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

Percentage Accurate: 99.5% → 99.8%

Time: 10.2s

Alternatives: 15

Speedup: 1.2×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 4\right), x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (fma z -6.0 4.0) x))

C

double code(double x, double y, double z) {
	return fma((y - x), fma(z, -6.0, 4.0), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), fma(z, -6.0, 4.0), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(z * -6.0 + 4.0), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.7%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. +-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\left(-z\right) + \frac{2}{3}\right)}, x\right) \]

   6. distribute-lft-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{6 \cdot \left(-z\right) + 6 \cdot \frac{2}{3}}, x\right) \]

   7. distribute-rgt-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(-6 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   8. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \left(-\color{blue}{z \cdot 6}\right) + 6 \cdot \frac{2}{3}, x\right) \]

   9. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(-6\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   10. fma-define 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, -6, 6 \cdot \frac{2}{3}\right)}, x\right) \]

   11. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, \color{blue}{-6}, 6 \cdot \frac{2}{3}\right), x\right) \]

   12. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 6 \cdot \color{blue}{0.6666666666666666}\right), x\right) \]

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 50.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+226}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+113}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -1.9e+226)
     (* 6.0 (* x z))
     (if (<= z -2.45e+113)
       (* -6.0 (* y z))
       (if (<= z -3.3)
         t_0
         (if (<= z -5.6e-112)
           (* y 4.0)
           (if (<= z 2.2e-203) (* x -3.0) (if (<= z 0.5) (* y 4.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -1.9e+226) {
		tmp = 6.0 * (x * z);
	} else if (z <= -2.45e+113) {
		tmp = -6.0 * (y * z);
	} else if (z <= -3.3) {
		tmp = t_0;
	} else if (z <= -5.6e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-1.9d+226)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-2.45d+113)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-3.3d0)) then
        tmp = t_0
    else if (z <= (-5.6d-112)) then
        tmp = y * 4.0d0
    else if (z <= 2.2d-203) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -1.9e+226) {
		tmp = 6.0 * (x * z);
	} else if (z <= -2.45e+113) {
		tmp = -6.0 * (y * z);
	} else if (z <= -3.3) {
		tmp = t_0;
	} else if (z <= -5.6e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -1.9e+226:
		tmp = 6.0 * (x * z)
	elif z <= -2.45e+113:
		tmp = -6.0 * (y * z)
	elif z <= -3.3:
		tmp = t_0
	elif z <= -5.6e-112:
		tmp = y * 4.0
	elif z <= 2.2e-203:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -1.9e+226)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -2.45e+113)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -3.3)
		tmp = t_0;
	elseif (z <= -5.6e-112)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.2e-203)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -1.9e+226)
		tmp = 6.0 * (x * z);
	elseif (z <= -2.45e+113)
		tmp = -6.0 * (y * z);
	elseif (z <= -3.3)
		tmp = t_0;
	elseif (z <= -5.6e-112)
		tmp = y * 4.0;
	elseif (z <= 2.2e-203)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+226], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.45e+113], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3], t$95$0, If[LessEqual[z, -5.6e-112], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.2e-203], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.89999999999999991e226

   1. Initial program 100.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in y around 0 73.7%

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

      1. *-commutative 73.7%

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

   6. Simplified 73.7%

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

   if -1.89999999999999991e226 < z < -2.45000000000000011e113

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -2.45000000000000011e113 < z < -3.2999999999999998 or 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 97.8%

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

   4. Taylor expanded in y around 0 57.7%

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

      1. *-commutative 57.7%

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

   6. Simplified 57.7%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

   8. Applied egg-rr 58.9%

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

   if -3.2999999999999998 < z < -5.60000000000000046e-112 or 2.2e-203 < z < 0.5

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.4%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around 0 61.7%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -5.60000000000000046e-112 < z < 2.2e-203

