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

Percentage Accurate: 62.4% → 100.0%

Time: 5.7s

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: 62.4% 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 63.5%

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

   1. cancel-sign-sub-inv 63.5%

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

   2. +-commutative 63.5%

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

   3. *-commutative 63.5%

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

   4. associate-+r+ 63.5%

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

   5. +-commutative 63.5%

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

   6. associate--l+ 75.4%

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

   7. +-inverses 98.0%

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

   8. +-rgt-identity 98.0%

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

   9. cancel-sign-sub-inv 98.0%

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

   10. 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. Add Preprocessing

Alternative 2: 77.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-51} \lor \neg \left(x \leq 7.2 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-51) (not (<= x 7.2e-11))) (* y x) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-51) || !(x <= 7.2e-11)) {
		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 <= (-3.8d-51)) .or. (.not. (x <= 7.2d-11))) 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 <= -3.8e-51) || !(x <= 7.2e-11)) {
		tmp = y * x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-51) or not (x <= 7.2e-11):
		tmp = y * x
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-51) || !(x <= 7.2e-11))
		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 <= -3.8e-51) || ~((x <= 7.2e-11)))
		tmp = y * x;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-51], N[Not[LessEqual[x, 7.2e-11]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000003e-51 or 7.19999999999999969e-11 < x

   1. Initial program 69.7%

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

      1. cancel-sign-sub-inv 69.7%

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

      2. +-commutative 69.7%

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

      3. *-commutative 69.7%

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

      4. associate-+r+ 69.7%

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

      5. +-commutative 69.7%

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

      6. associate--l+ 77.7%

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

      7. +-inverses 96.1%

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

      8. +-rgt-identity 96.1%

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

      9. cancel-sign-sub-inv 96.1%

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

      10. 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 76.0%

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

      1. *-commutative 76.0%

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

   7. Simplified 76.0%

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

   if -3.80000000000000003e-51 < x < 7.19999999999999969e-11

   1. Initial program 57.2%

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

      1. cancel-sign-sub-inv 57.2%

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

      2. +-commutative 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-+r+ 57.2%

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

      5. +-commutative 57.2%

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

      6. associate--l+ 73.0%

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

      7. +-inverses 100.0%

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

      8. +-rgt-identity 100.0%

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

      9. cancel-sign-sub-inv 100.0%

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

      10. 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 88.8%

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

      1. mul-1-neg 88.8%

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

      2. distribute-rgt-neg-out 88.8%

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

   7. Simplified 88.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-51} \lor \neg \left(x \leq 7.2 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.7% 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 63.5%

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

   1. cancel-sign-sub-inv 63.5%

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

   2. +-commutative 63.5%

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

   3. *-commutative 63.5%

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

   4. associate-+r+ 63.5%

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

   5. +-commutative 63.5%

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

   6. associate--l+ 75.4%

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

   7. +-inverses 98.0%

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

   8. +-rgt-identity 98.0%

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

   9. cancel-sign-sub-inv 98.0%

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

   10. 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 50.2%

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

   1. *-commutative 50.2%

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

7. Simplified 50.2%

   \[\leadsto \color{blue}{y \cdot x} \]
8. 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 2024091 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :alt
  (* (- x z) y)

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