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

Percentage Accurate: 99.6% → 99.6%

Time: 6.7s

Alternatives: 12

Speedup: 1.0×

• 21.9% 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: 99.6% 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: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((x * (-6.0d0)) + (6.0d0 * y)) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+241}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3300000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+14} \lor \neg \left(z \leq 1.06 \cdot 10^{+27}\right) \land z \leq 5.5 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -7.5e+241)
     t_0
     (if (<= z -5.2e+199)
       t_1
       (if (<= z -2.45e+79)
         t_0
         (if (<= z -6.2e+45)
           t_1
           (if (<= z -3300000000000.0)
             t_0
             (if (<= z -1.15e-39)
               t_1
               (if (<= z 7.6e-90)
                 x
                 (if (or (<= z 2.15e+14)
                         (and (not (<= z 1.06e+27)) (<= z 5.5e+140)))
                   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 <= -7.5e+241) {
		tmp = t_0;
	} else if (z <= -5.2e+199) {
		tmp = t_1;
	} else if (z <= -2.45e+79) {
		tmp = t_0;
	} else if (z <= -6.2e+45) {
		tmp = t_1;
	} else if (z <= -3300000000000.0) {
		tmp = t_0;
	} else if (z <= -1.15e-39) {
		tmp = t_1;
	} else if (z <= 7.6e-90) {
		tmp = x;
	} else if ((z <= 2.15e+14) || (!(z <= 1.06e+27) && (z <= 5.5e+140))) {
		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 <= (-7.5d+241)) then
        tmp = t_0
    else if (z <= (-5.2d+199)) then
        tmp = t_1
    else if (z <= (-2.45d+79)) then
        tmp = t_0
    else if (z <= (-6.2d+45)) then
        tmp = t_1
    else if (z <= (-3300000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.15d-39)) then
        tmp = t_1
    else if (z <= 7.6d-90) then
        tmp = x
    else if ((z <= 2.15d+14) .or. (.not. (z <= 1.06d+27)) .and. (z <= 5.5d+140)) 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 <= -7.5e+241) {
		tmp = t_0;
	} else if (z <= -5.2e+199) {
		tmp = t_1;
	} else if (z <= -2.45e+79) {
		tmp = t_0;
	} else if (z <= -6.2e+45) {
		tmp = t_1;
	} else if (z <= -3300000000000.0) {
		tmp = t_0;
	} else if (z <= -1.15e-39) {
		tmp = t_1;
	} else if (z <= 7.6e-90) {
		tmp = x;
	} else if ((z <= 2.15e+14) || (!(z <= 1.06e+27) && (z <= 5.5e+140))) {
		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 <= -7.5e+241:
		tmp = t_0
	elif z <= -5.2e+199:
		tmp = t_1
	elif z <= -2.45e+79:
		tmp = t_0
	elif z <= -6.2e+45:
		tmp = t_1
	elif z <= -3300000000000.0:
		tmp = t_0
	elif z <= -1.15e-39:
		tmp = t_1
	elif z <= 7.6e-90:
		tmp = x
	elif (z <= 2.15e+14) or (not (z <= 1.06e+27) and (z <= 5.5e+140)):
		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 <= -7.5e+241)
		tmp = t_0;
	elseif (z <= -5.2e+199)
		tmp = t_1;
	elseif (z <= -2.45e+79)
		tmp = t_0;
	elseif (z <= -6.2e+45)
		tmp = t_1;
	elseif (z <= -3300000000000.0)
		tmp = t_0;
	elseif (z <= -1.15e-39)
		tmp = t_1;
	elseif (z <= 7.6e-90)
		tmp = x;
	elseif ((z <= 2.15e+14) || (!(z <= 1.06e+27) && (z <= 5.5e+140)))
		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 <= -7.5e+241)
		tmp = t_0;
	elseif (z <= -5.2e+199)
		tmp = t_1;
	elseif (z <= -2.45e+79)
		tmp = t_0;
	elseif (z <= -6.2e+45)
		tmp = t_1;
	elseif (z <= -3300000000000.0)
		tmp = t_0;
	elseif (z <= -1.15e-39)
		tmp = t_1;
	elseif (z <= 7.6e-90)
		tmp = x;
	elseif ((z <= 2.15e+14) || (~((z <= 1.06e+27)) && (z <= 5.5e+140)))
		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, -7.5e+241], t$95$0, If[LessEqual[z, -5.2e+199], t$95$1, If[LessEqual[z, -2.45e+79], t$95$0, If[LessEqual[z, -6.2e+45], t$95$1, If[LessEqual[z, -3300000000000.0], t$95$0, If[LessEqual[z, -1.15e-39], t$95$1, If[LessEqual[z, 7.6e-90], x, If[Or[LessEqual[z, 2.15e+14], And[N[Not[LessEqual[z, 1.06e+27]], $MachinePrecision], LessEqual[z, 5.5e+140]]], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000001e241 or -5.2000000000000003e199 < z < -2.4499999999999999e79 or -6.19999999999999975e45 < z < -3.3e12 or 2.15e14 < z < 1.05999999999999994e27 or 5.5e140 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 73.0%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in x around 0 72.8%

