Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.6% → 99.8%

Time: 7.9s

Alternatives: 12

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(6 \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) (* 6.0 z))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * 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 - x) * (6.0d0 * z))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * z));
}

Python

def code(x, y, z):
	return x + ((y - x) * (6.0 * z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(6.0 * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (6.0 * z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

   1. associate-*l* 99.8%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(6 \cdot z\right)} \]
4. Add Preprocessing

5. Final simplification 99.8%

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

Alternative 2: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+194} \lor \neg \left(z \leq 6 \cdot 10^{+222}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -0.17)
     t_0
     (if (<= z 7.6e-40)
       x
       (if (or (<= z 4.6e+194) (not (<= z 6e+222))) (* 6.0 (* y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -0.17) {
		tmp = t_0;
	} else if (z <= 7.6e-40) {
		tmp = x;
	} else if ((z <= 4.6e+194) || !(z <= 6e+222)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    if (z <= (-0.17d0)) then
        tmp = t_0
    else if (z <= 7.6d-40) then
        tmp = x
    else if ((z <= 4.6d+194) .or. (.not. (z <= 6d+222))) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -0.17) {
		tmp = t_0;
	} else if (z <= 7.6e-40) {
		tmp = x;
	} else if ((z <= 4.6e+194) || !(z <= 6e+222)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -0.17:
		tmp = t_0
	elif z <= 7.6e-40:
		tmp = x
	elif (z <= 4.6e+194) or not (z <= 6e+222):
		tmp = 6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -0.17)
		tmp = t_0;
	elseif (z <= 7.6e-40)
		tmp = x;
	elseif ((z <= 4.6e+194) || !(z <= 6e+222))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -0.17)
		tmp = t_0;
	elseif (z <= 7.6e-40)
		tmp = x;
	elseif ((z <= 4.6e+194) || ~((z <= 6e+222)))
		tmp = 6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.17], t$95$0, If[LessEqual[z, 7.6e-40], x, If[Or[LessEqual[z, 4.6e+194], N[Not[LessEqual[z, 6e+222]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012 or 4.6000000000000001e194 < z < 6.00000000000000028e222

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 61.0%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

   4. Taylor expanded in z around inf 59.4%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

   if -0.170000000000000012 < z < 7.5999999999999998e-40

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.2%

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

   if 7.5999999999999998e-40 < z < 4.6000000000000001e194 or 6.00000000000000028e222 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.5%

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

      1. +-commutative 91.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 91.5%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 91.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 91.5%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 91.4%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 91.4%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 91.3%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 91.5%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around inf 65.9%

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

      1. *-commutative 65.9%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 65.9%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+194} \lor \neg \left(z \leq 6 \cdot 10^{+222}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+195} \lor \neg \left(z \leq 2.15 \cdot 10^{+223}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))))
   (if (<= z -0.17)
     t_0
     (if (<= z 5.5e-39)
       x
       (if (or (<= z 1.25e+195) (not (<= z 2.15e+223)))
         (* 6.0 (* y z))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double tmp;
	if (z <= -0.17) {
		tmp = t_0;
	} else if (z <= 5.5e-39) {
		tmp = x;
	} else if ((z <= 1.25e+195) || !(z <= 2.15e+223)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    if (z <= (-0.17d0)) then
        tmp = t_0
    else if (z <= 5.5d-39) then
        tmp = x
    else if ((z <= 1.25d+195) .or. (.not. (z <= 2.15d+223))) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double tmp;
	if (z <= -0.17) {
		tmp = t_0;
	} else if (z <= 5.5e-39) {
		tmp = x;
	} else if ((z <= 1.25e+195) || !(z <= 2.15e+223)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	tmp = 0
	if z <= -0.17:
		tmp = t_0
	elif z <= 5.5e-39:
		tmp = x
	elif (z <= 1.25e+195) or not (z <= 2.15e+223):
		tmp = 6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -0.17)
		tmp = t_0;
	elseif (z <= 5.5e-39)
		tmp = x;
	elseif ((z <= 1.25e+195) || !(z <= 2.15e+223))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -0.17)
		tmp = t_0;
	elseif (z <= 5.5e-39)
		tmp = x;
	elseif ((z <= 1.25e+195) || ~((z <= 2.15e+223)))
		tmp = 6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.17], t$95$0, If[LessEqual[z, 5.5e-39], x, If[Or[LessEqual[z, 1.25e+195], N[Not[LessEqual[z, 2.15e+223]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012 or 1.2499999999999999e195 < z < 2.15e223

