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

Percentage Accurate: 99.7% → 99.7%

Time: 14.1s

Alternatives: 10

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+213}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -165000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-105} \lor \neg \left(z \leq 1.52 \cdot 10^{-28}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.4e+213)
   (* 6.0 (* y z))
   (if (<= z -165000.0)
     (* -6.0 (* x z))
     (if (or (<= z -3.3e-105) (not (<= z 1.52e-28))) (* y (* 6.0 z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.4e+213) {
		tmp = 6.0 * (y * z);
	} else if (z <= -165000.0) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -3.3e-105) || !(z <= 1.52e-28)) {
		tmp = y * (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 <= (-9.4d+213)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= (-165000.0d0)) then
        tmp = (-6.0d0) * (x * z)
    else if ((z <= (-3.3d-105)) .or. (.not. (z <= 1.52d-28))) then
        tmp = y * (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 <= -9.4e+213) {
		tmp = 6.0 * (y * z);
	} else if (z <= -165000.0) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -3.3e-105) || !(z <= 1.52e-28)) {
		tmp = y * (6.0 * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.4e+213:
		tmp = 6.0 * (y * z)
	elif z <= -165000.0:
		tmp = -6.0 * (x * z)
	elif (z <= -3.3e-105) or not (z <= 1.52e-28):
		tmp = y * (6.0 * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.4e+213)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= -165000.0)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif ((z <= -3.3e-105) || !(z <= 1.52e-28))
		tmp = Float64(y * Float64(6.0 * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.4e+213)
		tmp = 6.0 * (y * z);
	elseif (z <= -165000.0)
		tmp = -6.0 * (x * z);
	elseif ((z <= -3.3e-105) || ~((z <= 1.52e-28)))
		tmp = y * (6.0 * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.4e+213], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -165000.0], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.3e-105], N[Not[LessEqual[z, 1.52e-28]], $MachinePrecision]], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.3999999999999995e213

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in y around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. fma-define 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in y around inf 65.8%

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

   if -9.3999999999999995e213 < z < -165000

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 64.0%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -165000 < z < -3.2999999999999999e-105 or 1.5199999999999999e-28 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in y around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. fma-define 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in y around inf 64.1%

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

       1. *-commutative 64.1%

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

       2. associate-*r* 64.2%

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

       3. *-commutative 64.2%

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

   11. Simplified 64.2%

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

   if -3.2999999999999999e-105 < z < 1.5199999999999999e-28

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+213}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -165000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-105} \lor \neg \left(z \leq 1.52 \cdot 10^{-28}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+206}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -400000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-103} \lor \neg \left(z \leq 2.15 \cdot 10^{-21}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -4.3e+206)
     t_0
     (if (<= z -400000.0)
       (* -6.0 (* x z))
       (if (or (<= z -2.4e-103) (not (<= z 2.15e-21))) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -4.3e+206) {
		tmp = t_0;
	} else if (z <= -400000.0) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -2.4e-103) || !(z <= 2.15e-21)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-4.3d+206)) then
        tmp = t_0
    else if (z <= (-400000.0d0)) then
        tmp = (-6.0d0) * (x * z)
    else if ((z <= (-2.4d-103)) .or. (.not. (z <= 2.15d-21))) then
        tmp = t_0
    else
        tmp = x
    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 tmp;
	if (z <= -4.3e+206) {
		tmp = t_0;
	} else if (z <= -400000.0) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -2.4e-103) || !(z <= 2.15e-21)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -4.3e+206:
		tmp = t_0
	elif z <= -400000.0:
		tmp = -6.0 * (x * z)
	elif (z <= -2.4e-103) or not (z <= 2.15e-21):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.3e+206)
		tmp = t_0;
	elseif (z <= -400000.0)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif ((z <= -2.4e-103) || !(z <= 2.15e-21))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.3e+206)
		tmp = t_0;
	elseif (z <= -400000.0)
		tmp = -6.0 * (x * z);
	elseif ((z <= -2.4e-103) || ~((z <= 2.15e-21)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+206], t$95$0, If[LessEqual[z, -400000.0], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.4e-103], N[Not[LessEqual[z, 2.15e-21]], $MachinePrecision]], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.29999999999999988e206 or -4e5 < z < -2.4000000000000002e-103 or 2.1499999999999999e-21 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. fma-define 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in y around inf 64.5%