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

   if -7.5000000000000001e241 < z < -5.2000000000000003e199 or -2.4499999999999999e79 < z < -6.19999999999999975e45 or -3.3e12 < z < -1.15000000000000004e-39 or 7.6e-90 < z < 2.15e14 or 1.05999999999999994e27 < z < 5.5e140

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 84.3%

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

   4. Taylor expanded in y around inf 71.3%

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

      1. *-commutative 71.3%

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

   6. Simplified 71.3%

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

   if -1.15000000000000004e-39 < z < 7.6e-90

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+241}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+199}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+79}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3300000000000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-39}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+14} \lor \neg \left(z \leq 1.06 \cdot 10^{+27}\right) \land z \leq 5.5 \cdot 10^{+140}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-6 \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ t_2 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+241}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1350000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+195}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* -6.0 z))) (t_1 (* -6.0 (* x z))) (t_2 (* 6.0 (* y z))))
   (if (<= z -6e+241)
     t_0
     (if (<= z -1.15e+200)
       t_2
       (if (<= z -2.4e+80)
         t_0
         (if (<= z -1.45e+47)
           t_2
           (if (<= z -1350000000000.0)
             t_1
             (if (<= z -5.4e-40)
               t_2
               (if (<= z 3.9e-89)
                 x
                 (if (<= z 2.7e+14)
                   t_2
                   (if (<= z 1.18e+27)
                     t_1
                     (if (<= z 3.6e+195) t_2 t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-6.0 * z);
	double t_1 = -6.0 * (x * z);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -6e+241) {
		tmp = t_0;
	} else if (z <= -1.15e+200) {
		tmp = t_2;
	} else if (z <= -2.4e+80) {
		tmp = t_0;
	} else if (z <= -1.45e+47) {
		tmp = t_2;
	} else if (z <= -1350000000000.0) {
		tmp = t_1;
	} else if (z <= -5.4e-40) {
		tmp = t_2;
	} else if (z <= 3.9e-89) {
		tmp = x;
	} else if (z <= 2.7e+14) {
		tmp = t_2;
	} else if (z <= 1.18e+27) {
		tmp = t_1;
	} else if (z <= 3.6e+195) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = x * ((-6.0d0) * z)
    t_1 = (-6.0d0) * (x * z)
    t_2 = 6.0d0 * (y * z)
    if (z <= (-6d+241)) then
        tmp = t_0
    else if (z <= (-1.15d+200)) then
        tmp = t_2
    else if (z <= (-2.4d+80)) then
        tmp = t_0
    else if (z <= (-1.45d+47)) then
        tmp = t_2
    else if (z <= (-1350000000000.0d0)) then
        tmp = t_1
    else if (z <= (-5.4d-40)) then
        tmp = t_2
    else if (z <= 3.9d-89) then
        tmp = x
    else if (z <= 2.7d+14) then
        tmp = t_2
    else if (z <= 1.18d+27) then
        tmp = t_1
    else if (z <= 3.6d+195) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-6.0 * z);
	double t_1 = -6.0 * (x * z);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -6e+241) {
		tmp = t_0;
	} else if (z <= -1.15e+200) {
		tmp = t_2;
	} else if (z <= -2.4e+80) {
		tmp = t_0;
	} else if (z <= -1.45e+47) {
		tmp = t_2;
	} else if (z <= -1350000000000.0) {
		tmp = t_1;
	} else if (z <= -5.4e-40) {
		tmp = t_2;
	} else if (z <= 3.9e-89) {
		tmp = x;
	} else if (z <= 2.7e+14) {
		tmp = t_2;
	} else if (z <= 1.18e+27) {
		tmp = t_1;
