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

Percentage Accurate: 99.7% → 99.8%

Time: 6.8s

Alternatives: 10

Speedup: 1.0×

• 20.9% 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 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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. Final simplification 99.8%

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

Alternative 2: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 14.5 \lor \neg \left(z \leq 3.2 \cdot 10^{+102}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -2.5e+93)
     t_0
     (if (<= z -5e+58)
       t_1
       (if (<= z -2.5e+18)
         t_0
         (if (<= z -1.05e-86)
           t_1
           (if (<= z 2.6e-126)
             x
             (if (or (<= z 14.5) (not (<= z 3.2e+102))) 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 <= -2.5e+93) {
		tmp = t_0;
	} else if (z <= -5e+58) {
		tmp = t_1;
	} else if (z <= -2.5e+18) {
		tmp = t_0;
	} else if (z <= -1.05e-86) {
		tmp = t_1;
	} else if (z <= 2.6e-126) {
		tmp = x;
	} else if ((z <= 14.5) || !(z <= 3.2e+102)) {
		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 <= (-2.5d+93)) then
        tmp = t_0
    else if (z <= (-5d+58)) then
        tmp = t_1
    else if (z <= (-2.5d+18)) then
        tmp = t_0
    else if (z <= (-1.05d-86)) then
        tmp = t_1
    else if (z <= 2.6d-126) then
        tmp = x
    else if ((z <= 14.5d0) .or. (.not. (z <= 3.2d+102))) 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 <= -2.5e+93) {
		tmp = t_0;
	} else if (z <= -5e+58) {
		tmp = t_1;
	} else if (z <= -2.5e+18) {
		tmp = t_0;
	} else if (z <= -1.05e-86) {
		tmp = t_1;
	} else if (z <= 2.6e-126) {
		tmp = x;
	} else if ((z <= 14.5) || !(z <= 3.2e+102)) {
		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 <= -2.5e+93:
		tmp = t_0
	elif z <= -5e+58:
		tmp = t_1
	elif z <= -2.5e+18:
		tmp = t_0
	elif z <= -1.05e-86:
		tmp = t_1
	elif z <= 2.6e-126:
		tmp = x
	elif (z <= 14.5) or not (z <= 3.2e+102):
		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 <= -2.5e+93)
		tmp = t_0;
	elseif (z <= -5e+58)
		tmp = t_1;
	elseif (z <= -2.5e+18)
		tmp = t_0;
	elseif (z <= -1.05e-86)
		tmp = t_1;
	elseif (z <= 2.6e-126)
		tmp = x;
	elseif ((z <= 14.5) || !(z <= 3.2e+102))
		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 <= -2.5e+93)
		tmp = t_0;
	elseif (z <= -5e+58)
		tmp = t_1;
	elseif (z <= -2.5e+18)
		tmp = t_0;
	elseif (z <= -1.05e-86)
		tmp = t_1;
	elseif (z <= 2.6e-126)
		tmp = x;
	elseif ((z <= 14.5) || ~((z <= 3.2e+102)))
		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, -2.5e+93], t$95$0, If[LessEqual[z, -5e+58], t$95$1, If[LessEqual[z, -2.5e+18], t$95$0, If[LessEqual[z, -1.05e-86], t$95$1, If[LessEqual[z, 2.6e-126], x, If[Or[LessEqual[z, 14.5], N[Not[LessEqual[z, 3.2e+102]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5000000000000001e93 or -4.99999999999999986e58 < z < -2.5e18 or 14.5 < z < 3.1999999999999999e102

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.5%

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

   4. Taylor expanded in y around 0 65.5%

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

   if -2.5000000000000001e93 < z < -4.99999999999999986e58 or -2.5e18 < z < -1.05e-86 or 2.59999999999999999e-126 < z < 14.5 or 3.1999999999999999e102 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 81.9%

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

   4. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   if -1.05e-86 < z < 2.59999999999999999e-126

