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

Percentage Accurate: 99.6% → 99.8%

Time: 10.2s

Alternatives: 11

Speedup: 1.0×

• 21.1% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot z, x\right) \]
6. Add Preprocessing

Alternative 2: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+183}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+88} \lor \neg \left(z \leq 8.8 \cdot 10^{+156}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -7e+183)
     t_0
     (if (<= z -7.5e+140)
       t_1
       (if (<= z -1.55e+35)
         t_0
         (if (<= z -5.5e-82)
           t_1
           (if (<= z 0.17)
             x
             (if (or (<= z 1.35e+88) (not (<= z 8.8e+156))) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -7e+183) {
		tmp = t_0;
	} else if (z <= -7.5e+140) {
		tmp = t_1;
	} else if (z <= -1.55e+35) {
		tmp = t_0;
	} else if (z <= -5.5e-82) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 1.35e+88) || !(z <= 8.8e+156)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (y * z)
    if (z <= (-7d+183)) then
        tmp = t_0
    else if (z <= (-7.5d+140)) then
        tmp = t_1
    else if (z <= (-1.55d+35)) then
        tmp = t_0
    else if (z <= (-5.5d-82)) then
        tmp = t_1
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 1.35d+88) .or. (.not. (z <= 8.8d+156))) then
        tmp = t_0
    else
        tmp = t_1
    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 t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -7e+183) {
		tmp = t_0;
	} else if (z <= -7.5e+140) {
		tmp = t_1;
	} else if (z <= -1.55e+35) {
		tmp = t_0;
	} else if (z <= -5.5e-82) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 1.35e+88) || !(z <= 8.8e+156)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -7e+183:
		tmp = t_0
	elif z <= -7.5e+140:
		tmp = t_1
	elif z <= -1.55e+35:
		tmp = t_0
	elif z <= -5.5e-82:
		tmp = t_1
	elif z <= 0.17:
		tmp = x
	elif (z <= 1.35e+88) or not (z <= 8.8e+156):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -7e+183)
		tmp = t_0;
	elseif (z <= -7.5e+140)
		tmp = t_1;
	elseif (z <= -1.55e+35)
		tmp = t_0;
	elseif (z <= -5.5e-82)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 1.35e+88) || !(z <= 8.8e+156))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -7e+183)
		tmp = t_0;
	elseif (z <= -7.5e+140)
		tmp = t_1;
	elseif (z <= -1.55e+35)
		tmp = t_0;
	elseif (z <= -5.5e-82)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 1.35e+88) || ~((z <= 8.8e+156)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+183], t$95$0, If[LessEqual[z, -7.5e+140], t$95$1, If[LessEqual[z, -1.55e+35], t$95$0, If[LessEqual[z, -5.5e-82], t$95$1, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 1.35e+88], N[Not[LessEqual[z, 8.8e+156]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999974e183 or -7.4999999999999997e140 < z < -1.54999999999999993e35 or 0.170000000000000012 < z < 1.35000000000000008e88 or 8.80000000000000016e156 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 69.5%

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

      1. +-commutative 69.5%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   6. Taylor expanded in z around inf 68.3%

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

   if -6.99999999999999974e183 < z < -7.4999999999999997e140 or -1.54999999999999993e35 < z < -5.4999999999999998e-82 or 1.35000000000000008e88 < z < 8.80000000000000016e156

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.7%

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

   4. Taylor expanded in y around inf 71.3%

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

      1. associate-*r/ 64.8%

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

   6. Simplified 64.8%

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

      1. *-commutative 64.8%

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

      2. distribute-rgt1-in 64.8%

         \[\leadsto \color{blue}{\left(6 \cdot \left(y \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

      3. associate-*r* 64.8%

         \[\leadsto \left(\color{blue}{\left(6 \cdot y\right) \cdot \frac{z}{x}} + 1\right) \cdot x \]

      4. *-commutative 64.8%

         \[\leadsto \left(\color{blue}{\left(y \cdot 6\right)} \cdot \frac{z}{x} + 1\right) \cdot x \]

