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

Percentage Accurate: 99.6% → 99.8%

Time: 11.4s

Alternatives: 14

Speedup: 1.0×

• 20.6% 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: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

   1. +-commutative 99.8%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+247}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z))))
   (if (<= z -2.2e-7)
     t_0
     (if (<= z 4.8e-16) x (if (<= z 4.1e+247) t_0 (* x (* z -6.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -2.2e-7) {
		tmp = t_0;
	} else if (z <= 4.8e-16) {
		tmp = x;
	} else if (z <= 4.1e+247) {
		tmp = t_0;
	} else {
		tmp = x * (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) :: t_0
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    if (z <= (-2.2d-7)) then
        tmp = t_0
    else if (z <= 4.8d-16) then
        tmp = x
    else if (z <= 4.1d+247) then
        tmp = t_0
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double tmp;
	if (z <= -2.2e-7) {
		tmp = t_0;
	} else if (z <= 4.8e-16) {
		tmp = x;
	} else if (z <= 4.1e+247) {
		tmp = t_0;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	tmp = 0
	if z <= -2.2e-7:
		tmp = t_0
	elif z <= 4.8e-16:
		tmp = x
	elif z <= 4.1e+247:
		tmp = t_0
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	tmp = 0.0
	if (z <= -2.2e-7)
		tmp = t_0;
	elseif (z <= 4.8e-16)
		tmp = x;
	elseif (z <= 4.1e+247)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	tmp = 0.0;
	if (z <= -2.2e-7)
		tmp = t_0;
	elseif (z <= 4.8e-16)
		tmp = x;
	elseif (z <= 4.1e+247)
		tmp = t_0;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-7], t$95$0, If[LessEqual[z, 4.8e-16], x, If[LessEqual[z, 4.1e+247], t$95$0, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e-7 or 4.8000000000000001e-16 < z < 4.1000000000000002e247

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 97.8%

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

   5. Taylor expanded in y around 0 94.4%

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

      1. +-commutative 94.4%

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

      2. metadata-eval 94.4%

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

      3. *-commutative 94.4%

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

      4. associate-*r* 94.4%

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

      5. neg-mul-1 94.4%

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

      6. distribute-rgt-neg-in 94.4%

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

      7. distribute-lft-out 94.5%

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

      8. *-commutative 94.5%

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

      9. distribute-rgt-out 97.8%

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

      10. sub-neg 97.8%

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

      11. associate-*l* 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-*r* 58.4%

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

   10. Simplified 58.4%

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

   if -2.2000000000000001e-7 < z < 4.8000000000000001e-16

   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 73.5%

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

   if 4.1000000000000002e247 < z

   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 inf 99.9%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*r* 72.7%

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

   7. Simplified 72.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+247}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+219}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -2.2e-7)
     t_0
     (if (<= z 5.8e-15) x (if (<= z 1.65e+219) t_0 (* -6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -2.2e-7) {
		tmp = t_0;
	} else if (z <= 5.8e-15) {
		tmp = x;
	} else if (z <= 1.65e+219) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-2.2d-7)) then
        tmp = t_0
    else if (z <= 5.8d-15) then
        tmp = x
    else if (z <= 1.65d+219) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (x * z)
    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 <= -2.2e-7) {
		tmp = t_0;
	} else if (z <= 5.8e-15) {
		tmp = x;
	} else if (z <= 1.65e+219) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -2.2e-7:
		tmp = t_0
	elif z <= 5.8e-15:
		tmp = x
	elif z <= 1.65e+219:
		tmp = t_0
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.2e-7)
		tmp = t_0;
	elseif (z <= 5.8e-15)
		tmp = x;
	elseif (z <= 1.65e+219)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.2e-7)
		tmp = t_0;
	elseif (z <= 5.8e-15)
		tmp = x;
	elseif (z <= 1.65e+219)
		tmp = t_0;
	else
		tmp = -6.0 * (x * z);
	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, -2.2e-7], t$95$0, If[LessEqual[z, 5.8e-15], x, If[LessEqual[z, 1.65e+219], t$95$0, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e-7 or 5.80000000000000037e-15 < z < 1.6500000000000001e219

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 97.7%

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

   5. Taylor expanded in y around inf 58.4%

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

   if -2.2000000000000001e-7 < z < 5.80000000000000037e-15

   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 73.5%

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

   if 1.6500000000000001e219 < z

   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 inf 99.9%

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

   4. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in y around 0 70.2%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+219}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -82000 \lor \neg \left(z \leq 1.75 \cdot 10^{-13}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -82000.0) (not (<= z 1.75e-13)))
   (* 6.0 (* (- y x) z))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -82000.0) || !(z <= 1.75e-13)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-82000.0d0)) .or. (.not. (z <= 1.75d-13))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -82000.0) || !(z <= 1.75e-13)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -82000.0) or not (z <= 1.75e-13):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -82000.0) || !(z <= 1.75e-13))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -82000.0) || ~((z <= 1.75e-13)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -82000.0], N[Not[LessEqual[z, 1.75e-13]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -82000 or 1.7500000000000001e-13 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 98.8%

