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

Percentage Accurate: 99.7% → 99.8%

Time: 10.1s

Alternatives: 10

Speedup: 1.0×

• 21.3% 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: 99.7% 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 99.4%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+238}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -1.08e+238)
     t_0
     (if (<= z -3.6e+148)
       t_1
       (if (<= z -1.35e+124)
         t_0
         (if (<= z -8e+66)
           t_1
           (if (<= z -1.38e+20)
             t_0
             (if (<= z -3.6e-66)
               t_1
               (if (<= z 5.1e-98) x (if (<= z 1.35e+229) t_1 t_0))))))))))

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 <= -1.08e+238) {
		tmp = t_0;
	} else if (z <= -3.6e+148) {
		tmp = t_1;
	} else if (z <= -1.35e+124) {
		tmp = t_0;
	} else if (z <= -8e+66) {
		tmp = t_1;
	} else if (z <= -1.38e+20) {
		tmp = t_0;
	} else if (z <= -3.6e-66) {
		tmp = t_1;
	} else if (z <= 5.1e-98) {
		tmp = x;
	} else if (z <= 1.35e+229) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (y * z)
    if (z <= (-1.08d+238)) then
        tmp = t_0
    else if (z <= (-3.6d+148)) then
        tmp = t_1
    else if (z <= (-1.35d+124)) then
        tmp = t_0
    else if (z <= (-8d+66)) then
        tmp = t_1
    else if (z <= (-1.38d+20)) then
        tmp = t_0
    else if (z <= (-3.6d-66)) then
        tmp = t_1
    else if (z <= 5.1d-98) then
        tmp = x
    else if (z <= 1.35d+229) then
        tmp = t_1
    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 t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.08e+238) {
		tmp = t_0;
	} else if (z <= -3.6e+148) {
		tmp = t_1;
	} else if (z <= -1.35e+124) {
		tmp = t_0;
	} else if (z <= -8e+66) {
		tmp = t_1;
	} else if (z <= -1.38e+20) {
		tmp = t_0;
	} else if (z <= -3.6e-66) {
		tmp = t_1;
	} else if (z <= 5.1e-98) {
		tmp = x;
	} else if (z <= 1.35e+229) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.08e+238:
		tmp = t_0
	elif z <= -3.6e+148:
		tmp = t_1
	elif z <= -1.35e+124:
		tmp = t_0
	elif z <= -8e+66:
		tmp = t_1
	elif z <= -1.38e+20:
		tmp = t_0
	elif z <= -3.6e-66:
		tmp = t_1
	elif z <= 5.1e-98:
		tmp = x
	elif z <= 1.35e+229:
		tmp = t_1
	else:
		tmp = t_0
	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 <= -1.08e+238)
		tmp = t_0;
	elseif (z <= -3.6e+148)
		tmp = t_1;
	elseif (z <= -1.35e+124)
		tmp = t_0;
	elseif (z <= -8e+66)
		tmp = t_1;
	elseif (z <= -1.38e+20)
		tmp = t_0;
	elseif (z <= -3.6e-66)
		tmp = t_1;
	elseif (z <= 5.1e-98)
		tmp = x;
	elseif (z <= 1.35e+229)
		tmp = t_1;
	else
		tmp = t_0;
	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 <= -1.08e+238)
		tmp = t_0;
	elseif (z <= -3.6e+148)
		tmp = t_1;
	elseif (z <= -1.35e+124)
		tmp = t_0;
	elseif (z <= -8e+66)
		tmp = t_1;
	elseif (z <= -1.38e+20)
		tmp = t_0;
	elseif (z <= -3.6e-66)
		tmp = t_1;
	elseif (z <= 5.1e-98)
		tmp = x;
	elseif (z <= 1.35e+229)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e+238], t$95$0, If[LessEqual[z, -3.6e+148], t$95$1, If[LessEqual[z, -1.35e+124], t$95$0, If[LessEqual[z, -8e+66], t$95$1, If[LessEqual[z, -1.38e+20], t$95$0, If[LessEqual[z, -3.6e-66], t$95$1, If[LessEqual[z, 5.1e-98], x, If[LessEqual[z, 1.35e+229], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08e238 or -3.60000000000000006e148 < z < -1.34999999999999989e124 or -7.99999999999999956e66 < z < -1.38e20 or 1.35e229 < 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 99.8%