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 94.5%

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

      1. +-commutative 94.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 94.5%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 94.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 94.5%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 94.5%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 94.5%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 94.5%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.1%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around 0 59.4%

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

      1. associate-*r* 59.4%

         \[\leadsto \color{blue}{\left(-6 \cdot x\right) \cdot z} \]

      2. *-commutative 59.4%

         \[\leadsto \color{blue}{\left(x \cdot -6\right)} \cdot z \]

      3. associate-*r* 59.5%

         \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z\right)} \]

   9. Simplified 59.5%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z\right)} \]

   if -0.170000000000000012 < z < 5.50000000000000018e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.2%

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

   if 5.50000000000000018e-39 < z < 1.2499999999999999e195 or 2.15e223 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.5%

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

      1. +-commutative 91.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 91.5%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 91.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 91.5%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 91.4%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 91.4%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 91.3%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 91.5%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around inf 65.9%

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

      1. *-commutative 65.9%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 65.9%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+195} \lor \neg \left(z \leq 2.15 \cdot 10^{+223}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-12} \lor \neg \left(z \leq 2.1 \cdot 10^{-39}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.56e-12) (not (<= z 2.1e-39))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-12) || !(z <= 2.1e-39)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = 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 <= (-1.56d-12)) .or. (.not. (z <= 2.1d-39))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-12) || !(z <= 2.1e-39)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.56e-12) or not (z <= 2.1e-39):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.56e-12) || !(z <= 2.1e-39))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.56e-12) || ~((z <= 2.1e-39)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.56e-12], N[Not[LessEqual[z, 2.1e-39]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.56000000000000002e-12 or 2.09999999999999993e-39 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 92.8%

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

      1. +-commutative 92.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 92.8%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 92.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 92.8%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 92.8%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 92.8%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 92.8%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 94.4%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -1.56000000000000002e-12 < z < 2.09999999999999993e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-12} \lor \neg \left(z \leq 2.1 \cdot 10^{-39}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.5e-10)
   (* (- y x) (* 6.0 z))
   (if (<= z 6.8e-39) x (* 6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e-10) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 6.8e-39) {
		tmp = x;
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	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 <= (-5.5d-10)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 6.8d-39) then
        tmp = x
    else
        tmp = 6.0d0 * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e-10) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 6.8e-39) {
		tmp = x;
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.5e-10:
		tmp = (y - x) * (6.0 * z)
	elif z <= 6.8e-39:
		tmp = x
	else:
		tmp = 6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.5e-10)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 6.8e-39)
		tmp = x;
	else
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.5e-10)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 6.8e-39)
		tmp = x;
	else
		tmp = 6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.5e-10], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-39], x, N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999996e-10

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 93.8%

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

      1. +-commutative 93.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 93.8%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 93.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 93.8%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 93.9%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 93.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 93.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around 0 92.1%

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

      1. metadata-eval 92.1%

         \[\leadsto \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right) \]

      2. distribute-lft-neg-in 92.1%

         \[\leadsto \color{blue}{\left(-6 \cdot \left(x \cdot z\right)\right)} + 6 \cdot \left(y \cdot z\right) \]

      3. *-commutative 92.1%

         \[\leadsto \left(-6 \cdot \color{blue}{\left(z \cdot x\right)}\right) + 6 \cdot \left(y \cdot z\right) \]