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

   if -4.29999999999999988e206 < z < -4e5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 64.0%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -2.4000000000000002e-103 < z < 2.1499999999999999e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+206}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -400000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-103} \lor \neg \left(z \leq 2.15 \cdot 10^{-21}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+207}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -390000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.2e+207)
   (* 6.0 (* y z))
   (if (<= z -390000.0)
     (* z (* x -6.0))
     (if (<= z -3.7e-104)
       (* y (* 6.0 z))
       (if (<= z 2.15e-25) x (* z (* y 6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e+207) {
		tmp = 6.0 * (y * z);
	} else if (z <= -390000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.7e-104) {
		tmp = y * (6.0 * z);
	} else if (z <= 2.15e-25) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.2d+207)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= (-390000.0d0)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-3.7d-104)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 2.15d-25) then
        tmp = x
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e+207) {
		tmp = 6.0 * (y * z);
	} else if (z <= -390000.0) {
		tmp = z * (x * -6.0);
	} else if (z <= -3.7e-104) {
		tmp = y * (6.0 * z);
	} else if (z <= 2.15e-25) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.2e+207:
		tmp = 6.0 * (y * z)
	elif z <= -390000.0:
		tmp = z * (x * -6.0)
	elif z <= -3.7e-104:
		tmp = y * (6.0 * z)
	elif z <= 2.15e-25:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.2e+207)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= -390000.0)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -3.7e-104)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 2.15e-25)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.2e+207)
		tmp = 6.0 * (y * z);
	elseif (z <= -390000.0)
		tmp = z * (x * -6.0);
	elseif (z <= -3.7e-104)
		tmp = y * (6.0 * z);
	elseif (z <= 2.15e-25)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.2e+207], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -390000.0], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e-104], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-25], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.2e207

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in y around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. fma-define 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in y around inf 65.8%

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

   if -8.2e207 < z < -3.9e5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 64.0%

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

   4. Taylor expanded in z around inf 62.7%

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

      1. associate-*r* 62.8%

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

      2. *-commutative 62.8%

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

      3. *-commutative 62.8%

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

   6. Simplified 62.8%

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

   if -3.9e5 < z < -3.6999999999999999e-104

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 94.2%

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

      1. *-commutative 94.2%

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

      2. fma-define 94.1%

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

   8. Simplified 94.1%

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

   9. Taylor expanded in y around inf 77.1%

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

       1. *-commutative 77.1%

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

       2. associate-*r* 77.1%

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

       3. *-commutative 77.1%

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

   11. Simplified 77.1%

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

   if -3.6999999999999999e-104 < z < 2.14999999999999988e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

   if 2.14999999999999988e-25 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

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

      2. fma-define 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in y around inf 61.1%

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

       1. *-commutative 61.1%

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

       2. associate-*r* 61.2%

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

       3. *-commutative 61.2%

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

   11. Simplified 61.2%

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

   12. Taylor expanded in y around 0 61.1%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

   14. Simplified 61.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+207}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -390000:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+208}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -400000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.16e+208)
   (* 6.0 (* y z))
   (if (<= z -400000.0)
     (* -6.0 (* x z))
     (if (<= z -3.8e-103)
       (* y (* 6.0 z))
       (if (<= z 1.65e-25) x (* z (* y 6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+208) {
		tmp = 6.0 * (y * z);
	} else if (z <= -400000.0) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3.8e-103) {
		tmp = y * (6.0 * z);
	} else if (z <= 1.65e-25) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.16d+208)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= (-400000.0d0)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-3.8d-103)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 1.65d-25) then
        tmp = x
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+208) {
		tmp = 6.0 * (y * z);
	} else if (z <= -400000.0) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3.8e-103) {
		tmp = y * (6.0 * z);
	} else if (z <= 1.65e-25) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.16e+208:
		tmp = 6.0 * (y * z)
	elif z <= -400000.0:
		tmp = -6.0 * (x * z)
	elif z <= -3.8e-103:
		tmp = y * (6.0 * z)
	elif z <= 1.65e-25:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.16e+208)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= -400000.0)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -3.8e-103)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 1.65e-25)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.16e+208)
		tmp = 6.0 * (y * z);
	elseif (z <= -400000.0)
		tmp = -6.0 * (x * z);
	elseif (z <= -3.8e-103)
		tmp = y * (6.0 * z);
	elseif (z <= 1.65e-25)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.16e+208], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -400000.0], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-103], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-25], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.15999999999999999e208

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in y around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. fma-define 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in y around inf 65.8%

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

   if -1.15999999999999999e208 < z < -4e5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 64.0%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -4e5 < z < -3.8000000000000001e-103

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 94.2%

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

      1. *-commutative 94.2%

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

      2. fma-define 94.1%

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

   8. Simplified 94.1%

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

   9. Taylor expanded in y around inf 77.1%

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

       1. *-commutative 77.1%

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

       2. associate-*r* 77.1%

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

       3. *-commutative 77.1%

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

   11. Simplified 77.1%

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

   if -3.8000000000000001e-103 < z < 1.6499999999999999e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.3%

