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

Percentage Accurate: 99.5% → 99.7%

Time: 12.3s

Alternatives: 15

Speedup: 1.2×

• 22.1% 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: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + \left(y - x\right) \cdot 4\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 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 = x + (((-6.0d0) * (z * (y - x))) + ((y - x) * 4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
}

Python

def code(x, y, z):
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
end

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around 0 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+234}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-242}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-256}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* x (* z 6.0))))
   (if (<= z -1.8e+234)
     t_0
     (if (<= z -4.6e+85)
       t_1
       (if (<= z -0.66)
         t_0
         (if (<= z -2.5e-126)
           (* y 4.0)
           (if (<= z -4.5e-148)
             (* x -3.0)
             (if (<= z -1.5e-203)
               (* y 4.0)
               (if (<= z -4.8e-242)
                 (* x -3.0)
                 (if (<= z 1.32e-256)
                   (* y 4.0)
                   (if (<= z 1.35e-152)
                     (* x -3.0)
                     (if (<= z 0.68)
                       (* y 4.0)
                       (if (<= z 6.2e+20) t_0 t_1)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.8e+234) {
		tmp = t_0;
	} else if (z <= -4.6e+85) {
		tmp = t_1;
	} else if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -2.5e-126) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.5e-203) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-242) {
		tmp = x * -3.0;
	} else if (z <= 1.32e-256) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-152) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 6.2e+20) {
		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) * (z * y)
    t_1 = x * (z * 6.0d0)
    if (z <= (-1.8d+234)) then
        tmp = t_0
    else if (z <= (-4.6d+85)) then
        tmp = t_1
    else if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-2.5d-126)) then
        tmp = y * 4.0d0
    else if (z <= (-4.5d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.5d-203)) then
        tmp = y * 4.0d0
    else if (z <= (-4.8d-242)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.32d-256) then
        tmp = y * 4.0d0
    else if (z <= 1.35d-152) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    else if (z <= 6.2d+20) 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 * (z * y);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.8e+234) {
		tmp = t_0;
	} else if (z <= -4.6e+85) {
		tmp = t_1;
	} else if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -2.5e-126) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.5e-203) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-242) {
		tmp = x * -3.0;
	} else if (z <= 1.32e-256) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-152) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 6.2e+20) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -1.8e+234:
		tmp = t_0
	elif z <= -4.6e+85:
		tmp = t_1
	elif z <= -0.66:
		tmp = t_0
	elif z <= -2.5e-126:
		tmp = y * 4.0
	elif z <= -4.5e-148:
		tmp = x * -3.0
	elif z <= -1.5e-203:
		tmp = y * 4.0
	elif z <= -4.8e-242:
		tmp = x * -3.0
	elif z <= 1.32e-256:
		tmp = y * 4.0
	elif z <= 1.35e-152:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	elif z <= 6.2e+20:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -1.8e+234)
		tmp = t_0;
	elseif (z <= -4.6e+85)
		tmp = t_1;
	elseif (z <= -0.66)
		tmp = t_0;
	elseif (z <= -2.5e-126)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.5e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.5e-203)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.8e-242)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.32e-256)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.35e-152)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.2e+20)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -1.8e+234)
		tmp = t_0;
	elseif (z <= -4.6e+85)
		tmp = t_1;
	elseif (z <= -0.66)
		tmp = t_0;
	elseif (z <= -2.5e-126)
		tmp = y * 4.0;
	elseif (z <= -4.5e-148)
		tmp = x * -3.0;
	elseif (z <= -1.5e-203)
		tmp = y * 4.0;
	elseif (z <= -4.8e-242)
		tmp = x * -3.0;
	elseif (z <= 1.32e-256)
		tmp = y * 4.0;
	elseif (z <= 1.35e-152)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	elseif (z <= 6.2e+20)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+234], t$95$0, If[LessEqual[z, -4.6e+85], t$95$1, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -2.5e-126], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.5e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.5e-203], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.8e-242], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.32e-256], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.35e-152], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.2e+20], t$95$0, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e234 or -4.5999999999999998e85 < z < -0.660000000000000031 or 0.680000000000000049 < z < 6.2e20