      4. associate-*r* 92.1%

         \[\leadsto \left(-\color{blue}{\left(6 \cdot z\right) \cdot x}\right) + 6 \cdot \left(y \cdot z\right) \]

      5. distribute-rgt-neg-out 92.1%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(-x\right)} + 6 \cdot \left(y \cdot z\right) \]

      6. *-commutative 92.1%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

      7. associate-*r* 92.2%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + \color{blue}{\left(6 \cdot z\right) \cdot y} \]

      8. distribute-lft-out 98.0%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(\left(-x\right) + y\right)} \]

      9. +-commutative 98.0%

         \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{\left(y + \left(-x\right)\right)} \]

      10. *-commutative 98.0%

          \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y + \left(-x\right)\right) \]

      11. sub-neg 98.0%

          \[\leadsto \left(z \cdot 6\right) \cdot \color{blue}{\left(y - x\right)} \]

   9. Simplified 98.0%

      \[\leadsto \color{blue}{\left(z \cdot 6\right) \cdot \left(y - x\right)} \]

   if -5.4999999999999996e-10 < z < 6.7999999999999998e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.2%

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

   if 6.7999999999999998e-39 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 92.1%

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

      1. +-commutative 92.1%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 92.1%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 92.1%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 92.1%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 92.0%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 92.0%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 92.0%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 92.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.78:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 180:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.78)
   (* (- y x) (* 6.0 z))
   (if (<= z 180.0) (+ x (* -6.0 (* x z))) (* 6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.78) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 180.0) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	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 <= (-0.78d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 180.0d0) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = 6.0d0 * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.78) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 180.0) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.78:
		tmp = (y - x) * (6.0 * z)
	elif z <= 180.0:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = 6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.78)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 180.0)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.78)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 180.0)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = 6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.78], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 180.0], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.78000000000000003

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 93.7%

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

      1. +-commutative 93.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 93.7%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 93.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 93.7%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 93.8%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 93.8%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 93.8%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 99.5%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around 0 93.5%

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

      1. metadata-eval 93.5%

         \[\leadsto \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right) \]

      2. distribute-lft-neg-in 93.5%

         \[\leadsto \color{blue}{\left(-6 \cdot \left(x \cdot z\right)\right)} + 6 \cdot \left(y \cdot z\right) \]

      3. *-commutative 93.5%

         \[\leadsto \left(-6 \cdot \color{blue}{\left(z \cdot x\right)}\right) + 6 \cdot \left(y \cdot z\right) \]

      4. associate-*r* 93.5%

         \[\leadsto \left(-\color{blue}{\left(6 \cdot z\right) \cdot x}\right) + 6 \cdot \left(y \cdot z\right) \]

      5. distribute-rgt-neg-out 93.5%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(-x\right)} + 6 \cdot \left(y \cdot z\right) \]

      6. *-commutative 93.5%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

      7. associate-*r* 93.6%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + \color{blue}{\left(6 \cdot z\right) \cdot y} \]

      8. distribute-lft-out 99.6%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(\left(-x\right) + y\right)} \]

      9. +-commutative 99.6%

         \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{\left(y + \left(-x\right)\right)} \]

      10. *-commutative 99.6%

          \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y + \left(-x\right)\right) \]

      11. sub-neg 99.6%

          \[\leadsto \left(z \cdot 6\right) \cdot \color{blue}{\left(y - x\right)} \]

   9. Simplified 99.6%

      \[\leadsto \color{blue}{\left(z \cdot 6\right) \cdot \left(y - x\right)} \]

   if -0.78000000000000003 < z < 180

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 73.5%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

   if 180 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. +-commutative 91.0%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 91.0%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 91.0%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 91.0%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 90.9%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 90.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 90.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 99.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.78:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 180:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.2:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.2)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.166) (+ x (* 6.0 (* y z))) (* 6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.2) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.166) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	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 <= (-0.2d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 0.166d0) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = 6.0d0 * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.2) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.166) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.2:
		tmp = (y - x) * (6.0 * z)
	elif z <= 0.166:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = 6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.2)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.166)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.2)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 0.166)
		tmp = x + (6.0 * (y * z));
	else
		tmp = 6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.2], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.166], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.20000000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 93.8%

