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

Percentage Accurate: 99.7% → 99.7%

Time: 5.4s

Alternatives: 9

Speedup: 1.0×

• 20.8% 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: 99.7% 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.46 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+177}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z -6.0)))))
   (if (<= y -5.8e+151)
     (* y (* 6.0 z))
     (if (<= y -8.2e+99)
       t_0
       (if (<= y -2.46e+14)
         (* 6.0 (* y z))
         (if (<= y 8e+177) t_0 (* z (* y 6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * -6.0));
	double tmp;
	if (y <= -5.8e+151) {
		tmp = y * (6.0 * z);
	} else if (y <= -8.2e+99) {
		tmp = t_0;
	} else if (y <= -2.46e+14) {
		tmp = 6.0 * (y * z);
	} else if (y <= 8e+177) {
		tmp = t_0;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 + (z * (-6.0d0)))
    if (y <= (-5.8d+151)) then
        tmp = y * (6.0d0 * z)
    else if (y <= (-8.2d+99)) then
        tmp = t_0
    else if (y <= (-2.46d+14)) then
        tmp = 6.0d0 * (y * z)
    else if (y <= 8d+177) then
        tmp = t_0
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * -6.0));
	double tmp;
	if (y <= -5.8e+151) {
		tmp = y * (6.0 * z);
	} else if (y <= -8.2e+99) {
		tmp = t_0;
	} else if (y <= -2.46e+14) {
		tmp = 6.0 * (y * z);
	} else if (y <= 8e+177) {
		tmp = t_0;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * -6.0))
	tmp = 0
	if y <= -5.8e+151:
		tmp = y * (6.0 * z)
	elif y <= -8.2e+99:
		tmp = t_0
	elif y <= -2.46e+14:
		tmp = 6.0 * (y * z)
	elif y <= 8e+177:
		tmp = t_0
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -5.8e+151)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (y <= -8.2e+99)
		tmp = t_0;
	elseif (y <= -2.46e+14)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (y <= 8e+177)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (z * -6.0));
	tmp = 0.0;
	if (y <= -5.8e+151)
		tmp = y * (6.0 * z);
	elseif (y <= -8.2e+99)
		tmp = t_0;
	elseif (y <= -2.46e+14)
		tmp = 6.0 * (y * z);
	elseif (y <= 8e+177)
		tmp = t_0;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+151], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e+99], t$95$0, If[LessEqual[y, -2.46e+14], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+177], t$95$0, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.80000000000000036e151

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 96.6%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. associate-*r* 85.7%

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

      2. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in z around 0 85.8%

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

      1. associate-*r* 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*r* 85.9%

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

   8. Simplified 85.9%

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

   if -5.80000000000000036e151 < y < -8.19999999999999959e99 or -2.46e14 < y < 8.0000000000000001e177

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 80.1%

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

   if -8.19999999999999959e99 < y < -2.46e14

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 88.1%

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

   3. Taylor expanded in x around 0 71.7%

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

   if 8.0000000000000001e177 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 97.1%

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

   3. Taylor expanded in x around 0 81.5%

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

      1. associate-*r* 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq -2.46 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 3: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -4.8e+52)
     t_0
     (if (<= z -1.05e-37)
       t_1
       (if (<= z 9.5e-13) x (if (<= z 2.2e+147) 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 <= -4.8e+52) {
		tmp = t_0;
	} else if (z <= -1.05e-37) {
		tmp = t_1;
	} else if (z <= 9.5e-13) {
		tmp = x;
	} else if (z <= 2.2e+147) {
		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 <= (-4.8d+52)) then
        tmp = t_0
    else if (z <= (-1.05d-37)) then
        tmp = t_1
    else if (z <= 9.5d-13) then
        tmp = x
    else if (z <= 2.2d+147) 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 <= -4.8e+52) {
		tmp = t_0;
	} else if (z <= -1.05e-37) {
		tmp = t_1;
	} else if (z <= 9.5e-13) {
		tmp = x;
	} else if (z <= 2.2e+147) {
		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 <= -4.8e+52:
		tmp = t_0
	elif z <= -1.05e-37:
		tmp = t_1
	elif z <= 9.5e-13:
		tmp = x
	elif z <= 2.2e+147:
		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 <= -4.8e+52)
		tmp = t_0;
	elseif (z <= -1.05e-37)
		tmp = t_1;
	elseif (z <= 9.5e-13)
		tmp = x;
	elseif (z <= 2.2e+147)
		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 <= -4.8e+52)
		tmp = t_0;
	elseif (z <= -1.05e-37)
		tmp = t_1;
	elseif (z <= 9.5e-13)
		tmp = x;
	elseif (z <= 2.2e+147)
		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, -4.8e+52], t$95$0, If[LessEqual[z, -1.05e-37], t$95$1, If[LessEqual[z, 9.5e-13], x, If[LessEqual[z, 2.2e+147], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e52 or 2.2000000000000002e147 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 64.2%