	} else if (z <= 3.6e+195) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-6.0 * z)
	t_1 = -6.0 * (x * z)
	t_2 = 6.0 * (y * z)
	tmp = 0
	if z <= -6e+241:
		tmp = t_0
	elif z <= -1.15e+200:
		tmp = t_2
	elif z <= -2.4e+80:
		tmp = t_0
	elif z <= -1.45e+47:
		tmp = t_2
	elif z <= -1350000000000.0:
		tmp = t_1
	elif z <= -5.4e-40:
		tmp = t_2
	elif z <= 3.9e-89:
		tmp = x
	elif z <= 2.7e+14:
		tmp = t_2
	elif z <= 1.18e+27:
		tmp = t_1
	elif z <= 3.6e+195:
		tmp = t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-6.0 * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	t_2 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -6e+241)
		tmp = t_0;
	elseif (z <= -1.15e+200)
		tmp = t_2;
	elseif (z <= -2.4e+80)
		tmp = t_0;
	elseif (z <= -1.45e+47)
		tmp = t_2;
	elseif (z <= -1350000000000.0)
		tmp = t_1;
	elseif (z <= -5.4e-40)
		tmp = t_2;
	elseif (z <= 3.9e-89)
		tmp = x;
	elseif (z <= 2.7e+14)
		tmp = t_2;
	elseif (z <= 1.18e+27)
		tmp = t_1;
	elseif (z <= 3.6e+195)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-6.0 * z);
	t_1 = -6.0 * (x * z);
	t_2 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -6e+241)
		tmp = t_0;
	elseif (z <= -1.15e+200)
		tmp = t_2;
	elseif (z <= -2.4e+80)
		tmp = t_0;
	elseif (z <= -1.45e+47)
		tmp = t_2;
	elseif (z <= -1350000000000.0)
		tmp = t_1;
	elseif (z <= -5.4e-40)
		tmp = t_2;
	elseif (z <= 3.9e-89)
		tmp = x;
	elseif (z <= 2.7e+14)
		tmp = t_2;
	elseif (z <= 1.18e+27)
		tmp = t_1;
	elseif (z <= 3.6e+195)
		tmp = t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-6.0 * z), $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, -6e+241], t$95$0, If[LessEqual[z, -1.15e+200], t$95$2, If[LessEqual[z, -2.4e+80], t$95$0, If[LessEqual[z, -1.45e+47], t$95$2, If[LessEqual[z, -1350000000000.0], t$95$1, If[LessEqual[z, -5.4e-40], t$95$2, If[LessEqual[z, 3.9e-89], x, If[LessEqual[z, 2.7e+14], t$95$2, If[LessEqual[z, 1.18e+27], t$95$1, If[LessEqual[z, 3.6e+195], t$95$2, t$95$0]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.00000000000000031e241 or -1.15000000000000002e200 < z < -2.39999999999999979e80 or 3.5999999999999999e195 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 71.9%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -6.00000000000000031e241 < z < -1.15000000000000002e200 or -2.39999999999999979e80 < z < -1.4499999999999999e47 or -1.35e12 < z < -5.4e-40 or 3.89999999999999978e-89 < z < 2.7e14 or 1.18000000000000006e27 < z < 3.5999999999999999e195

   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%

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

   3. Taylor expanded in z around inf 86.0%

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

   4. Taylor expanded in y around inf 69.1%

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

      1. *-commutative 69.1%

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

   6. Simplified 69.1%

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

   if -1.4499999999999999e47 < z < -1.35e12 or 2.7e14 < z < 1.18000000000000006e27

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 99.7%

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

   3. Taylor expanded in z around inf 98.4%

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

      1. *-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around 0 98.7%

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

   if -5.4e-40 < z < 3.89999999999999978e-89

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+200}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1350000000000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-40}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+27}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+195}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \end{array} \]