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

   if -82000 < z < 1.7500000000000001e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -82000 \lor \neg \left(z \leq 1.75 \cdot 10^{-13}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7} \lor \neg \left(z \leq 4.5 \cdot 10^{-15}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e-7) (not (<= z 4.5e-15))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-7) || !(z <= 4.5e-15)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.3d-7)) .or. (.not. (z <= 4.5d-15))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-7) || !(z <= 4.5e-15)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e-7) or not (z <= 4.5e-15):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e-7) || !(z <= 4.5e-15))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.3e-7) || ~((z <= 4.5e-15)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e-7], N[Not[LessEqual[z, 4.5e-15]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999995e-7 or 4.4999999999999998e-15 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 98.0%

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

   if -2.29999999999999995e-7 < z < 4.4999999999999998e-15

   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 73.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7} \lor \neg \left(z \leq 4.5 \cdot 10^{-15}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -140.0)
   (* (- y x) (* 6.0 z))
   (if (<= z 1.75e-13) (+ x (* z (* y 6.0))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -140.0) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.75e-13) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = z * ((y - x) * 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 <= (-140.0d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 1.75d-13) then
        tmp = x + (z * (y * 6.0d0))
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -140.0) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.75e-13) {
		tmp = x + (z * (y * 6.0));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -140.0:
		tmp = (y - x) * (6.0 * z)
	elif z <= 1.75e-13:
		tmp = x + (z * (y * 6.0))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -140.0)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 1.75e-13)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -140.0)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 1.75e-13)
		tmp = x + (z * (y * 6.0));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -140.0], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-13], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -140

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 97.0%

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

   5. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. metadata-eval 92.0%

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

      3. *-commutative 92.0%

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

      4. associate-*r* 92.0%

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

      5. neg-mul-1 92.0%

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

      6. distribute-rgt-neg-in 92.0%

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

      7. distribute-lft-out 92.0%

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

      8. *-commutative 92.0%

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

      9. distribute-rgt-out 97.0%

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

      10. sub-neg 97.0%

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

      11. associate-*l* 97.1%

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

   7. Simplified 97.1%

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

   if -140 < z < 1.7500000000000001e-13

   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 99.3%

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

   if 1.7500000000000001e-13 < z

   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 inf 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

   5. Taylor expanded in y around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. metadata-eval 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 97.3%

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

      5. neg-mul-1 97.3%

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

      6. distribute-rgt-neg-in 97.3%

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

      7. distribute-lft-out 97.4%

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

      8. *-commutative 97.4%

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

      9. distribute-rgt-out 98.8%

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

      10. sub-neg 98.8%

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

      11. associate-*l* 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in z around 0 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-*l* 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -140.0)
   (* (- y x) (* 6.0 z))
   (if (<= z 1.75e-13) (+ x (* y (* 6.0 z))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -140.0) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.75e-13) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * ((y - x) * 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 <= (-140.0d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 1.75d-13) then
        tmp = x + (y * (6.0d0 * z))
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -140.0) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.75e-13) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -140.0:
		tmp = (y - x) * (6.0 * z)
	elif z <= 1.75e-13:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -140.0)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 1.75e-13)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -140.0)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 1.75e-13)
		tmp = x + (y * (6.0 * z));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -140.0], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-13], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -140

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 97.0%

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

   5. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. metadata-eval 92.0%

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

      3. *-commutative 92.0%

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

      4. associate-*r* 92.0%

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

      5. neg-mul-1 92.0%

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

      6. distribute-rgt-neg-in 92.0%

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

      7. distribute-lft-out 92.0%

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

      8. *-commutative 92.0%

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

      9. distribute-rgt-out 97.0%

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

      10. sub-neg 97.0%

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

      11. associate-*l* 97.1%

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

   7. Simplified 97.1%

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

   if -140 < z < 1.7500000000000001e-13

   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 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*r* 99.2%

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

   5. Simplified 99.2%

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

   if 1.7500000000000001e-13 < z

   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 inf 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

   5. Taylor expanded in y around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. metadata-eval 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 97.3%

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

      5. neg-mul-1 97.3%

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

      6. distribute-rgt-neg-in 97.3%

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

      7. distribute-lft-out 97.4%

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

      8. *-commutative 97.4%

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

      9. distribute-rgt-out 98.8%

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

      10. sub-neg 98.8%

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

      11. associate-*l* 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in z around 0 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-*l* 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.195:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.195)
   (* (- y x) (* 6.0 z))
   (if (<= z 1.75e-13) (+ x (* 6.0 (* y z))) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.195) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.75e-13) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.195d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 1.75d-13) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.195) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.75e-13) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.195:
		tmp = (y - x) * (6.0 * z)
	elif z <= 1.75e-13:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.195)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 1.75e-13)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.195)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 1.75e-13)
		tmp = x + (6.0 * (y * z));
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.195], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-13], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.19500000000000001