      5. associate-*l* 64.8%

         \[\leadsto \left(\color{blue}{y \cdot \left(6 \cdot \frac{z}{x}\right)} + 1\right) \cdot x \]

   8. Applied egg-rr 64.8%

      \[\leadsto \color{blue}{\left(y \cdot \left(6 \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

   9. Taylor expanded in y around inf 77.9%

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

   if -5.4999999999999998e-82 < z < 0.170000000000000012

   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 73.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+183}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+140}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+88} \lor \neg \left(z \leq 8.8 \cdot 10^{+156}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+186}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+48}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+87} \lor \neg \left(z \leq 4.1 \cdot 10^{+156}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -1.1e+186)
     t_0
     (if (<= z -1.6e+141)
       t_1
       (if (<= z -5.5e+48)
         t_0
         (if (<= z -1.65e-81)
           t_1
           (if (<= z 0.17)
             x
             (if (or (<= z 6.8e+87) (not (<= z 4.1e+156))) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.1e+186) {
		tmp = t_0;
	} else if (z <= -1.6e+141) {
		tmp = t_1;
	} else if (z <= -5.5e+48) {
		tmp = t_0;
	} else if (z <= -1.65e-81) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 6.8e+87) || !(z <= 4.1e+156)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-1.1d+186)) then
        tmp = t_0
    else if (z <= (-1.6d+141)) then
        tmp = t_1
    else if (z <= (-5.5d+48)) then
        tmp = t_0
    else if (z <= (-1.65d-81)) then
        tmp = t_1
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 6.8d+87) .or. (.not. (z <= 4.1d+156))) then
        tmp = t_0
    else
        tmp = t_1
    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 t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.1e+186) {
		tmp = t_0;
	} else if (z <= -1.6e+141) {
		tmp = t_1;
	} else if (z <= -5.5e+48) {
		tmp = t_0;
	} else if (z <= -1.65e-81) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 6.8e+87) || !(z <= 4.1e+156)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.1e+186:
		tmp = t_0
	elif z <= -1.6e+141:
		tmp = t_1
	elif z <= -5.5e+48:
		tmp = t_0
	elif z <= -1.65e-81:
		tmp = t_1
	elif z <= 0.17:
		tmp = x
	elif (z <= 6.8e+87) or not (z <= 4.1e+156):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.1e+186)
		tmp = t_0;
	elseif (z <= -1.6e+141)
		tmp = t_1;
	elseif (z <= -5.5e+48)
		tmp = t_0;
	elseif (z <= -1.65e-81)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 6.8e+87) || !(z <= 4.1e+156))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.1e+186)
		tmp = t_0;
	elseif (z <= -1.6e+141)
		tmp = t_1;
	elseif (z <= -5.5e+48)
		tmp = t_0;
	elseif (z <= -1.65e-81)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 6.8e+87) || ~((z <= 4.1e+156)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+186], t$95$0, If[LessEqual[z, -1.6e+141], t$95$1, If[LessEqual[z, -5.5e+48], t$95$0, If[LessEqual[z, -1.65e-81], t$95$1, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 6.8e+87], N[Not[LessEqual[z, 4.1e+156]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0999999999999999e186 or -1.60000000000000009e141 < z < -5.5000000000000002e48 or 0.170000000000000012 < z < 6.8000000000000004e87 or 4.1000000000000002e156 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 69.5%

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

      1. +-commutative 69.5%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   6. Taylor expanded in z around inf 68.3%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*l* 68.4%

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

   8. Simplified 68.4%

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

   if -1.0999999999999999e186 < z < -1.60000000000000009e141 or -5.5000000000000002e48 < z < -1.64999999999999994e-81 or 6.8000000000000004e87 < z < 4.1000000000000002e156

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.7%

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

   4. Taylor expanded in y around inf 71.3%

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

      1. associate-*r/ 64.8%

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

   6. Simplified 64.8%

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

      1. *-commutative 64.8%

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

      2. distribute-rgt1-in 64.8%

         \[\leadsto \color{blue}{\left(6 \cdot \left(y \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