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

   4. Taylor expanded in x around inf 84.4%

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

      1. +-commutative 84.4%

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

      2. *-commutative 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in z around inf 84.4%

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

   if -1.08e238 < z < -3.60000000000000006e148 or -1.34999999999999989e124 < z < -7.99999999999999956e66 or -1.38e20 < z < -3.60000000000000012e-66 or 5.10000000000000022e-98 < z < 1.35e229

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 73.2%

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

      1. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in x around inf 58.6%

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

   7. Taylor expanded in y around inf 51.8%

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

   8. Taylor expanded in x around 0 66.3%

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

   if -3.60000000000000012e-66 < z < 5.10000000000000022e-98

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 82.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+238}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+148}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+124}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+66}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{+20}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-66}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+229}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ t_2 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+238}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+120}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+229}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* -6.0 (* x z))) (t_2 (* 6.0 (* y z))))
   (if (<= z -1.8e+238)
     t_0
     (if (<= z -3.2e+149)
       t_2
       (if (<= z -2.3e+120)
         t_0
         (if (<= z -3.3e+60)
           t_2
           (if (<= z -1.38e+20)
             t_1
             (if (<= z -1.76e-65)
               t_2
               (if (<= z 3.05e-99) x (if (<= z 1.95e+229) t_2 t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = -6.0 * (x * z);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.8e+238) {
		tmp = t_0;
	} else if (z <= -3.2e+149) {
		tmp = t_2;
	} else if (z <= -2.3e+120) {
		tmp = t_0;
	} else if (z <= -3.3e+60) {
		tmp = t_2;
	} else if (z <= -1.38e+20) {
		tmp = t_1;
	} else if (z <= -1.76e-65) {
		tmp = t_2;
	} else if (z <= 3.05e-99) {
		tmp = x;
	} else if (z <= 1.95e+229) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = (-6.0d0) * (x * z)
    t_2 = 6.0d0 * (y * z)
    if (z <= (-1.8d+238)) then
        tmp = t_0
    else if (z <= (-3.2d+149)) then
        tmp = t_2
    else if (z <= (-2.3d+120)) then
        tmp = t_0
    else if (z <= (-3.3d+60)) then
        tmp = t_2
    else if (z <= (-1.38d+20)) then
        tmp = t_1
    else if (z <= (-1.76d-65)) then
        tmp = t_2
    else if (z <= 3.05d-99) then
        tmp = x
    else if (z <= 1.95d+229) then
        tmp = t_2
    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 * (x * z);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.8e+238) {
		tmp = t_0;
	} else if (z <= -3.2e+149) {
		tmp = t_2;
	} else if (z <= -2.3e+120) {
		tmp = t_0;
	} else if (z <= -3.3e+60) {
		tmp = t_2;
	} else if (z <= -1.38e+20) {
		tmp = t_1;
	} else if (z <= -1.76e-65) {
		tmp = t_2;
	} else if (z <= 3.05e-99) {
		tmp = x;
	} else if (z <= 1.95e+229) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = -6.0 * (x * z)
	t_2 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.8e+238:
		tmp = t_0
	elif z <= -3.2e+149:
		tmp = t_2
	elif z <= -2.3e+120:
		tmp = t_0
	elif z <= -3.3e+60:
		tmp = t_2
	elif z <= -1.38e+20:
		tmp = t_1
	elif z <= -1.76e-65:
		tmp = t_2
	elif z <= 3.05e-99:
		tmp = x
	elif z <= 1.95e+229:
		tmp = t_2
	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(x * z))
	t_2 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.8e+238)
		tmp = t_0;
	elseif (z <= -3.2e+149)
		tmp = t_2;
	elseif (z <= -2.3e+120)
		tmp = t_0;
	elseif (z <= -3.3e+60)
		tmp = t_2;
	elseif (z <= -1.38e+20)
		tmp = t_1;
	elseif (z <= -1.76e-65)
		tmp = t_2;
	elseif (z <= 3.05e-99)
		tmp = x;
	elseif (z <= 1.95e+229)
		tmp = t_2;
	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 * (x * z);
	t_2 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.8e+238)
		tmp = t_0;
	elseif (z <= -3.2e+149)
		tmp = t_2;
	elseif (z <= -2.3e+120)
		tmp = t_0;
	elseif (z <= -3.3e+60)
		tmp = t_2;
	elseif (z <= -1.38e+20)
		tmp = t_1;
	elseif (z <= -1.76e-65)
		tmp = t_2;
	elseif (z <= 3.05e-99)
		tmp = x;
	elseif (z <= 1.95e+229)
		tmp = t_2;
	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[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+238], t$95$0, If[LessEqual[z, -3.2e+149], t$95$2, If[LessEqual[z, -2.3e+120], t$95$0, If[LessEqual[z, -3.3e+60], t$95$2, If[LessEqual[z, -1.38e+20], t$95$1, If[LessEqual[z, -1.76e-65], t$95$2, If[LessEqual[z, 3.05e-99], x, If[LessEqual[z, 1.95e+229], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.79999999999999986e238 or -3.2000000000000002e149 < z < -2.29999999999999993e120