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   6. Simplified 57.2%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+226}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+113}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+220}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+115}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.1:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -8.8e+220)
     t_0
     (if (<= z -1.85e+115)
       (* -6.0 (* y z))
       (if (<= z -3.1)
         (* z (* x 6.0))
         (if (<= z -3.9e-112)
           (* y 4.0)
           (if (<= z 2.3e-203) (* x -3.0) (if (<= z 0.5) (* y 4.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.8e+220) {
		tmp = t_0;
	} else if (z <= -1.85e+115) {
		tmp = -6.0 * (y * z);
	} else if (z <= -3.1) {
		tmp = z * (x * 6.0);
	} else if (z <= -3.9e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.3e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-8.8d+220)) then
        tmp = t_0
    else if (z <= (-1.85d+115)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-3.1d0)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-3.9d-112)) then
        tmp = y * 4.0d0
    else if (z <= 2.3d-203) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.8e+220) {
		tmp = t_0;
	} else if (z <= -1.85e+115) {
		tmp = -6.0 * (y * z);
	} else if (z <= -3.1) {
		tmp = z * (x * 6.0);
	} else if (z <= -3.9e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.3e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -8.8e+220:
		tmp = t_0
	elif z <= -1.85e+115:
		tmp = -6.0 * (y * z)
	elif z <= -3.1:
		tmp = z * (x * 6.0)
	elif z <= -3.9e-112:
		tmp = y * 4.0
	elif z <= 2.3e-203:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -8.8e+220)
		tmp = t_0;
	elseif (z <= -1.85e+115)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -3.1)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -3.9e-112)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.3e-203)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -8.8e+220)
		tmp = t_0;
	elseif (z <= -1.85e+115)
		tmp = -6.0 * (y * z);
	elseif (z <= -3.1)
		tmp = z * (x * 6.0);
	elseif (z <= -3.9e-112)
		tmp = y * 4.0;
	elseif (z <= 2.3e-203)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+220], t$95$0, If[LessEqual[z, -1.85e+115], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-112], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.3e-203], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.79999999999999957e220 or 0.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 98.9%

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

   4. Taylor expanded in y around 0 61.7%

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

      1. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if -8.79999999999999957e220 < z < -1.85000000000000003e115

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -1.85000000000000003e115 < z < -3.10000000000000009

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 95.9%

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

      1. associate-*r* 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-*r* 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in y around 0 56.6%

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

   if -3.10000000000000009 < z < -3.9000000000000001e-112 or 2.29999999999999991e-203 < z < 0.5

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.4%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around 0 61.7%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -3.9000000000000001e-112 < z < 2.29999999999999991e-203

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   6. Simplified 57.2%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+220}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+115}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.1:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+222}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{+115}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -3e+222)
     t_0
     (if (<= z -1.52e+115)
       (* -6.0 (* y z))
       (if (<= z -3.3)
         t_0
         (if (<= z -3.7e-112)
           (* y 4.0)
           (if (<= z 3e-203) (* x -3.0) (if (<= z 0.5) (* y 4.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -3e+222) {
		tmp = t_0;
	} else if (z <= -1.52e+115) {
		tmp = -6.0 * (y * z);
	} else if (z <= -3.3) {
		tmp = t_0;
	} else if (z <= -3.7e-112) {
		tmp = y * 4.0;
	} else if (z <= 3e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-3d+222)) then
        tmp = t_0
    else if (z <= (-1.52d+115)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-3.3d0)) then
        tmp = t_0
    else if (z <= (-3.7d-112)) then
        tmp = y * 4.0d0
    else if (z <= 3d-203) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -3e+222) {
		tmp = t_0;
	} else if (z <= -1.52e+115) {
		tmp = -6.0 * (y * z);
	} else if (z <= -3.3) {
		tmp = t_0;
	} else if (z <= -3.7e-112) {
		tmp = y * 4.0;
	} else if (z <= 3e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -3e+222:
		tmp = t_0
	elif z <= -1.52e+115:
		tmp = -6.0 * (y * z)
	elif z <= -3.3:
		tmp = t_0
	elif z <= -3.7e-112:
		tmp = y * 4.0
	elif z <= 3e-203:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3e+222)
		tmp = t_0;
	elseif (z <= -1.52e+115)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -3.3)
		tmp = t_0;
	elseif (z <= -3.7e-112)
		tmp = Float64(y * 4.0);
	elseif (z <= 3e-203)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -3e+222)
		tmp = t_0;
	elseif (z <= -1.52e+115)
		tmp = -6.0 * (y * z);
	elseif (z <= -3.3)
		tmp = t_0;
	elseif (z <= -3.7e-112)
		tmp = y * 4.0;
	elseif (z <= 3e-203)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+222], t$95$0, If[LessEqual[z, -1.52e+115], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3], t$95$0, If[LessEqual[z, -3.7e-112], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3e-203], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.00000000000000014e222 or -1.52e115 < z < -3.2999999999999998 or 0.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 98.2%