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 78.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+93}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+58}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-86}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 14.5 \lor \neg \left(z \leq 3.2 \cdot 10^{+102}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 14.5 \lor \neg \left(z \leq 6.2 \cdot 10^{+104}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -5.8e+92)
     (* x (* z -6.0))
     (if (<= z -5.5e+55)
       t_1
       (if (<= z -4e+19)
         t_0
         (if (<= z -1.3e-83)
           t_1
           (if (<= z 2.6e-126)
             x
             (if (or (<= z 14.5) (not (<= z 6.2e+104))) 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 <= -5.8e+92) {
		tmp = x * (z * -6.0);
	} else if (z <= -5.5e+55) {
		tmp = t_1;
	} else if (z <= -4e+19) {
		tmp = t_0;
	} else if (z <= -1.3e-83) {
		tmp = t_1;
	} else if (z <= 2.6e-126) {
		tmp = x;
	} else if ((z <= 14.5) || !(z <= 6.2e+104)) {
		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 <= (-5.8d+92)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-5.5d+55)) then
        tmp = t_1
    else if (z <= (-4d+19)) then
        tmp = t_0
    else if (z <= (-1.3d-83)) then
        tmp = t_1
    else if (z <= 2.6d-126) then
        tmp = x
    else if ((z <= 14.5d0) .or. (.not. (z <= 6.2d+104))) 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 <= -5.8e+92) {
		tmp = x * (z * -6.0);
	} else if (z <= -5.5e+55) {
		tmp = t_1;
	} else if (z <= -4e+19) {
		tmp = t_0;
	} else if (z <= -1.3e-83) {
		tmp = t_1;
	} else if (z <= 2.6e-126) {
		tmp = x;
	} else if ((z <= 14.5) || !(z <= 6.2e+104)) {
		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 <= -5.8e+92:
		tmp = x * (z * -6.0)
	elif z <= -5.5e+55:
		tmp = t_1
	elif z <= -4e+19:
		tmp = t_0
	elif z <= -1.3e-83:
		tmp = t_1
	elif z <= 2.6e-126:
		tmp = x
	elif (z <= 14.5) or not (z <= 6.2e+104):
		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 <= -5.8e+92)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -5.5e+55)
		tmp = t_1;
	elseif (z <= -4e+19)
		tmp = t_0;
	elseif (z <= -1.3e-83)
		tmp = t_1;
	elseif (z <= 2.6e-126)
		tmp = x;
	elseif ((z <= 14.5) || !(z <= 6.2e+104))
		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 <= -5.8e+92)
		tmp = x * (z * -6.0);
	elseif (z <= -5.5e+55)
		tmp = t_1;
	elseif (z <= -4e+19)
		tmp = t_0;
	elseif (z <= -1.3e-83)
		tmp = t_1;
	elseif (z <= 2.6e-126)
		tmp = x;
	elseif ((z <= 14.5) || ~((z <= 6.2e+104)))
		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, -5.8e+92], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e+55], t$95$1, If[LessEqual[z, -4e+19], t$95$0, If[LessEqual[z, -1.3e-83], t$95$1, If[LessEqual[z, 2.6e-126], x, If[Or[LessEqual[z, 14.5], N[Not[LessEqual[z, 6.2e+104]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.8000000000000001e92

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf 64.5%

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

   3. Taylor expanded in z around inf 64.5%

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

   if -5.8000000000000001e92 < z < -5.5000000000000004e55 or -4e19 < z < -1.30000000000000004e-83 or 2.59999999999999999e-126 < z < 14.5 or 6.20000000000000033e104 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 81.9%

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

   4. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   if -5.5000000000000004e55 < z < -4e19 or 14.5 < z < 6.20000000000000033e104

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 96.6%

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

   4. Taylor expanded in y around 0 67.1%

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

   if -1.30000000000000004e-83 < z < 2.59999999999999999e-126

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 78.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+19}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-83}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 14.5 \lor \neg \left(z \leq 6.2 \cdot 10^{+104}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 14.5 \lor \neg \left(z \leq 2.2 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -3.3e+93)
     (* x (* z -6.0))
     (if (<= z -1e+56)
       t_1
       (if (<= z -3.6e+19)
         t_0
         (if (<= z -1.02e-85)
           t_1
           (if (<= z 2.5e-126)
             x
             (if (or (<= z 14.5) (not (<= z 2.2e+105)))
               (* z (* y 6.0))
               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 <= -3.3e+93) {
		tmp = x * (z * -6.0);
	} else if (z <= -1e+56) {
		tmp = t_1;
	} else if (z <= -3.6e+19) {
		tmp = t_0;
	} else if (z <= -1.02e-85) {
		tmp = t_1;
	} else if (z <= 2.5e-126) {
		tmp = x;
	} else if ((z <= 14.5) || !(z <= 2.2e+105)) {
		tmp = z * (y * 6.0);
	} 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 <= (-3.3d+93)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-1d+56)) then
        tmp = t_1
    else if (z <= (-3.6d+19)) then
        tmp = t_0
    else if (z <= (-1.02d-85)) then
        tmp = t_1
    else if (z <= 2.5d-126) then
        tmp = x
    else if ((z <= 14.5d0) .or. (.not. (z <= 2.2d+105))) then
        tmp = z * (y * 6.0d0)
    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 <= -3.3e+93) {
		tmp = x * (z * -6.0);
	} else if (z <= -1e+56) {
		tmp = t_1;
	} else if (z <= -3.6e+19) {
		tmp = t_0;
	} else if (z <= -1.02e-85) {
		tmp = t_1;
	} else if (z <= 2.5e-126) {
		tmp = x;
	} else if ((z <= 14.5) || !(z <= 2.2e+105)) {
		tmp = z * (y * 6.0);
	} 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 <= -3.3e+93:
		tmp = x * (z * -6.0)
	elif z <= -1e+56:
		tmp = t_1
	elif z <= -3.6e+19:
		tmp = t_0
	elif z <= -1.02e-85:
		tmp = t_1
	elif z <= 2.5e-126:
		tmp = x
	elif (z <= 14.5) or not (z <= 2.2e+105):
		tmp = z * (y * 6.0)
	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 <= -3.3e+93)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -1e+56)
		tmp = t_1;
	elseif (z <= -3.6e+19)
		tmp = t_0;
	elseif (z <= -1.02e-85)
		tmp = t_1;
	elseif (z <= 2.5e-126)
		tmp = x;
	elseif ((z <= 14.5) || !(z <= 2.2e+105))
		tmp = Float64(z * Float64(y * 6.0));
	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 <= -3.3e+93)
		tmp = x * (z * -6.0);
	elseif (z <= -1e+56)
		tmp = t_1;
	elseif (z <= -3.6e+19)
		tmp = t_0;
	elseif (z <= -1.02e-85)
		tmp = t_1;
	elseif (z <= 2.5e-126)
		tmp = x;
	elseif ((z <= 14.5) || ~((z <= 2.2e+105)))
		tmp = z * (y * 6.0);
	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, -3.3e+93], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e+56], t$95$1, If[LessEqual[z, -3.6e+19], t$95$0, If[LessEqual[z, -1.02e-85], t$95$1, If[LessEqual[z, 2.5e-126], x, If[Or[LessEqual[z, 14.5], N[Not[LessEqual[z, 2.2e+105]], $MachinePrecision]], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.30000000000000009e93