Alternative 4: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot y\right) \cdot z\\ t_1 := x \cdot \left(-6 \cdot z\right)\\ t_2 := -6 \cdot \left(x \cdot z\right)\\ t_3 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1050000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+201}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 y) z))
        (t_1 (* x (* -6.0 z)))
        (t_2 (* -6.0 (* x z)))
        (t_3 (* 6.0 (* y z))))
   (if (<= z -7.5e+241)
     t_1
     (if (<= z -1.25e+200)
       t_3
       (if (<= z -1.05e+81)
         t_1
         (if (<= z -1.45e+47)
           t_3
           (if (<= z -1050000000000.0)
             t_2
             (if (<= z -1.26e-39)
               t_0
               (if (<= z 2.35e-98)
                 x
                 (if (<= z 4e+14)
                   t_0
                   (if (<= z 3.2e+26)
                     t_2
                     (if (<= z 1.18e+201) t_0 t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double t_1 = x * (-6.0 * z);
	double t_2 = -6.0 * (x * z);
	double t_3 = 6.0 * (y * z);
	double tmp;
	if (z <= -7.5e+241) {
		tmp = t_1;
	} else if (z <= -1.25e+200) {
		tmp = t_3;
	} else if (z <= -1.05e+81) {
		tmp = t_1;
	} else if (z <= -1.45e+47) {
		tmp = t_3;
	} else if (z <= -1050000000000.0) {
		tmp = t_2;
	} else if (z <= -1.26e-39) {
		tmp = t_0;
	} else if (z <= 2.35e-98) {
		tmp = x;
	} else if (z <= 4e+14) {
		tmp = t_0;
	} else if (z <= 3.2e+26) {
		tmp = t_2;
	} else if (z <= 1.18e+201) {
		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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (6.0d0 * y) * z
    t_1 = x * ((-6.0d0) * z)
    t_2 = (-6.0d0) * (x * z)
    t_3 = 6.0d0 * (y * z)
    if (z <= (-7.5d+241)) then
        tmp = t_1
    else if (z <= (-1.25d+200)) then
        tmp = t_3
    else if (z <= (-1.05d+81)) then
        tmp = t_1
    else if (z <= (-1.45d+47)) then
        tmp = t_3
    else if (z <= (-1050000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.26d-39)) then
        tmp = t_0
    else if (z <= 2.35d-98) then
        tmp = x
    else if (z <= 4d+14) then
        tmp = t_0
    else if (z <= 3.2d+26) then
        tmp = t_2
    else if (z <= 1.18d+201) 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 * y) * z;
	double t_1 = x * (-6.0 * z);
	double t_2 = -6.0 * (x * z);
	double t_3 = 6.0 * (y * z);
	double tmp;
	if (z <= -7.5e+241) {
		tmp = t_1;
	} else if (z <= -1.25e+200) {
		tmp = t_3;
	} else if (z <= -1.05e+81) {
		tmp = t_1;
	} else if (z <= -1.45e+47) {
		tmp = t_3;
	} else if (z <= -1050000000000.0) {
		tmp = t_2;
	} else if (z <= -1.26e-39) {
		tmp = t_0;
	} else if (z <= 2.35e-98) {
		tmp = x;
	} else if (z <= 4e+14) {
		tmp = t_0;
	} else if (z <= 3.2e+26) {
		tmp = t_2;
	} else if (z <= 1.18e+201) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (6.0 * y) * z
	t_1 = x * (-6.0 * z)
	t_2 = -6.0 * (x * z)
	t_3 = 6.0 * (y * z)
	tmp = 0
	if z <= -7.5e+241:
		tmp = t_1
	elif z <= -1.25e+200:
		tmp = t_3
	elif z <= -1.05e+81:
		tmp = t_1
	elif z <= -1.45e+47:
		tmp = t_3
	elif z <= -1050000000000.0:
		tmp = t_2
	elif z <= -1.26e-39:
		tmp = t_0
	elif z <= 2.35e-98:
		tmp = x
	elif z <= 4e+14:
		tmp = t_0
	elif z <= 3.2e+26:
		tmp = t_2
	elif z <= 1.18e+201:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * y) * z)
	t_1 = Float64(x * Float64(-6.0 * z))
	t_2 = Float64(-6.0 * Float64(x * z))
	t_3 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -7.5e+241)
		tmp = t_1;
	elseif (z <= -1.25e+200)
		tmp = t_3;
	elseif (z <= -1.05e+81)
		tmp = t_1;
	elseif (z <= -1.45e+47)
		tmp = t_3;
	elseif (z <= -1050000000000.0)
		tmp = t_2;
	elseif (z <= -1.26e-39)
		tmp = t_0;
	elseif (z <= 2.35e-98)
		tmp = x;
	elseif (z <= 4e+14)
		tmp = t_0;
	elseif (z <= 3.2e+26)
		tmp = t_2;
	elseif (z <= 1.18e+201)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (6.0 * y) * z;
	t_1 = x * (-6.0 * z);
	t_2 = -6.0 * (x * z);
	t_3 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -7.5e+241)
		tmp = t_1;
	elseif (z <= -1.25e+200)
		tmp = t_3;
	elseif (z <= -1.05e+81)
		tmp = t_1;
	elseif (z <= -1.45e+47)
		tmp = t_3;
	elseif (z <= -1050000000000.0)
		tmp = t_2;
	elseif (z <= -1.26e-39)
		tmp = t_0;
	elseif (z <= 2.35e-98)
		tmp = x;
	elseif (z <= 4e+14)
		tmp = t_0;
	elseif (z <= 3.2e+26)
		tmp = t_2;
	elseif (z <= 1.18e+201)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+241], t$95$1, If[LessEqual[z, -1.25e+200], t$95$3, If[LessEqual[z, -1.05e+81], t$95$1, If[LessEqual[z, -1.45e+47], t$95$3, If[LessEqual[z, -1050000000000.0], t$95$2, If[LessEqual[z, -1.26e-39], t$95$0, If[LessEqual[z, 2.35e-98], x, If[LessEqual[z, 4e+14], t$95$0, If[LessEqual[z, 3.2e+26], t$95$2, If[LessEqual[z, 1.18e+201], t$95$0, t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.5000000000000001e241 or -1.25000000000000005e200 < z < -1.0499999999999999e81 or 1.18e201 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 71.9%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -7.5000000000000001e241 < z < -1.25000000000000005e200 or -1.0499999999999999e81 < z < -1.4499999999999999e47