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

   4. Taylor expanded in y around 0 60.5%

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

      1. *-commutative 60.5%

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

   6. Simplified 60.5%

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

   if -3.00000000000000014e222 < z < -1.52e115

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -3.2999999999999998 < z < -3.6999999999999998e-112 or 3.0000000000000001e-203 < z < 0.5

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.4%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around 0 61.7%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -3.6999999999999998e-112 < z < 3.0000000000000001e-203

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   6. Simplified 57.2%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+222}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{+115}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-110}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -2000.0)
     t_1
     (if (<= z -1.05e-110)
       t_0
       (if (<= z 1.95e-203) (* x -3.0) (if (<= z 5e+14) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2000.0) {
		tmp = t_1;
	} else if (z <= -1.05e-110) {
		tmp = t_0;
	} else if (z <= 1.95e-203) {
		tmp = x * -3.0;
	} else if (z <= 5e+14) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-2000.0d0)) then
        tmp = t_1
    else if (z <= (-1.05d-110)) then
        tmp = t_0
    else if (z <= 1.95d-203) then
        tmp = x * (-3.0d0)
    else if (z <= 5d+14) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2000.0) {
		tmp = t_1;
	} else if (z <= -1.05e-110) {
		tmp = t_0;
	} else if (z <= 1.95e-203) {
		tmp = x * -3.0;
	} else if (z <= 5e+14) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -2000.0:
		tmp = t_1
	elif z <= -1.05e-110:
		tmp = t_0
	elif z <= 1.95e-203:
		tmp = x * -3.0
	elif z <= 5e+14:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -2000.0)
		tmp = t_1;
	elseif (z <= -1.05e-110)
		tmp = t_0;
	elseif (z <= 1.95e-203)
		tmp = Float64(x * -3.0);
	elseif (z <= 5e+14)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -2000.0)
		tmp = t_1;
	elseif (z <= -1.05e-110)
		tmp = t_0;
	elseif (z <= 1.95e-203)
		tmp = x * -3.0;
	elseif (z <= 5e+14)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2000.0], t$95$1, If[LessEqual[z, -1.05e-110], t$95$0, If[LessEqual[z, 1.95e-203], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5e+14], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e3 or 5e14 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.1%

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

   if -2e3 < z < -1.05000000000000001e-110 or 1.95e-203 < z < 5e14

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.3%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -1.05000000000000001e-110 < z < 1.95e-203

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around inf 57.0%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto \color{blue}{x \cdot -3} \]

   6. Simplified 57.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-110}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.028:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.028)
     t_0
     (if (<= z -4.5e-112)
       (* y 4.0)
       (if (<= z 2.15e-203) (* x -3.0) (if (<= z 0.55) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.028) {
		tmp = t_0;
	} else if (z <= -4.5e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.028d0)) then
        tmp = t_0
    else if (z <= (-4.5d-112)) then
        tmp = y * 4.0d0
    else if (z <= 2.15d-203) then
        tmp = x * (-3.0d0)
    else if (z <= 0.55d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.028) {
		tmp = t_0;
	} else if (z <= -4.5e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.028:
		tmp = t_0
	elif z <= -4.5e-112:
		tmp = y * 4.0
	elif z <= 2.15e-203:
		tmp = x * -3.0
	elif z <= 0.55:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.028)
		tmp = t_0;
	elseif (z <= -4.5e-112)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.15e-203)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.55)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.028)
		tmp = t_0;
	elseif (z <= -4.5e-112)
		tmp = y * 4.0;
	elseif (z <= 2.15e-203)
		tmp = x * -3.0;
	elseif (z <= 0.55)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.028], t$95$0, If[LessEqual[z, -4.5e-112], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.15e-203], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0280000000000000006 or 0.55000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.8%

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

   if -0.0280000000000000006 < z < -4.50000000000000012e-112 or 2.15000000000000014e-203 < z < 0.55000000000000004

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 95.4%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -4.50000000000000012e-112 < z < 2.15000000000000014e-203