   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 99.8%

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

   4. Taylor expanded in x around inf 95.2%

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

      1. +-commutative 95.2%

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

      2. *-commutative 95.2%

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

   6. Simplified 95.2%

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

   7. Taylor expanded in z around inf 95.2%

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

      1. *-commutative 95.2%

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

   9. Simplified 95.2%

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

   if -1.79999999999999986e238 < z < -3.2000000000000002e149 or -2.29999999999999993e120 < z < -3.2999999999999998e60 or -1.38e20 < z < -1.7600000000000001e-65 or 3.0500000000000002e-99 < z < 1.9499999999999999e229

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 73.2%

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

      1. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in x around inf 58.6%

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

   7. Taylor expanded in y around inf 51.8%

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

   8. Taylor expanded in x around 0 66.3%

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

   if -3.2999999999999998e60 < z < -1.38e20 or 1.9499999999999999e229 < z

   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 99.7%

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

   4. Taylor expanded in x around inf 77.3%

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

      1. +-commutative 77.3%

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

      2. *-commutative 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in z around inf 77.3%

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

   if -1.7600000000000001e-65 < z < 3.0500000000000002e-99

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 82.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+238}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+149}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+60}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{+20}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-65}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+229}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ t_2 := -6 \cdot \left(x \cdot z\right)\\ t_3 := y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+149}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+72}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-66}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+229}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z)))
        (t_1 (* x (* z -6.0)))
        (t_2 (* -6.0 (* x z)))
        (t_3 (* y (* 6.0 z))))
   (if (<= z -4.5e+237)
     t_1
     (if (<= z -3.1e+149)
       t_3
       (if (<= z -1.5e+124)
         t_1
         (if (<= z -2.55e+72)
           t_3
           (if (<= z -7.2e+19)
             t_2
             (if (<= z -3.6e-66)
               t_0
               (if (<= z 3.05e-99) x (if (<= z 4.6e+229) t_0 t_2))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double t_2 = -6.0 * (x * z);
	double t_3 = y * (6.0 * z);
	double tmp;
	if (z <= -4.5e+237) {
		tmp = t_1;
	} else if (z <= -3.1e+149) {
		tmp = t_3;
	} else if (z <= -1.5e+124) {
		tmp = t_1;
	} else if (z <= -2.55e+72) {
		tmp = t_3;
	} else if (z <= -7.2e+19) {
		tmp = t_2;
	} else if (z <= -3.6e-66) {
		tmp = t_0;
	} else if (z <= 3.05e-99) {
		tmp = x;
	} else if (z <= 4.6e+229) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = x * (z * (-6.0d0))
    t_2 = (-6.0d0) * (x * z)
    t_3 = y * (6.0d0 * z)
    if (z <= (-4.5d+237)) then
        tmp = t_1
    else if (z <= (-3.1d+149)) then
        tmp = t_3
    else if (z <= (-1.5d+124)) then
        tmp = t_1
    else if (z <= (-2.55d+72)) then
        tmp = t_3
    else if (z <= (-7.2d+19)) then
        tmp = t_2
    else if (z <= (-3.6d-66)) then
        tmp = t_0
    else if (z <= 3.05d-99) then
        tmp = x