   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%

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

   3. Taylor expanded in z around inf 99.8%

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

   4. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   6. Simplified 85.6%

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

   if -1.4499999999999999e47 < z < -1.05e12 or 4e14 < z < 3.20000000000000029e26

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 99.7%

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

   3. Taylor expanded in z around inf 98.4%

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

      1. *-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around 0 98.7%

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

   if -1.05e12 < z < -1.26e-39 or 2.35000000000000003e-98 < z < 4e14 or 3.20000000000000029e26 < z < 1.18e201

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 82.7%

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

   4. Taylor expanded in y around inf 65.7%

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

      1. associate-*r* 65.8%

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

      2. *-commutative 65.8%

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

      3. *-commutative 65.8%

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

      4. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   if -1.26e-39 < z < 2.35000000000000003e-98

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 77.2%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+200}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1050000000000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-39}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+201}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-6 \cdot z\right)\\ \end{array} \]

Alternative 5: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-40} \lor \neg \left(z \leq 9 \cdot 10^{-89}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.6e-40) (not (<= z 9e-89))) (* 6.0 (* z (- y x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.6e-40) || !(z <= 9e-89)) {
		tmp = 6.0 * (z * (y - x));
	} 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 <= (-7.6d-40)) .or. (.not. (z <= 9d-89))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.6e-40) || !(z <= 9e-89)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.6e-40) or not (z <= 9e-89):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.6e-40) || !(z <= 9e-89))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.6e-40) || ~((z <= 9e-89)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.6e-40], N[Not[LessEqual[z, 9e-89]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999998e-40 or 8.9999999999999998e-89 < 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%

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

   3. Taylor expanded in z around inf 91.2%

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

   if -7.5999999999999998e-40 < z < 8.9999999999999998e-89

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-40} \lor \neg \left(z \leq 9 \cdot 10^{-89}\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-39} \lor \neg \left(z \leq 2.9 \cdot 10^{-90}\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e-39) (not (<= z 2.9e-90))) (* (- y x) (* 6.0 z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-39) || !(z <= 2.9e-90)) {
		tmp = (y - x) * (6.0 * 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 <= (-1d-39)) .or. (.not. (z <= 2.9d-90))) then
        tmp = (y - x) * (6.0d0 * 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 <= -1e-39) || !(z <= 2.9e-90)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e-39) or not (z <= 2.9e-90):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e-39) || !(z <= 2.9e-90))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e-39) || ~((z <= 2.9e-90)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e-39], N[Not[LessEqual[z, 2.9e-90]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999929e-40 or 2.89999999999999983e-90 < 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%