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   6. Simplified 57.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.028:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.66)
     t_0
     (if (<= z -3.6e-112)
       (* y 4.0)
       (if (<= z 2.1e-203) (* x -3.0) (if (<= z 0.65) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -3.6e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.1e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-3.6d-112)) then
        tmp = y * 4.0d0
    else if (z <= 2.1d-203) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -3.6e-112) {
		tmp = y * 4.0;
	} else if (z <= 2.1e-203) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= -3.6e-112:
		tmp = y * 4.0
	elif z <= 2.1e-203:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -3.6e-112)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.1e-203)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -3.6e-112)
		tmp = y * 4.0;
	elseif (z <= 2.1e-203)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = t_0;
	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, -0.66], t$95$0, If[LessEqual[z, -3.6e-112], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.1e-203], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031 or 0.650000000000000022 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 97.4%

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

   4. Taylor expanded in y around inf 45.7%

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

      1. *-commutative 45.7%

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

   6. Simplified 45.7%

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

   if -0.660000000000000031 < z < -3.6000000000000001e-112 or 2.10000000000000002e-203 < z < 0.650000000000000022

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.0%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around 0 63.3%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -3.6000000000000001e-112 < z < 2.10000000000000002e-203

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto \color{blue}{x \cdot -3} \]

   6. Simplified 57.2%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-203}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -45000000000000 \lor \neg \left(y \leq 13500000000000\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -45000000000000.0) (not (<= y 13500000000000.0)))
   (* y (+ 4.0 (* z -6.0)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -45000000000000.0) || !(y <= 13500000000000.0)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-45000000000000.0d0)) .or. (.not. (y <= 13500000000000.0d0))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -45000000000000.0) || !(y <= 13500000000000.0)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -45000000000000.0) or not (y <= 13500000000000.0):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -45000000000000.0) || !(y <= 13500000000000.0))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -45000000000000.0) || ~((y <= 13500000000000.0)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -45000000000000.0], N[Not[LessEqual[y, 13500000000000.0]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e13 or 1.35e13 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\left(-z\right) + \frac{2}{3}\right)}, x\right) \]

      6. distribute-lft-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{6 \cdot \left(-z\right) + 6 \cdot \frac{2}{3}}, x\right) \]

      7. distribute-rgt-neg-out 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(-6 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. *-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \left(-\color{blue}{z \cdot 6}\right) + 6 \cdot \frac{2}{3}, x\right) \]

      9. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(-6\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, -6, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, \color{blue}{-6}, 6 \cdot \frac{2}{3}\right), x\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, \mathsf{fma}\left(z, -6, 6 \cdot \color{blue}{0.6666666666666666}\right), x\right) \]

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if -4.5e13 < y < 1.35e13

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 80.8%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right) + 1\right)} \]

      2. sub-neg 80.8%

         \[\leadsto x \cdot \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)} + 1\right) \]

      3. distribute-lft-in 80.8%

         \[\leadsto x \cdot \left(\color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)} + 1\right) \]

      4. metadata-eval 80.8%

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

      5. neg-mul-1 80.8%

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

      6. *-commutative 80.8%

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

      7. associate-*l* 80.8%

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

      8. metadata-eval 80.8%

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

      9. distribute-rgt-in 80.8%

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

      10. +-commutative 80.8%

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

      11. distribute-rgt-in 80.8%

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

      12. metadata-eval 80.8%

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

      13. associate-+r+ 80.8%

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

      14. metadata-eval 80.8%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      15. *-commutative 80.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      16. associate-*l* 80.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      17. metadata-eval 80.8%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   5. Simplified 80.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -45000000000000 \lor \neg \left(y \leq 13500000000000\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -255000 \lor \neg \left(y \leq 2200000000000\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -255000.0) (not (<= y 2200000000000.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -255000.0) || !(y <= 2200000000000.0)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-255000.0d0)) .or. (.not. (y <= 2200000000000.0d0))) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -255000.0) || !(y <= 2200000000000.0)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -255000.0) or not (y <= 2200000000000.0):
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -255000.0) || !(y <= 2200000000000.0))
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -255000.0) || ~((y <= 2200000000000.0)))
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -255000.0], N[Not[LessEqual[y, 2200000000000.0]], $MachinePrecision]], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -255000 or 2.2e12 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.4%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -255000 < y < 2.2e12

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative 80.8%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right) + 1\right)} \]

      2. sub-neg 80.8%

         \[\leadsto x \cdot \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)} + 1\right) \]

      3. distribute-lft-in 80.8%

         \[\leadsto x \cdot \left(\color{blue}{\left(-6 \cdot 0.6666666666666666 + -6 \cdot \left(-z\right)\right)} + 1\right) \]