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

   if 1.6499999999999999e-25 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

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

      2. fma-define 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in y around inf 61.1%

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

       1. *-commutative 61.1%

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

       2. associate-*r* 61.2%

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

       3. *-commutative 61.2%

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

   11. Simplified 61.2%

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

   12. Taylor expanded in y around 0 61.1%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

   14. Simplified 61.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+208}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -400000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-116} \lor \neg \left(y \leq 4.9 \cdot 10^{-82}\right):\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.55e-116) (not (<= y 4.9e-82)))
   (+ x (* z (* y 6.0)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.55e-116) || !(y <= 4.9e-82)) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (-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 ((y <= (-1.55d-116)) .or. (.not. (y <= 4.9d-82))) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.55e-116) || !(y <= 4.9e-82)) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.55e-116) or not (y <= 4.9e-82):
		tmp = x + (z * (y * 6.0))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.55e-116) || !(y <= 4.9e-82))
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.55e-116) || ~((y <= 4.9e-82)))
		tmp = x + (z * (y * 6.0));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.55e-116], N[Not[LessEqual[y, 4.9e-82]], $MachinePrecision]], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000009e-116 or 4.9000000000000003e-82 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 88.1%

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

   if -1.55000000000000009e-116 < y < 4.9000000000000003e-82

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 88.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-116} \lor \neg \left(y \leq 4.9 \cdot 10^{-82}\right):\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-116} \lor \neg \left(y \leq 5.1 \cdot 10^{-82}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e-116) (not (<= y 5.1e-82)))
   (+ x (* 6.0 (* y z)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-116) || !(y <= 5.1e-82)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-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 ((y <= (-1d-116)) .or. (.not. (y <= 5.1d-82))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-116) || !(y <= 5.1e-82)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e-116) or not (y <= 5.1e-82):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e-116) || !(y <= 5.1e-82))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e-116) || ~((y <= 5.1e-82)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e-116], N[Not[LessEqual[y, 5.1e-82]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999999e-117 or 5.09999999999999992e-82 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

   if -9.9999999999999999e-117 < y < 5.09999999999999992e-82

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 88.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-116} \lor \neg \left(y \leq 5.1 \cdot 10^{-82}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-14}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.15e-14)
   (* 6.0 (* y z))
   (if (<= y 1.9e+15) (+ x (* -6.0 (* x z))) (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e-14) {
		tmp = 6.0 * (y * z);
	} else if (y <= 1.9e+15) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.15d-14)) then
        tmp = 6.0d0 * (y * z)
    else if (y <= 1.9d+15) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e-14) {
		tmp = 6.0 * (y * z);
	} else if (y <= 1.9e+15) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.15e-14:
		tmp = 6.0 * (y * z)
	elif y <= 1.9e+15:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.15e-14)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (y <= 1.9e+15)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.15e-14)
		tmp = 6.0 * (y * z);
	elseif (y <= 1.9e+15)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.15e-14], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+15], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.14999999999999999e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 89.8%

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

      1. *-commutative 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in y around inf 89.7%

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

      1. *-commutative 89.7%

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

      2. fma-define 89.7%

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

   8. Simplified 89.7%

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

   9. Taylor expanded in y around inf 73.3%

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

   if -1.14999999999999999e-14 < y < 1.9e15

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 81.9%

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

   if 1.9e15 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 92.2%

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

      1. *-commutative 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in y around inf 92.2%

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

      1. *-commutative 92.2%

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

      2. fma-define 92.2%

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

   8. Simplified 92.2%

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

   9. Taylor expanded in y around inf 74.0%

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

       1. *-commutative 74.0%

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

       2. associate-*r* 74.0%

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

       3. *-commutative 74.0%

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

   11. Simplified 74.0%

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

   12. Taylor expanded in y around 0 74.0%

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

       1. associate-*r* 74.1%

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

       2. *-commutative 74.1%

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

   14. Simplified 74.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-14}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-13} \lor \neg \left(z \leq 0.0068\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e-13) (not (<= z 0.0068))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e-13) || !(z <= 0.0068)) {
		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 <= (-4.2d-13)) .or. (.not. (z <= 0.0068d0))) 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 <= -4.2e-13) || !(z <= 0.0068)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e-13) or not (z <= 0.0068):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e-13) || !(z <= 0.0068))
		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 <= -4.2e-13) || ~((z <= 0.0068)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e-13], N[Not[LessEqual[z, 0.0068]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999977e-13 or 0.00679999999999999962 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 50.7%

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

   4. Taylor expanded in z around inf 50.3%

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

   if -4.19999999999999977e-13 < z < 0.00679999999999999962

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 64.4%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-13} \lor \neg \left(z \leq 0.0068\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0 32.3%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 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 2024170 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

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