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

      1. +-commutative 93.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 93.8%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 93.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 93.8%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 93.9%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 93.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 93.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around 0 92.1%

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

      1. metadata-eval 92.1%

         \[\leadsto \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right) \]

      2. distribute-lft-neg-in 92.1%

         \[\leadsto \color{blue}{\left(-6 \cdot \left(x \cdot z\right)\right)} + 6 \cdot \left(y \cdot z\right) \]

      3. *-commutative 92.1%

         \[\leadsto \left(-6 \cdot \color{blue}{\left(z \cdot x\right)}\right) + 6 \cdot \left(y \cdot z\right) \]

      4. associate-*r* 92.1%

         \[\leadsto \left(-\color{blue}{\left(6 \cdot z\right) \cdot x}\right) + 6 \cdot \left(y \cdot z\right) \]

      5. distribute-rgt-neg-out 92.1%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(-x\right)} + 6 \cdot \left(y \cdot z\right) \]

      6. *-commutative 92.1%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

      7. associate-*r* 92.2%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + \color{blue}{\left(6 \cdot z\right) \cdot y} \]

      8. distribute-lft-out 98.0%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(\left(-x\right) + y\right)} \]

      9. +-commutative 98.0%

         \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{\left(y + \left(-x\right)\right)} \]

      10. *-commutative 98.0%

          \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y + \left(-x\right)\right) \]

      11. sub-neg 98.0%

          \[\leadsto \left(z \cdot 6\right) \cdot \color{blue}{\left(y - x\right)} \]

   9. Simplified 98.0%

      \[\leadsto \color{blue}{\left(z \cdot 6\right) \cdot \left(y - x\right)} \]

   if -0.20000000000000001 < z < 0.166000000000000009

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 98.7%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot z\right)} \]

   if 0.166000000000000009 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.3%

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

      1. +-commutative 91.3%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 91.3%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 91.3%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 91.3%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 91.2%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 91.2%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 91.1%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 97.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.2:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.2:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.2)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.166) (+ x (* z (* y 6.0))) (* 6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.2) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.166) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	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 <= (-0.2d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 0.166d0) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = 6.0d0 * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.2) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.166) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = 6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.2:
		tmp = (y - x) * (6.0 * z)
	elif z <= 0.166:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = 6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.2)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.166)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.2)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 0.166)
		tmp = x + (z * (y * 6.0));
	else
		tmp = 6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.2], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.166], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.20000000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 93.8%

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

      1. +-commutative 93.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 93.8%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 93.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 93.8%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 93.9%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 93.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 93.9%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.8%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 98.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around 0 92.1%

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

      1. metadata-eval 92.1%

         \[\leadsto \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right) \]

      2. distribute-lft-neg-in 92.1%

         \[\leadsto \color{blue}{\left(-6 \cdot \left(x \cdot z\right)\right)} + 6 \cdot \left(y \cdot z\right) \]

      3. *-commutative 92.1%

         \[\leadsto \left(-6 \cdot \color{blue}{\left(z \cdot x\right)}\right) + 6 \cdot \left(y \cdot z\right) \]

      4. associate-*r* 92.1%

         \[\leadsto \left(-\color{blue}{\left(6 \cdot z\right) \cdot x}\right) + 6 \cdot \left(y \cdot z\right) \]

      5. distribute-rgt-neg-out 92.1%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(-x\right)} + 6 \cdot \left(y \cdot z\right) \]

      6. *-commutative 92.1%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

      7. associate-*r* 92.2%

         \[\leadsto \left(6 \cdot z\right) \cdot \left(-x\right) + \color{blue}{\left(6 \cdot z\right) \cdot y} \]

      8. distribute-lft-out 98.0%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(\left(-x\right) + y\right)} \]