      4. metadata-eval 80.8%

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

      5. neg-mul-1 80.8%

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

      6. *-commutative 80.8%

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

      7. associate-*l* 80.8%

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

      8. metadata-eval 80.8%

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

      9. distribute-rgt-in 80.8%

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

      10. +-commutative 80.8%

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

      11. distribute-rgt-in 80.8%

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

      12. metadata-eval 80.8%

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

      13. associate-+r+ 80.8%

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

      14. metadata-eval 80.8%

          \[\leadsto x \cdot \left(\color{blue}{-3} + \left(-6 \cdot z\right) \cdot -1\right) \]

      15. *-commutative 80.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(z \cdot -6\right)} \cdot -1\right) \]

      16. associate-*l* 80.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot \left(-6 \cdot -1\right)}\right) \]

      17. metadata-eval 80.8%

          \[\leadsto x \cdot \left(-3 + z \cdot \color{blue}{6}\right) \]

   5. Simplified 80.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -255000 \lor \neg \left(y \leq 2200000000000\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* z (* (- y x) -6.0))
   (if (<= z 0.55) (+ (* y 4.0) (* x -3.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.55d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.55d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.55:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.55)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.55)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.4%

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

      1. associate-*r* 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-*r* 96.5%

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

   5. Applied egg-rr 96.5%

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

   if -0.55000000000000004 < z < 0.55000000000000004

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 97.1%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around 0 97.1%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 0.55000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 98.5%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* z (* (- y x) -6.0))
   (if (<= z 0.65) (+ x (* (- y x) 4.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.55d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.65d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.65:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.65)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.65)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.4%

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

      1. associate-*r* 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-*r* 96.5%

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

   5. Applied egg-rr 96.5%

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

   if -0.55000000000000004 < z < 0.650000000000000022

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 97.1%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 0.650000000000000022 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 98.5%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000 \lor \neg \left(y \leq 8.4 \cdot 10^{-41}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7000.0) (not (<= y 8.4e-41))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7000.0) || !(y <= 8.4e-41)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	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 <= (-7000.0d0)) .or. (.not. (y <= 8.4d-41))) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7000.0) || !(y <= 8.4e-41)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7000.0) or not (y <= 8.4e-41):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7000.0) || !(y <= 8.4e-41))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7000.0) || ~((y <= 8.4e-41)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7000.0], N[Not[LessEqual[y, 8.4e-41]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e3 or 8.40000000000000051e-41 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 47.3%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around 0 36.8%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -7e3 < y < 8.40000000000000051e-41

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 44.6%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   4. Taylor expanded in x around inf 35.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 35.6%

         \[\leadsto \color{blue}{x \cdot -3} \]

   6. Simplified 35.6%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7000 \lor \neg \left(y \leq 8.4 \cdot 10^{-41}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (- y x) (* 6.0 (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * (0.6666666666666666 - 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 * (0.6666666666666666d0 - z)))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * (0.6666666666666666 - z)));
}

Python

def code(x, y, z):
	return x + ((y - x) * (6.0 * (0.6666666666666666 - z)))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(6.0 * Float64(0.6666666666666666 - z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (6.0 * (0.6666666666666666 - z)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-*l* 99.8%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \]

   2. metadata-eval 99.8%

      \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot \left(\color{blue}{0.6666666666666666} - z\right)\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
5. Add Preprocessing

Alternative 14: 26.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y \cdot 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 4.0))

C

double code(double x, double y, double z) {
	return y * 4.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * 4.0d0
end function

Java

public static double code(double x, double y, double z) {
	return y * 4.0;
}

Python

def code(x, y, z):
	return y * 4.0

Julia

function code(x, y, z)
	return Float64(y * 4.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * 4.0;
end

Wolfram

code[x_, y_, z_] := N[(y * 4.0), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 46.1%

   \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

4. Taylor expanded in x around 0 25.2%

   \[\leadsto \color{blue}{4 \cdot y} \]

5. Final simplification 25.2%

   \[\leadsto y \cdot 4 \]
6. Add Preprocessing

Alternative 15: 2.6% accurate, 13.0× 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 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around inf 54.5%

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

   1. associate-*r* 54.5%

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

   2. *-commutative 54.5%

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

5. Simplified 54.5%

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

6. Taylor expanded in z around 0 2.6%

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

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))