      3. associate-*r* 64.8%

         \[\leadsto \left(\color{blue}{\left(6 \cdot y\right) \cdot \frac{z}{x}} + 1\right) \cdot x \]

      4. *-commutative 64.8%

         \[\leadsto \left(\color{blue}{\left(y \cdot 6\right)} \cdot \frac{z}{x} + 1\right) \cdot x \]

      5. associate-*l* 64.8%

         \[\leadsto \left(\color{blue}{y \cdot \left(6 \cdot \frac{z}{x}\right)} + 1\right) \cdot x \]

   8. Applied egg-rr 64.8%

      \[\leadsto \color{blue}{\left(y \cdot \left(6 \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

   9. Taylor expanded in y around inf 77.9%

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

   if -1.64999999999999994e-81 < z < 0.170000000000000012

   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 73.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+141}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-81}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+87} \lor \neg \left(z \leq 4.1 \cdot 10^{+156}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+181}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+87} \lor \neg \left(z \leq 4.8 \cdot 10^{+156}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -3.5e+181)
     t_0
     (if (<= z -1.1e+141)
       t_1
       (if (<= z -1.95e+38)
         t_0
         (if (<= z -1.8e-83)
           t_1
           (if (<= z 0.17)
             x
             (if (or (<= z 9e+87) (not (<= z 4.8e+156)))
               t_0
               (* z (* y 6.0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.5e+181) {
		tmp = t_0;
	} else if (z <= -1.1e+141) {
		tmp = t_1;
	} else if (z <= -1.95e+38) {
		tmp = t_0;
	} else if (z <= -1.8e-83) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 9e+87) || !(z <= 4.8e+156)) {
		tmp = t_0;
	} else {
		tmp = z * (y * 6.0);
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-3.5d+181)) then
        tmp = t_0
    else if (z <= (-1.1d+141)) then
        tmp = t_1
    else if (z <= (-1.95d+38)) then
        tmp = t_0
    else if (z <= (-1.8d-83)) then
        tmp = t_1
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 9d+87) .or. (.not. (z <= 4.8d+156))) then
        tmp = t_0
    else
        tmp = z * (y * 6.0d0)
    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 t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.5e+181) {
		tmp = t_0;
	} else if (z <= -1.1e+141) {
		tmp = t_1;
	} else if (z <= -1.95e+38) {
		tmp = t_0;
	} else if (z <= -1.8e-83) {
		tmp = t_1;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 9e+87) || !(z <= 4.8e+156)) {
		tmp = t_0;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -3.5e+181:
		tmp = t_0
	elif z <= -1.1e+141:
		tmp = t_1
	elif z <= -1.95e+38:
		tmp = t_0
	elif z <= -1.8e-83:
		tmp = t_1
	elif z <= 0.17:
		tmp = x
	elif (z <= 9e+87) or not (z <= 4.8e+156):
		tmp = t_0
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.5e+181)
		tmp = t_0;
	elseif (z <= -1.1e+141)
		tmp = t_1;
	elseif (z <= -1.95e+38)
		tmp = t_0;
	elseif (z <= -1.8e-83)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 9e+87) || !(z <= 4.8e+156))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.5e+181)
		tmp = t_0;
	elseif (z <= -1.1e+141)
		tmp = t_1;
	elseif (z <= -1.95e+38)
		tmp = t_0;
	elseif (z <= -1.8e-83)
		tmp = t_1;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 9e+87) || ~((z <= 4.8e+156)))
		tmp = t_0;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+181], t$95$0, If[LessEqual[z, -1.1e+141], t$95$1, If[LessEqual[z, -1.95e+38], t$95$0, If[LessEqual[z, -1.8e-83], t$95$1, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 9e+87], N[Not[LessEqual[z, 4.8e+156]], $MachinePrecision]], t$95$0, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.50000000000000008e181 or -1.1e141 < z < -1.95000000000000012e38 or 0.170000000000000012 < z < 9.0000000000000005e87 or 4.8000000000000002e156 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 69.5%

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

      1. +-commutative 69.5%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 69.5%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   6. Taylor expanded in z around inf 68.3%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*l* 68.4%

