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

Percentage Accurate: 68.2% → 100.0%

Time: 2.8s

Alternatives: 3

Speedup: 3.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))

C

double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * 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 = (((x * y) - (y * y)) + (y * y)) - (y * z)
end function

Java

public static double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * z);
}

Python

def code(x, y, z):
	return (((x * y) - (y * y)) + (y * y)) - (y * z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(x * y) - Float64(y * y)) + Float64(y * y)) - Float64(y * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (((x * y) - (y * y)) + (y * y)) - (y * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(x * y), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))

C

double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * 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 = (((x * y) - (y * y)) + (y * y)) - (y * z)
end function

Java

public static double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * z);
}

Python

def code(x, y, z):
	return (((x * y) - (y * y)) + (y * y)) - (y * z)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(x * y) - Float64(y * y)) + Float64(y * y)) - Float64(y * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (((x * y) - (y * y)) + (y * y)) - (y * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(x * y), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision] - N[(y * z), $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 70.5%

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

   1. associate-+l- 76.1%

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

   2. +-inverses 97.6%

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

   3. associate--l- 97.6%

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

   4. *-commutative 97.6%

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

   5. +-lft-identity 97.6%

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

   6. 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: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+105} \lor \neg \left(z \leq -9 \cdot 10^{-43} \lor \neg \left(z \leq -7.6 \cdot 10^{-62}\right) \land z \leq 4.5 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e+105)
         (not (or (<= z -9e-43) (and (not (<= z -7.6e-62)) (<= z 4.5e+17)))))
   (* y (- z))
   (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e+105) || !((z <= -9e-43) || (!(z <= -7.6e-62) && (z <= 4.5e+17)))) {
		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 ((z <= (-3.3d+105)) .or. (.not. (z <= (-9d-43)) .or. (.not. (z <= (-7.6d-62))) .and. (z <= 4.5d+17))) 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 ((z <= -3.3e+105) || !((z <= -9e-43) || (!(z <= -7.6e-62) && (z <= 4.5e+17)))) {
		tmp = y * -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.3e+105) or not ((z <= -9e-43) or (not (z <= -7.6e-62) and (z <= 4.5e+17))):
		tmp = y * -z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.3e+105) || !((z <= -9e-43) || (!(z <= -7.6e-62) && (z <= 4.5e+17))))
		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 ((z <= -3.3e+105) || ~(((z <= -9e-43) || (~((z <= -7.6e-62)) && (z <= 4.5e+17)))))
		tmp = y * -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.3e+105], N[Not[Or[LessEqual[z, -9e-43], And[N[Not[LessEqual[z, -7.6e-62]], $MachinePrecision], LessEqual[z, 4.5e+17]]]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.29999999999999997e105 or -9.0000000000000005e-43 < z < -7.60000000000000013e-62 or 4.5e17 < z

   1. Initial program 73.8%

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

      1. associate-+l- 73.8%

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

      2. +-inverses 95.2%

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

      3. associate--l- 95.2%

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

      4. *-commutative 95.2%

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

      5. +-lft-identity 95.2%

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

      6. 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 80.9%

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

      1. associate-*r* 80.9%

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

      2. neg-mul-1 80.9%

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

      3. *-commutative 80.9%

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

   6. Simplified 80.9%

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

   if -3.29999999999999997e105 < z < -9.0000000000000005e-43 or -7.60000000000000013e-62 < z < 4.5e17

   1. Initial program 67.3%

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

      1. associate-+l- 78.4%

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

      2. +-inverses 100.0%

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

      3. associate--l- 100.0%

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

      4. *-commutative 100.0%

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

      5. +-lft-identity 100.0%

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

      6. 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 80.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+105} \lor \neg \left(z \leq -9 \cdot 10^{-43} \lor \neg \left(z \leq -7.6 \cdot 10^{-62}\right) \land z \leq 4.5 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

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 70.5%

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

   1. associate-+l- 76.1%

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

   2. +-inverses 97.6%

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

   3. associate--l- 97.6%

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

   4. *-commutative 97.6%

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

   5. +-lft-identity 97.6%

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

   6. 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 51.9%

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

5. Final simplification 51.9%

   \[\leadsto y \cdot x \]

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 2023221 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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