      9. +-commutative 98.0%

         \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{\left(y + \left(-x\right)\right)} \]

      10. *-commutative 98.0%

          \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y + \left(-x\right)\right) \]

      11. sub-neg 98.0%

          \[\leadsto \left(z \cdot 6\right) \cdot \color{blue}{\left(y - x\right)} \]

   9. Simplified 98.0%

      \[\leadsto \color{blue}{\left(z \cdot 6\right) \cdot \left(y - x\right)} \]

   if -0.20000000000000001 < z < 0.166000000000000009

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 98.7%

      \[\leadsto x + \color{blue}{\left(6 \cdot y\right)} \cdot z \]

   if 0.166000000000000009 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.3%

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

      1. +-commutative 91.3%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

      2. metadata-eval 91.3%

         \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

      3. cancel-sign-sub-inv 91.3%

         \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

      4. *-commutative 91.3%

         \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

      5. associate-*l* 91.2%

         \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 91.2%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

      7. associate-*l* 91.1%

         \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

      8. distribute-lft-out-- 99.7%

         \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      9. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in z around inf 97.0%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.2:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.166:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 0.166))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = 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 <= (-0.17d0)) .or. (.not. (z <= 0.166d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 0.166):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 0.166))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.17) || ~((z <= 0.166)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 0.166000000000000009 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 51.0%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

   4. Taylor expanded in z around inf 48.6%

      \[\leadsto \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

   if -0.170000000000000012 < z < 0.166000000000000009

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 71.9%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + 6 \cdot \left(\left(y - x\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* 6.0 (* (- y x) z))))

C

double code(double x, double y, double z) {
	return x + (6.0 * ((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 = x + (6.0d0 * ((y - x) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (6.0 * ((y - x) * z));
}

Python

def code(x, y, z):
	return x + (6.0 * ((y - x) * z))

Julia

function code(x, y, z)
	return Float64(x + Float64(6.0 * Float64(Float64(y - x) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (6.0 * ((y - x) * z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 96.3%

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

   1. +-commutative 96.3%

      \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) + -6 \cdot \left(x \cdot z\right)\right)} \]

   2. metadata-eval 96.3%

      \[\leadsto x + \left(6 \cdot \left(y \cdot z\right) + \color{blue}{\left(-6\right)} \cdot \left(x \cdot z\right)\right) \]

   3. cancel-sign-sub-inv 96.3%

      \[\leadsto x + \color{blue}{\left(6 \cdot \left(y \cdot z\right) - 6 \cdot \left(x \cdot z\right)\right)} \]

   4. *-commutative 96.3%

      \[\leadsto x + \left(6 \cdot \color{blue}{\left(z \cdot y\right)} - 6 \cdot \left(x \cdot z\right)\right) \]

   5. associate-*l* 96.3%

      \[\leadsto x + \left(\color{blue}{\left(6 \cdot z\right) \cdot y} - 6 \cdot \left(x \cdot z\right)\right) \]

   6. *-commutative 96.3%

      \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - 6 \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

   7. associate-*l* 96.3%

      \[\leadsto x + \left(\left(6 \cdot z\right) \cdot y - \color{blue}{\left(6 \cdot z\right) \cdot x}\right) \]

   8. distribute-lft-out-- 99.8%

      \[\leadsto x + \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

   9. associate-*r* 99.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

5. Simplified 99.8%

   \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

6. Final simplification 99.8%

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

Alternative 11: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + z \cdot \left(\left(y - x\right) \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* z (* (- y x) 6.0))))

C

double code(double x, double y, double z) {
	return x + (z * ((y - x) * 6.0));
}

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 - x) * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + (z * ((y - x) * 6.0));
}

Python

def code(x, y, z):
	return x + (z * ((y - x) * 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(z * Float64(Float64(y - x) * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (z * ((y - x) * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 12: 37.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0 39.4%

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

4. Final simplification 39.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - 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 - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))