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

   3. Taylor expanded in z around inf 64.2%

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

   4. Taylor expanded in z around 0 64.2%

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

   if -4.8e52 < z < -1.05e-37 or 9.49999999999999991e-13 < z < 2.2000000000000002e147

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 73.3%

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

   3. Taylor expanded in x around 0 66.3%

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

   if -1.05e-37 < z < 9.49999999999999991e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.3%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+52}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-37}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+147}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+147}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -3.3e+50)
     t_0
     (if (<= z -1.2e-37)
       (* y (* 6.0 z))
       (if (<= z 4.3e-13) x (if (<= z 1.55e+147) (* 6.0 (* y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.3e+50) {
		tmp = t_0;
	} else if (z <= -1.2e-37) {
		tmp = y * (6.0 * z);
	} else if (z <= 4.3e-13) {
		tmp = x;
	} else if (z <= 1.55e+147) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    if (z <= (-3.3d+50)) then
        tmp = t_0
    else if (z <= (-1.2d-37)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 4.3d-13) then
        tmp = x
    else if (z <= 1.55d+147) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.3e+50) {
		tmp = t_0;
	} else if (z <= -1.2e-37) {
		tmp = y * (6.0 * z);
	} else if (z <= 4.3e-13) {
		tmp = x;
	} else if (z <= 1.55e+147) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -3.3e+50:
		tmp = t_0
	elif z <= -1.2e-37:
		tmp = y * (6.0 * z)
	elif z <= 4.3e-13:
		tmp = x
	elif z <= 1.55e+147:
		tmp = 6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.3e+50)
		tmp = t_0;
	elseif (z <= -1.2e-37)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 4.3e-13)
		tmp = x;
	elseif (z <= 1.55e+147)
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -3.3e+50)
		tmp = t_0;
	elseif (z <= -1.2e-37)
		tmp = y * (6.0 * z);
	elseif (z <= 4.3e-13)
		tmp = x;
	elseif (z <= 1.55e+147)
		tmp = 6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+50], t$95$0, If[LessEqual[z, -1.2e-37], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-13], x, If[LessEqual[z, 1.55e+147], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3e50 or 1.55e147 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 64.2%

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

   3. Taylor expanded in z around inf 64.2%

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

   4. Taylor expanded in z around 0 64.2%

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

   if -3.3e50 < z < -1.19999999999999995e-37

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 75.7%

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

   3. Taylor expanded in x around 0 58.2%

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

      1. associate-*r* 58.3%

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

      2. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in z around 0 58.2%

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

      1. associate-*r* 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*r* 58.3%

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

   8. Simplified 58.3%

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

   if -1.19999999999999995e-37 < z < 4.2999999999999999e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.3%

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

   if 4.2999999999999999e-13 < z < 1.55e147

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 71.8%

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

   3. Taylor expanded in x around 0 71.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+50}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+147}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+154}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.35e+51)
   (* x (* z -6.0))
   (if (<= z -1.2e-37)
     (* y (* 6.0 z))
     (if (<= z 4.3e-13)
       x
       (if (<= z 3e+154) (* 6.0 (* y z)) (* -6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.35e+51) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.2e-37) {
		tmp = y * (6.0 * z);
	} else if (z <= 4.3e-13) {
		tmp = x;
	} else if (z <= 3e+154) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.35d+51)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= (-1.2d-37)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 4.3d-13) then
        tmp = x
    else if (z <= 3d+154) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.35e+51) {
		tmp = x * (z * -6.0);
	} else if (z <= -1.2e-37) {
		tmp = y * (6.0 * z);
	} else if (z <= 4.3e-13) {
		tmp = x;
	} else if (z <= 3e+154) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.35e+51:
		tmp = x * (z * -6.0)
	elif z <= -1.2e-37:
		tmp = y * (6.0 * z)
	elif z <= 4.3e-13:
		tmp = x
	elif z <= 3e+154:
		tmp = 6.0 * (y * z)
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.35e+51)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= -1.2e-37)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 4.3e-13)
		tmp = x;
	elseif (z <= 3e+154)
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.35e+51)
		tmp = x * (z * -6.0);
	elseif (z <= -1.2e-37)
		tmp = y * (6.0 * z);
	elseif (z <= 4.3e-13)
		tmp = x;
	elseif (z <= 3e+154)
		tmp = 6.0 * (y * z);
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.35e+51], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-37], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-13], x, If[LessEqual[z, 3e+154], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.34999999999999996e51