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in x around inf 64.5%

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

   3. Taylor expanded in z around inf 64.5%

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

   if -3.30000000000000009e93 < z < -1.00000000000000009e56 or -3.6e19 < z < -1.02000000000000001e-85

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 79.3%

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

   4. Taylor expanded in y around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -1.00000000000000009e56 < z < -3.6e19 or 14.5 < z < 2.20000000000000007e105

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 96.6%

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

   4. Taylor expanded in y around 0 67.1%

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

   if -1.02000000000000001e-85 < z < 2.50000000000000003e-126

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 78.5%

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

   if 2.50000000000000003e-126 < z < 14.5 or 2.20000000000000007e105 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 83.2%

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

   4. Taylor expanded in y around inf 63.5%

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

      1. associate-*r* 63.7%

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

      2. *-commutative 63.7%

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

   6. Simplified 63.7%

      \[\leadsto \color{blue}{\left(y \cdot 6\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+56}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+19}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-85}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 14.5 \lor \neg \left(z \leq 2.2 \cdot 10^{+105}\right):\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-104} \lor \neg \left(z \leq 2.6 \cdot 10^{-126}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e-104) (not (<= z 2.6e-126))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-104) || !(z <= 2.6e-126)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.4d-104)) .or. (.not. (z <= 2.6d-126))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-104) || !(z <= 2.6e-126)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e-104) or not (z <= 2.6e-126):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e-104) || !(z <= 2.6e-126))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.4e-104) || ~((z <= 2.6e-126)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e-104], N[Not[LessEqual[z, 2.6e-126]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000015e-104 or 2.59999999999999999e-126 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 88.6%

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

   if -3.40000000000000015e-104 < z < 2.59999999999999999e-126

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 80.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-104} \lor \neg \left(z \leq 2.6 \cdot 10^{-126}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -115000 \lor \neg \left(z \leq 2.8 \cdot 10^{-18}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -115000.0) (not (<= z 2.8e-18)))
   (* 6.0 (* (- y x) z))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -115000.0) || !(z <= 2.8e-18)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-115000.0d0)) .or. (.not. (z <= 2.8d-18))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -115000.0) || !(z <= 2.8e-18)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -115000.0) or not (z <= 2.8e-18):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -115000.0) || !(z <= 2.8e-18))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -115000.0) || ~((z <= 2.8e-18)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -115000.0], N[Not[LessEqual[z, 2.8e-18]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -115000 or 2.80000000000000012e-18 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 98.7%

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

   if -115000 < z < 2.80000000000000012e-18

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in y around inf 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115000 \lor \neg \left(z \leq 2.8 \cdot 10^{-18}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 7: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.83\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 0.83)))
   (* 6.0 (* (- y x) z))
   (+ x (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.83)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (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 ((z <= (-0.17d0)) .or. (.not. (z <= 0.83d0))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (z * (y * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.83)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 0.83):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 0.83))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.17) || ~((z <= 0.83)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 0.83]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 0.82999999999999996 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.8%

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

   if -0.170000000000000012 < z < 0.82999999999999996

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in y around inf 99.3%

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

      1. associate-*r* 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.83\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 8: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2300000000000 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2300000000000.0) (not (<= z 0.166))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2300000000000.0) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2300000000000.0d0)) .or. (.not. (z <= 0.166d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2300000000000.0) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2300000000000.0) or not (z <= 0.166):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2300000000000.0) || !(z <= 0.166))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2300000000000.0) || ~((z <= 0.166)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2300000000000.0], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e12 or 0.166000000000000009 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.9%

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

   4. Taylor expanded in y around 0 55.5%

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

   if -2.3e12 < z < 0.166000000000000009

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

   2. Taylor expanded in z around 0 59.7%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2300000000000 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

2. Final simplification 99.8%

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

Alternative 10: 36.2% 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. Taylor expanded in z around 0 31.1%

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

3. Final simplification 31.1%

   \[\leadsto x \]

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 2023173 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

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

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