   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. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 76.0%

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

   6. Taylor expanded in z around inf 73.9%

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

   if -1.8e234 < z < -4.5999999999999998e85 or 6.2e20 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around inf 67.6%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   if -0.660000000000000031 < z < -2.50000000000000003e-126 or -4.50000000000000015e-148 < z < -1.5000000000000001e-203 or -4.8000000000000002e-242 < z < 1.32e-256 or 1.34999999999999999e-152 < z < 0.680000000000000049

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 96.8%

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

   5. Taylor expanded in x around 0 64.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

   if -2.50000000000000003e-126 < z < -4.50000000000000015e-148 or -1.5000000000000001e-203 < z < -4.8000000000000002e-242 or 1.32e-256 < z < 1.34999999999999999e-152

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+234}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-242}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-256}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 3: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+234}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-199}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-243}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* x (* z 6.0))))
   (if (<= z -4.2e+234)
     (* z (* -6.0 y))
     (if (<= z -1.95e+86)
       t_1
       (if (<= z -0.66)
         t_0
         (if (<= z -1e-127)
           (* y 4.0)
           (if (<= z -5e-148)
             (* x -3.0)
             (if (<= z -9.5e-199)
               (* y 4.0)
               (if (<= z -5.6e-243)
                 (* x -3.0)
                 (if (<= z 4.2e-257)
                   (* y 4.0)
                   (if (<= z 5.2e-150)
                     (* x -3.0)
                     (if (<= z 0.68)
                       (* y 4.0)
                       (if (<= z 5.7e+20) t_0 t_1)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -4.2e+234) {
		tmp = z * (-6.0 * y);
	} else if (z <= -1.95e+86) {
		tmp = t_1;
	} else if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -1e-127) {
		tmp = y * 4.0;
	} else if (z <= -5e-148) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-199) {
		tmp = y * 4.0;
	} else if (z <= -5.6e-243) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-257) {
		tmp = y * 4.0;
	} else if (z <= 5.2e-150) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 5.7e+20) {
		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) * (z * y)
    t_1 = x * (z * 6.0d0)
    if (z <= (-4.2d+234)) then
        tmp = z * ((-6.0d0) * y)
    else if (z <= (-1.95d+86)) then
        tmp = t_1
    else if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-1d-127)) then
        tmp = y * 4.0d0
    else if (z <= (-5d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9.5d-199)) then
        tmp = y * 4.0d0
    else if (z <= (-5.6d-243)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d-257) then
        tmp = y * 4.0d0
    else if (z <= 5.2d-150) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    else if (z <= 5.7d+20) 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 * (z * y);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -4.2e+234) {
		tmp = z * (-6.0 * y);
	} else if (z <= -1.95e+86) {
		tmp = t_1;
	} else if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -1e-127) {
		tmp = y * 4.0;
	} else if (z <= -5e-148) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-199) {
		tmp = y * 4.0;
	} else if (z <= -5.6e-243) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-257) {
		tmp = y * 4.0;
	} else if (z <= 5.2e-150) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 5.7e+20) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -4.2e+234:
		tmp = z * (-6.0 * y)
	elif z <= -1.95e+86:
		tmp = t_1
	elif z <= -0.66:
		tmp = t_0
	elif z <= -1e-127:
		tmp = y * 4.0
	elif z <= -5e-148:
		tmp = x * -3.0
	elif z <= -9.5e-199:
		tmp = y * 4.0
	elif z <= -5.6e-243:
		tmp = x * -3.0
	elif z <= 4.2e-257:
		tmp = y * 4.0
	elif z <= 5.2e-150:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	elif z <= 5.7e+20:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -4.2e+234)
		tmp = Float64(z * Float64(-6.0 * y));
	elseif (z <= -1.95e+86)
		tmp = t_1;
	elseif (z <= -0.66)
		tmp = t_0;
	elseif (z <= -1e-127)
		tmp = Float64(y * 4.0);
	elseif (z <= -5e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -9.5e-199)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.6e-243)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.2e-150)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.7e+20)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -4.2e+234)
		tmp = z * (-6.0 * y);
	elseif (z <= -1.95e+86)
		tmp = t_1;
	elseif (z <= -0.66)
		tmp = t_0;
	elseif (z <= -1e-127)
		tmp = y * 4.0;
	elseif (z <= -5e-148)
		tmp = x * -3.0;
	elseif (z <= -9.5e-199)
		tmp = y * 4.0;
	elseif (z <= -5.6e-243)
		tmp = x * -3.0;
	elseif (z <= 4.2e-257)
		tmp = y * 4.0;
	elseif (z <= 5.2e-150)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	elseif (z <= 5.7e+20)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+234], N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e+86], t$95$1, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -1e-127], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9.5e-199], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.6e-243], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.2e-150], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.7e+20], t$95$0, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2e234