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 97.0%

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

   5. Taylor expanded in y around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. metadata-eval 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-*r* 92.1%

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

      5. neg-mul-1 92.1%

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

      6. distribute-rgt-neg-in 92.1%

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

      7. distribute-lft-out 92.1%

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

      8. *-commutative 92.1%

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

      9. distribute-rgt-out 97.0%

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

      10. sub-neg 97.0%

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

      11. associate-*l* 97.2%

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

   7. Simplified 97.2%

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

   if -0.19500000000000001 < z < 1.7500000000000001e-13

   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 99.1%

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

      1. *-commutative 99.1%

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

   5. Simplified 99.1%

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

   if 1.7500000000000001e-13 < z

   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 inf 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

   5. Taylor expanded in y around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. metadata-eval 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 97.3%

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

      5. neg-mul-1 97.3%

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

      6. distribute-rgt-neg-in 97.3%

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

      7. distribute-lft-out 97.4%

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

      8. *-commutative 97.4%

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

      9. distribute-rgt-out 98.8%

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

      10. sub-neg 98.8%

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

      11. associate-*l* 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in z around 0 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-*l* 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.195:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -82000:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -82000.0)
   (* (- y x) (* 6.0 z))
   (if (<= z 1.1e-15) (* x (+ (* z -6.0) 1.0)) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -82000.0) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.1e-15) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * ((y - x) * 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 <= (-82000.0d0)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 1.1d-15) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -82000.0) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 1.1e-15) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -82000.0:
		tmp = (y - x) * (6.0 * z)
	elif z <= 1.1e-15:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -82000.0)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 1.1e-15)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -82000.0)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 1.1e-15)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -82000.0], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-15], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -82000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 98.8%

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

   5. Taylor expanded in y around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. metadata-eval 93.7%

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

      3. *-commutative 93.7%

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

      4. associate-*r* 93.7%

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

      5. neg-mul-1 93.7%

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

      6. distribute-rgt-neg-in 93.7%

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

      7. distribute-lft-out 93.7%

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

      8. *-commutative 93.7%

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

      9. distribute-rgt-out 98.8%

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

      10. sub-neg 98.8%

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

      11. associate-*l* 98.9%

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

   7. Simplified 98.9%

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

   if -82000 < z < 1.09999999999999993e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 1.09999999999999993e-15 < z

   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 inf 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

   5. Taylor expanded in y around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. metadata-eval 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 97.3%

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

      5. neg-mul-1 97.3%

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

      6. distribute-rgt-neg-in 97.3%

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

      7. distribute-lft-out 97.4%

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

      8. *-commutative 97.4%

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

      9. distribute-rgt-out 98.8%

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

      10. sub-neg 98.8%

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

      11. associate-*l* 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in z around 0 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-*l* 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -82000:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -82000:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -82000.0)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.75e-13) (* x (+ (* z -6.0) 1.0)) (* z (* (- y x) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -82000.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.75e-13) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * ((y - x) * 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 <= (-82000.0d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.75d-13) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = z * ((y - x) * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -82000.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.75e-13) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * ((y - x) * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -82000.0:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.75e-13:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = z * ((y - x) * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -82000.0)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.75e-13)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -82000.0)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.75e-13)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = z * ((y - x) * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -82000.0], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-13], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -82000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 98.8%

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

   if -82000 < z < 1.7500000000000001e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 1.7500000000000001e-13 < z

   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 inf 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

   5. Taylor expanded in y around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. metadata-eval 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 97.3%

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

      5. neg-mul-1 97.3%

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

      6. distribute-rgt-neg-in 97.3%

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

      7. distribute-lft-out 97.4%

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

      8. *-commutative 97.4%

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

      9. distribute-rgt-out 98.8%

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

      10. sub-neg 98.8%

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

      11. associate-*l* 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in z around 0 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-*l* 98.8%

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

   10. Simplified 98.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -82000:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 1.75 \cdot 10^{-13}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 1.75e-13))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 1.75e-13)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.17d0)) .or. (.not. (z <= 1.75d-13))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 1.75e-13)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 1.75e-13):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 1.75e-13))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.17) || ~((z <= 1.75e-13)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 1.75e-13]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 1.7500000000000001e-13 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in z around inf 98.0%

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

   5. Taylor expanded in y around 0 45.2%

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

   if -0.170000000000000012 < z < 1.7500000000000001e-13

   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 73.5%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 1.75 \cdot 10^{-13}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

   1. associate-*l* 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(6 \cdot z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 13: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 14: 36.5% 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 35.1%

   \[\leadsto \color{blue}{x} \]
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 2024191 
(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)))