999999999998e-79 or 1.85e24 < x

   1. Initial program 73.0%

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

      1. sqr-neg 73.0%

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

      2. cancel-sign-sub 73.0%

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

      3. +-commutative 73.0%

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

      4. +-commutative 73.0%

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

      5. *-commutative 73.0%

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

      6. associate--l+ 73.0%

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

      7. associate-+r+ 79.6%

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

      8. sqr-neg 79.6%

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

      9. distribute-lft-neg-out 79.6%

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

      10. sub-neg 79.6%

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

      11. +-inverses 96.5%

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

      12. +-lft-identity 96.5%

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

      13. 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 77.4%

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

      1. *-commutative 77.4%

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

   6. Simplified 77.4%

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

   if -8.4000000000000001e-66 < x < 1.5499999999999999e-138 or 3.2999999999999998e-79 < x < 1.85e24

   1. Initial program 59.0%

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

      1. sqr-neg 59.0%

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

      2. cancel-sign-sub 59.0%

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

      3. +-commutative 59.0%

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

      4. +-commutative 59.0%

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

      5. *-commutative 59.0%

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

      6. associate--l+ 59.0%

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

      7. associate-+r+ 79.8%

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

      8. sqr-neg 79.8%

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

      9. distribute-lft-neg-out 79.8%

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

      10. sub-neg 79.8%

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

      11. +-inverses 100.0%

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

      12. +-lft-identity 100.0%

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

      13. 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 87.6%

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

      1. mul-1-neg 87.6%

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

      2. distribute-rgt-neg-out 87.6%

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

   6. Simplified 87.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-66}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-138} \lor \neg \left(x \leq 3.3 \cdot 10^{-79}\right) \land x \leq 1.85 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 54.2% 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 66.7%

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

   1. sqr-neg 66.7%

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

   2. cancel-sign-sub 66.7%

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

   3. +-commutative 66.7%

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

   4. +-commutative 66.7%

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

   5. *-commutative 66.7%

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

   6. associate--l+ 66.7%

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

   7. associate-+r+ 79.7%

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

   8. sqr-neg 79.7%

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

   9. distribute-lft-neg-out 79.7%

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

   10. sub-neg 79.7%

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

   11. +-inverses 98.0%

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

   12. +-lft-identity 98.0%

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

   13. 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 51.8%

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

   1. *-commutative 51.8%

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

6. Simplified 51.8%

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

7. Final simplification 51.8%

   \[\leadsto y \cdot x \]

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 2023271 
(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)))