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 71.1%

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

   6. Taylor expanded in z around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*r* 71.1%

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

      3. *-commutative 71.1%

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

      4. associate-*l* 71.2%

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

   8. Simplified 71.2%

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

   if -4.2e234 < z < -1.9500000000000001e86 or 5.7e20 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around inf 67.6%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   if -1.9500000000000001e86 < z < -0.660000000000000031 or 0.680000000000000049 < z < 5.7e20

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around 0 80.1%

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

   6. Taylor expanded in z around inf 76.3%

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

   if -0.660000000000000031 < z < -1e-127 or -4.9999999999999999e-148 < z < -9.5000000000000005e-199 or -5.59999999999999987e-243 < z < 4.2000000000000002e-257 or 5.1999999999999995e-150 < z < 0.680000000000000049

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 96.8%

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

   5. Taylor expanded in x around 0 64.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

   if -1e-127 < z < -4.9999999999999999e-148 or -9.5000000000000005e-199 < z < -5.59999999999999987e-243 or 4.2000000000000002e-257 < z < 5.1999999999999995e-150

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+234}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-199}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-243}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+20}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.0126:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-203}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-39}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6400:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.0126)
     t_0
     (if (<= z -5.5e-126)
       (* y 4.0)
       (if (<= z -5e-148)
         (* x -3.0)
         (if (<= z -9e-203)
           (* y 4.0)
           (if (<= z -7.8e-241)
             (* x -3.0)
             (if (<= z 4.5e-257)
               (* y 4.0)
               (if (<= z 1.3e-151)
                 (* x -3.0)
                 (if (<= z 3.3e-39)
                   (* y 4.0)
                   (if (<= z 6400.0) (* x (- (* z 6.0) 3.0)) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.0126) {
		tmp = t_0;
	} else if (z <= -5.5e-126) {
		tmp = y * 4.0;
	} else if (z <= -5e-148) {
		tmp = x * -3.0;
	} else if (z <= -9e-203) {
		tmp = y * 4.0;
	} else if (z <= -7.8e-241) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-151) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-39) {
		tmp = y * 4.0;
	} else if (z <= 6400.0) {
		tmp = x * ((z * 6.0) - 3.0);
	} 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) * (z * (y - x))
    if (z <= (-0.0126d0)) then
        tmp = t_0
    else if (z <= (-5.5d-126)) then
        tmp = y * 4.0d0
    else if (z <= (-5d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9d-203)) then
        tmp = y * 4.0d0
    else if (z <= (-7.8d-241)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d-257) then
        tmp = y * 4.0d0
    else if (z <= 1.3d-151) then
        tmp = x * (-3.0d0)
    else if (z <= 3.3d-39) then
        tmp = y * 4.0d0
    else if (z <= 6400.0d0) then
        tmp = x * ((z * 6.0d0) - 3.0d0)
    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 * (z * (y - x));
	double tmp;
	if (z <= -0.0126) {
		tmp = t_0;
	} else if (z <= -5.5e-126) {
		tmp = y * 4.0;
	} else if (z <= -5e-148) {
		tmp = x * -3.0;
	} else if (z <= -9e-203) {
		tmp = y * 4.0;