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 60.6%

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

   3. Taylor expanded in z around inf 60.6%

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

   if -1.34999999999999996e51 < z < -1.19999999999999995e-37

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 75.7%

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

   3. Taylor expanded in x around 0 58.2%

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

      1. associate-*r* 58.3%

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

      2. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in z around 0 58.2%

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

      1. associate-*r* 58.3%

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

      2. *-commutative 58.3%

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

      3. associate-*r* 58.3%

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

   8. Simplified 58.3%

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

   if -1.19999999999999995e-37 < z < 4.2999999999999999e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.3%

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

   if 4.2999999999999999e-13 < z < 3.00000000000000026e154

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 71.8%

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

   3. Taylor expanded in x around 0 71.1%

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

   if 3.00000000000000026e154 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 70.9%

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

   3. Taylor expanded in z around inf 70.9%

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

   4. Taylor expanded in z around 0 70.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+154}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-30} \lor \neg \left(y \leq 3.45 \cdot 10^{-59}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.45e-30) (not (<= y 3.45e-59)))
   (+ x (* 6.0 (* y z)))
   (* x (+ 1.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e-30) || !(y <= 3.45e-59)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * (1.0 + (z * -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 ((y <= (-1.45d-30)) .or. (.not. (y <= 3.45d-59))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e-30) || !(y <= 3.45e-59)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * (1.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.45e-30) or not (y <= 3.45e-59):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x * (1.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.45e-30) || !(y <= 3.45e-59))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.45e-30) || ~((y <= 3.45e-59)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x * (1.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.45e-30], N[Not[LessEqual[y, 3.45e-59]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999995e-30 or 3.44999999999999991e-59 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 90.7%

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

   if -1.44999999999999995e-30 < y < 3.44999999999999991e-59

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 90.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-30} \lor \neg \left(y \leq 3.45 \cdot 10^{-59}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \end{array} \]

Alternative 7: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-30}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e-30)
   (+ x (* 6.0 (* y z)))
   (if (<= y 1.15e-59) (* x (+ 1.0 (* z -6.0))) (+ x (* z (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-30) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 1.15e-59) {
		tmp = x * (1.0 + (z * -6.0));
	} 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 (y <= (-1.4d-30)) then
        tmp = x + (6.0d0 * (y * z))
    else if (y <= 1.15d-59) then
        tmp = x * (1.0d0 + (z * (-6.0d0)))
    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 (y <= -1.4e-30) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 1.15e-59) {
		tmp = x * (1.0 + (z * -6.0));
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e-30:
		tmp = x + (6.0 * (y * z))
	elif y <= 1.15e-59:
		tmp = x * (1.0 + (z * -6.0))
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e-30)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif (y <= 1.15e-59)
		tmp = Float64(x * Float64(1.0 + Float64(z * -6.0)));
	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 (y <= -1.4e-30)
		tmp = x + (6.0 * (y * z));
	elseif (y <= 1.15e-59)
		tmp = x * (1.0 + (z * -6.0));
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e-30], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-59], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999994e-30

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 87.4%

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

   if -1.39999999999999994e-30 < y < 1.1499999999999999e-59

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 90.0%

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

   if 1.1499999999999999e-59 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 94.2%

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

      1. associate-*r* 94.2%

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

   4. Simplified 94.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-30}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 8: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-10} \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.5e-10) (not (<= z 0.165))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-10) || !(z <= 0.165)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9.5d-10)) .or. (.not. (z <= 0.165d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-10) || !(z <= 0.165)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.5e-10) or not (z <= 0.165):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.5e-10) || !(z <= 0.165))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.5e-10) || ~((z <= 0.165)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.5e-10], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000028e-10 or 0.165000000000000008 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 51.8%

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

   3. Taylor expanded in z around inf 51.0%

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

   4. Taylor expanded in z around 0 51.0%

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

   if -9.50000000000000028e-10 < z < 0.165000000000000008

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.3%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-10} \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 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 40.6%

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

3. Final simplification 40.6%

   \[\leadsto x \]

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 2023240 
(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)))