    else if (z <= 4.6d+229) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double t_2 = -6.0 * (x * z);
	double t_3 = y * (6.0 * z);
	double tmp;
	if (z <= -4.5e+237) {
		tmp = t_1;
	} else if (z <= -3.1e+149) {
		tmp = t_3;
	} else if (z <= -1.5e+124) {
		tmp = t_1;
	} else if (z <= -2.55e+72) {
		tmp = t_3;
	} else if (z <= -7.2e+19) {
		tmp = t_2;
	} else if (z <= -3.6e-66) {
		tmp = t_0;
	} else if (z <= 3.05e-99) {
		tmp = x;
	} else if (z <= 4.6e+229) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = x * (z * -6.0)
	t_2 = -6.0 * (x * z)
	t_3 = y * (6.0 * z)
	tmp = 0
	if z <= -4.5e+237:
		tmp = t_1
	elif z <= -3.1e+149:
		tmp = t_3
	elif z <= -1.5e+124:
		tmp = t_1
	elif z <= -2.55e+72:
		tmp = t_3
	elif z <= -7.2e+19:
		tmp = t_2
	elif z <= -3.6e-66:
		tmp = t_0
	elif z <= 3.05e-99:
		tmp = x
	elif z <= 4.6e+229:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * -6.0))
	t_2 = Float64(-6.0 * Float64(x * z))
	t_3 = Float64(y * Float64(6.0 * z))
	tmp = 0.0
	if (z <= -4.5e+237)
		tmp = t_1;
	elseif (z <= -3.1e+149)
		tmp = t_3;
	elseif (z <= -1.5e+124)
		tmp = t_1;
	elseif (z <= -2.55e+72)
		tmp = t_3;
	elseif (z <= -7.2e+19)
		tmp = t_2;
	elseif (z <= -3.6e-66)
		tmp = t_0;
	elseif (z <= 3.05e-99)
		tmp = x;
	elseif (z <= 4.6e+229)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = x * (z * -6.0);
	t_2 = -6.0 * (x * z);
	t_3 = y * (6.0 * z);
	tmp = 0.0;
	if (z <= -4.5e+237)
		tmp = t_1;
	elseif (z <= -3.1e+149)
		tmp = t_3;
	elseif (z <= -1.5e+124)
		tmp = t_1;
	elseif (z <= -2.55e+72)
		tmp = t_3;
	elseif (z <= -7.2e+19)
		tmp = t_2;
	elseif (z <= -3.6e-66)
		tmp = t_0;
	elseif (z <= 3.05e-99)
		tmp = x;
	elseif (z <= 4.6e+229)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+237], t$95$1, If[LessEqual[z, -3.1e+149], t$95$3, If[LessEqual[z, -1.5e+124], t$95$1, If[LessEqual[z, -2.55e+72], t$95$3, If[LessEqual[z, -7.2e+19], t$95$2, If[LessEqual[z, -3.6e-66], t$95$0, If[LessEqual[z, 3.05e-99], x, If[LessEqual[z, 4.6e+229], t$95$0, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.49999999999999964e237 or -3.09999999999999987e149 < z < -1.5e124

   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 99.8%

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

   4. Taylor expanded in x around inf 95.2%

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

      1. +-commutative 95.2%

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

      2. *-commutative 95.2%

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

   6. Simplified 95.2%

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

   7. Taylor expanded in z around inf 95.2%

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

      1. *-commutative 95.2%

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

   9. Simplified 95.2%

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

   if -4.49999999999999964e237 < z < -3.09999999999999987e149 or -1.5e124 < z < -2.54999999999999989e72

   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 inf 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in x around inf 48.3%

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

   7. Taylor expanded in y around inf 48.0%

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

   8. Taylor expanded in x around 0 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-*l* 69.3%

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

      3. *-commutative 69.3%

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

   10. Simplified 69.3%

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

   if -2.54999999999999989e72 < z < -7.2e19 or 4.5999999999999999e229 < z

   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 99.7%

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

   4. Taylor expanded in x around inf 77.3%

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

      1. +-commutative 77.3%

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

      2. *-commutative 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in z around inf 77.3%

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

   if -7.2e19 < z < -3.60000000000000012e-66 or 3.0500000000000002e-99 < z < 4.5999999999999999e229