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

   8. Simplified 68.4%

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

   if -3.50000000000000008e181 < z < -1.1e141 or -1.95000000000000012e38 < z < -1.80000000000000006e-83

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 89.6%

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

   4. Taylor expanded in y around inf 75.4%

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

      1. associate-*r/ 72.0%

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

   6. Simplified 72.0%

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

      1. *-commutative 72.0%

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

      2. distribute-rgt1-in 72.0%

         \[\leadsto \color{blue}{\left(6 \cdot \left(y \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

      3. associate-*r* 72.0%

         \[\leadsto \left(\color{blue}{\left(6 \cdot y\right) \cdot \frac{z}{x}} + 1\right) \cdot x \]

      4. *-commutative 72.0%

         \[\leadsto \left(\color{blue}{\left(y \cdot 6\right)} \cdot \frac{z}{x} + 1\right) \cdot x \]

      5. associate-*l* 72.0%

         \[\leadsto \left(\color{blue}{y \cdot \left(6 \cdot \frac{z}{x}\right)} + 1\right) \cdot x \]

   8. Applied egg-rr 72.0%

      \[\leadsto \color{blue}{\left(y \cdot \left(6 \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

   9. Taylor expanded in y around inf 72.0%

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

   if -1.80000000000000006e-83 < z < 0.170000000000000012

   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 73.2%

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

   if 9.0000000000000005e87 < z < 4.8000000000000002e156

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.1%

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

   4. Taylor expanded in y around inf 64.0%

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

      1. associate-*r/ 52.1%

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

   6. Simplified 52.1%

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

      1. *-commutative 52.1%

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

      2. distribute-rgt1-in 52.1%

         \[\leadsto \color{blue}{\left(6 \cdot \left(y \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

      3. associate-*r* 52.1%

         \[\leadsto \left(\color{blue}{\left(6 \cdot y\right) \cdot \frac{z}{x}} + 1\right) \cdot x \]

      4. *-commutative 52.1%

         \[\leadsto \left(\color{blue}{\left(y \cdot 6\right)} \cdot \frac{z}{x} + 1\right) \cdot x \]

      5. associate-*l* 52.1%

         \[\leadsto \left(\color{blue}{y \cdot \left(6 \cdot \frac{z}{x}\right)} + 1\right) \cdot x \]

   8. Applied egg-rr 52.1%

      \[\leadsto \color{blue}{\left(y \cdot \left(6 \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

   9. Taylor expanded in y around inf 88.2%

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

       1. *-commutative 88.2%

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

       2. associate-*r* 87.9%

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

       3. *-commutative 87.9%

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

       4. associate-*l* 88.3%

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

   11. Simplified 88.3%

       \[\leadsto \color{blue}{z \cdot \left(6 \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+181}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+141}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+87} \lor \neg \left(z \leq 4.8 \cdot 10^{+156}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-104} \lor \neg \left(x \leq 3.9 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e-104) (not (<= x 3.9e-88)))
   (* x (+ (* z -6.0) 1.0))
   (* z (* y 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e-104) || !(x <= 3.9e-88)) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * (y * 6.0);
	}
	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) :: tmp
    if ((x <= (-3.7d-104)) .or. (.not. (x <= 3.9d-88))) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e-104) || !(x <= 3.9e-88)) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e-104) or not (x <= 3.9e-88):
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e-104) || !(x <= 3.9e-88))
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.7e-104) || ~((x <= 3.9e-88)))
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e-104], N[Not[LessEqual[x, 3.9e-88]], $MachinePrecision]], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6999999999999999e-104 or 3.89999999999999992e-88 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 80.5%

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

      1. +-commutative 80.5%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 80.5%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   if -3.6999999999999999e-104 < x < 3.89999999999999992e-88

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 78.3%

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

   4. Taylor expanded in y around inf 67.3%

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

      1. associate-*r/ 61.1%

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

   6. Simplified 61.1%

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

      1. *-commutative 61.1%

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

      2. distribute-rgt1-in 61.1%

         \[\leadsto \color{blue}{\left(6 \cdot \left(y \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