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

   3. Taylor expanded in z around inf 91.2%

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

   4. Taylor expanded in y around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. associate-*r* 87.2%

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

      3. *-commutative 87.2%

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

      4. associate-*r* 87.2%

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

      5. distribute-rgt-out 91.3%

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

      6. metadata-eval 91.3%

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

      7. associate-*r* 91.3%

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

      8. neg-mul-1 91.3%

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

      9. *-commutative 91.3%

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

      10. distribute-rgt-in 91.3%

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

      11. sub-neg 91.3%

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

      12. associate-*r* 91.3%

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

      13. *-commutative 91.3%

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

   6. Simplified 91.3%

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

   if -9.99999999999999929e-40 < z < 2.89999999999999983e-90

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-39} \lor \neg \left(z \leq 2.9 \cdot 10^{-90}\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.142:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.142)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.17) (+ x (* 6.0 (* y z))) (* 6.0 (* z (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.142) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.142d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 0.17d0) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = 6.0d0 * (z * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.142) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.17) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.142:
		tmp = (y - x) * (6.0 * z)
	elif z <= 0.17:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.142)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.17)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.142)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 0.17)
		tmp = x + (6.0 * (y * z));
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.142], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.141999999999999987

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.6%

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

   4. Taylor expanded in y around 0 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-*r* 89.8%

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

      3. *-commutative 89.8%

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

      4. associate-*r* 89.8%

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

      5. distribute-rgt-out 99.6%

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

      6. metadata-eval 99.6%

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

      7. associate-*r* 99.6%

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

      8. neg-mul-1 99.6%

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

      9. *-commutative 99.6%

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

      10. distribute-rgt-in 99.6%

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

      11. sub-neg 99.6%

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

      12. associate-*r* 99.6%

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

      13. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   if -0.141999999999999987 < z < 0.170000000000000012

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 98.7%

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

      1. *-commutative 98.7%

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

   4. Simplified 98.7%

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

   if 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 97.3%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.142:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 8: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0056:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0056)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.17) (+ x (* (* 6.0 y) z)) (* 6.0 (* z (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0056) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.17) {
		tmp = x + ((6.0 * y) * z);
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.0056d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 0.17d0) then
        tmp = x + ((6.0d0 * y) * z)
    else
        tmp = 6.0d0 * (z * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0056) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.17) {
		tmp = x + ((6.0 * y) * z);
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0056:
		tmp = (y - x) * (6.0 * z)
	elif z <= 0.17:
		tmp = x + ((6.0 * y) * z)
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0056)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.17)
		tmp = Float64(x + Float64(Float64(6.0 * y) * z));
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0056)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 0.17)
		tmp = x + ((6.0 * y) * z);
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0056], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(x + N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00559999999999999994

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.6%

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

   4. Taylor expanded in y around 0 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-*r* 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*r* 89.9%

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

      5. distribute-rgt-out 99.5%

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

      6. metadata-eval 99.5%

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

      7. associate-*r* 99.5%

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

      8. neg-mul-1 99.5%

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

      9. *-commutative 99.5%

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

      10. distribute-rgt-in 99.5%

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

      11. sub-neg 99.5%

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

      12. associate-*r* 99.6%

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

      13. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   if -0.00559999999999999994 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 98.7%

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

   if 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 97.3%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0056:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x + \left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 9: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0056 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0056) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0056) || !(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 <= (-0.0056d0)) .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 <= -0.0056) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0056) 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 <= -0.0056) || !(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 <= -0.0056) || ~((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, -0.0056], 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 < -0.00559999999999999994 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 51.7%

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

   3. Taylor expanded in z around inf 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around 0 50.3%

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

   if -0.00559999999999999994 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 67.6%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0056 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (6.0d0 * (z * (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in z around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 11: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (z * (6.0d0 * (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 12: 36.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in z around 0 38.0%

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

3. Final simplification 38.0%

   \[\leadsto x \]

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 2023311 
(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)))