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 74.6%

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

      1. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in x around inf 62.7%

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

   7. Taylor expanded in y around inf 53.3%

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

   8. Taylor expanded in x around 0 65.2%

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

   if -3.60000000000000012e-66 < z < 3.0500000000000002e-99

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 82.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+19}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-66}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+229}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+78} \lor \neg \left(y \leq 6.5 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.02e+78) (not (<= y 6.5e+76)))
   (* y (* 6.0 z))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e+78) || !(y <= 6.5e+76)) {
		tmp = 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 <= (-1.02d+78)) .or. (.not. (y <= 6.5d+76))) then
        tmp = 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 <= -1.02e+78) || !(y <= 6.5e+76)) {
		tmp = y * (6.0 * z);
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.02e+78) or not (y <= 6.5e+76):
		tmp = 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 <= -1.02e+78) || !(y <= 6.5e+76))
		tmp = 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 <= -1.02e+78) || ~((y <= 6.5e+76)))
		tmp = 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, -1.02e+78], N[Not[LessEqual[y, 6.5e+76]], $MachinePrecision]], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999994e78 or 6.5000000000000005e76 < y

   1. Initial program 98.9%

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

   3. Taylor expanded in y around inf 97.2%

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

      1. *-commutative 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in x around inf 84.6%

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

   7. Taylor expanded in y around inf 64.5%

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

   8. Taylor expanded in x around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l* 77.2%

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

      3. *-commutative 77.2%

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

   10. Simplified 77.2%

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

   if -1.01999999999999994e78 < y < 6.5000000000000005e76

   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 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+78} \lor \neg \left(y \leq 6.5 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-130} \lor \neg \left(y \leq 7.8 \cdot 10^{+62}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e-130) (not (<= y 7.8e+62)))
   (+ x (* 6.0 (* y z)))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-130) || !(y <= 7.8e+62)) {
		tmp = x + (6.0 * (y * 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 <= (-6.2d-130)) .or. (.not. (y <= 7.8d+62))) then
        tmp = x + (6.0d0 * (y * 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 <= -6.2e-130) || !(y <= 7.8e+62)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e-130) or not (y <= 7.8e+62):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e-130) || !(y <= 7.8e+62))
		tmp = Float64(x + Float64(6.0 * Float64(y * 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 <= -6.2e-130) || ~((y <= 7.8e+62)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e-130], N[Not[LessEqual[y, 7.8e+62]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * 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 < -6.20000000000000021e-130 or 7.8e62 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   if -6.20000000000000021e-130 < y < 7.8e62

   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 84.6%

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

      1. +-commutative 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-130} \lor \neg \left(y \leq 7.8 \cdot 10^{+62}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-130} \lor \neg \left(y \leq 8.2 \cdot 10^{+62}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6e-130) (not (<= y 8.2e+62)))
   (+ x (* y (* 6.0 z)))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e-130) || !(y <= 8.2e+62)) {
		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 <= (-6d-130)) .or. (.not. (y <= 8.2d+62))) 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 <= -6e-130) || !(y <= 8.2e+62)) {
		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 <= -6e-130) or not (y <= 8.2e+62):
		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 <= -6e-130) || !(y <= 8.2e+62))
		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 <= -6e-130) || ~((y <= 8.2e+62)))
		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, -6e-130], N[Not[LessEqual[y, 8.2e+62]], $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 < -5.99999999999999972e-130 or 8.19999999999999967e62 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*r* 90.5%

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

   5. Simplified 90.5%

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

   if -5.99999999999999972e-130 < y < 8.19999999999999967e62

   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 84.6%

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

      1. +-commutative 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-130} \lor \neg \left(y \leq 8.2 \cdot 10^{+62}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 0.165))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.165)) {
		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 <= 0.165d0))) 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 <= 0.165)) {
		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 <= 0.165):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 0.165))
		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 <= 0.165)))
		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, 0.165]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 0.165000000000000008 < z

   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 99.7%

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

   4. Taylor expanded in x around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. *-commutative 52.3%

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

   6. Simplified 52.3%

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

   7. Taylor expanded in z around inf 51.7%

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

   if -0.170000000000000012 < z < 0.165000000000000008

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 70.6%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.7% 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 99.4%

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

3. Final simplification 99.4%

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

Alternative 10: 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 99.4%

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

3. Taylor expanded in z around 0 32.3%

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

4. Final simplification 32.3%

   \[\leadsto x \]
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 2024071 
(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)))