      3. associate-*r* 61.2%

         \[\leadsto \left(\color{blue}{\left(6 \cdot y\right) \cdot \frac{z}{x}} + 1\right) \cdot x \]

      4. *-commutative 61.2%

         \[\leadsto \left(\color{blue}{\left(y \cdot 6\right)} \cdot \frac{z}{x} + 1\right) \cdot x \]

      5. associate-*l* 61.2%

         \[\leadsto \left(\color{blue}{y \cdot \left(6 \cdot \frac{z}{x}\right)} + 1\right) \cdot x \]

   8. Applied egg-rr 61.2%

      \[\leadsto \color{blue}{\left(y \cdot \left(6 \cdot \frac{z}{x}\right) + 1\right) \cdot x} \]

   9. Taylor expanded in y around inf 74.1%

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

       1. *-commutative 74.1%

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

       2. associate-*r* 74.1%

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

       3. *-commutative 74.1%

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

       4. associate-*l* 74.2%

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

   11. Simplified 74.2%

       \[\leadsto \color{blue}{z \cdot \left(6 \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-104} \lor \neg \left(x \leq 3.9 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-96} \lor \neg \left(y \leq 2.75 \cdot 10^{-53}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e-96) (not (<= y 2.75e-53)))
   (+ x (* y (* 6.0 z)))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e-96) || !(y <= 2.75e-53)) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	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) :: tmp
    if ((y <= (-3.1d-96)) .or. (.not. (y <= 2.75d-53))) then
        tmp = x + (y * (6.0d0 * z))
    else
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e-96) || !(y <= 2.75e-53)) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e-96) or not (y <= 2.75e-53):
		tmp = x + (y * (6.0 * z))
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e-96) || !(y <= 2.75e-53))
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1e-96) || ~((y <= 2.75e-53)))
		tmp = x + (y * (6.0 * z));
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e-96], N[Not[LessEqual[y, 2.75e-53]], $MachinePrecision]], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e-96 or 2.75000000000000011e-53 < y

   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 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*r* 87.2%

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

   5. Simplified 87.2%

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

   if -3.0999999999999999e-96 < y < 2.75000000000000011e-53

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.9%

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

      1. +-commutative 88.9%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 88.9%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-96} \lor \neg \left(y \leq 2.75 \cdot 10^{-53}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e-93)
   (+ x (* z (* y 6.0)))
   (if (<= y 1.4e-53) (* x (+ (* z -6.0) 1.0)) (+ x (* y (* 6.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e-93) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 1.4e-53) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = x + (y * (6.0 * 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 (y <= (-2.6d-93)) then
        tmp = x + (z * (y * 6.0d0))
    else if (y <= 1.4d-53) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e-93) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 1.4e-53) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e-93:
		tmp = x + (z * (y * 6.0))
	elif y <= 1.4e-53:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e-93)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	elseif (y <= 1.4e-53)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.6e-93)
		tmp = x + (z * (y * 6.0));
	elseif (y <= 1.4e-53)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e-93], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-53], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5999999999999998e-93

   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 89.4%

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

   if -2.5999999999999998e-93 < y < 1.39999999999999993e-53

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.9%

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

      1. +-commutative 88.9%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 88.9%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   if 1.39999999999999993e-53 < y

   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 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*r* 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -60000000000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -60000000000000.0) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -60000000000000.0) || !(z <= 0.17)) {
		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 <= (-60000000000000.0d0)) .or. (.not. (z <= 0.17d0))) 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 <= -60000000000000.0) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -60000000000000.0) or not (z <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -60000000000000.0) || !(z <= 0.17))
		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 <= -60000000000000.0) || ~((z <= 0.17)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -60000000000000.0], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6e13 or 0.170000000000000012 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. +-commutative 59.3%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 59.3%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   6. Taylor expanded in z around inf 58.3%

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

   if -6e13 < z < 0.170000000000000012

   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 68.5%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -60000000000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 10: 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 11: 36.3% 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 33.5%

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

4. Final simplification 33.5%

   \[\leadsto x \]
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 2024096 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (- x (* (* 6.0 z) (- x y)))

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