	} else if (z <= -7.8e-241) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-151) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-39) {
		tmp = y * 4.0;
	} else if (z <= 6400.0) {
		tmp = x * ((z * 6.0) - 3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.0126:
		tmp = t_0
	elif z <= -5.5e-126:
		tmp = y * 4.0
	elif z <= -5e-148:
		tmp = x * -3.0
	elif z <= -9e-203:
		tmp = y * 4.0
	elif z <= -7.8e-241:
		tmp = x * -3.0
	elif z <= 4.5e-257:
		tmp = y * 4.0
	elif z <= 1.3e-151:
		tmp = x * -3.0
	elif z <= 3.3e-39:
		tmp = y * 4.0
	elif z <= 6400.0:
		tmp = x * ((z * 6.0) - 3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.0126)
		tmp = t_0;
	elseif (z <= -5.5e-126)
		tmp = Float64(y * 4.0);
	elseif (z <= -5e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -9e-203)
		tmp = Float64(y * 4.0);
	elseif (z <= -7.8e-241)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.3e-151)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.3e-39)
		tmp = Float64(y * 4.0);
	elseif (z <= 6400.0)
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.0126)
		tmp = t_0;
	elseif (z <= -5.5e-126)
		tmp = y * 4.0;
	elseif (z <= -5e-148)
		tmp = x * -3.0;
	elseif (z <= -9e-203)
		tmp = y * 4.0;
	elseif (z <= -7.8e-241)
		tmp = x * -3.0;
	elseif (z <= 4.5e-257)
		tmp = y * 4.0;
	elseif (z <= 1.3e-151)
		tmp = x * -3.0;
	elseif (z <= 3.3e-39)
		tmp = y * 4.0;
	elseif (z <= 6400.0)
		tmp = x * ((z * 6.0) - 3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0126], t$95$0, If[LessEqual[z, -5.5e-126], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9e-203], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -7.8e-241], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.3e-151], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.3e-39], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6400.0], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0126 or 6400 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.0%

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

   if -0.0126 < z < -5.49999999999999987e-126 or -4.9999999999999999e-148 < z < -9.0000000000000003e-203 or -7.7999999999999998e-241 < z < 4.5000000000000003e-257 or 1.3e-151 < z < 3.29999999999999985e-39

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 97.9%

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

   5. Taylor expanded in x around 0 66.9%

      \[\leadsto \color{blue}{4 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -5.49999999999999987e-126 < z < -4.9999999999999999e-148 or -9.0000000000000003e-203 < z < -7.7999999999999998e-241 or 4.5000000000000003e-257 < z < 1.3e-151

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

   7. Simplified 81.5%

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

   if 3.29999999999999985e-39 < z < 6400

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 99.6%

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

   5. Taylor expanded in x around inf 52.1%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0126:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-203}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-39}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6400:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 5: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.034:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-208}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.034)
     t_0
     (if (<= z -5.5e-129)
       (* y 4.0)
       (if (<= z -1.9e-148)
         (* x -3.0)
         (if (<= z -2.9e-208)
           (* y 4.0)
           (if (<= z -1e-241)
             (* x -3.0)
             (if (<= z 3.7e-257)
               (* y 4.0)
               (if (<= z 2.35e-151)
                 (* 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 * (z * (y - x));
	double tmp;
	if (z <= -0.034) {
		tmp = t_0;
	} else if (z <= -5.5e-129) {
		tmp = y * 4.0;
	} else if (z <= -1.9e-148) {
		tmp = x * -3.0;
	} else if (z <= -2.9e-208) {
		tmp = y * 4.0;
	} else if (z <= -1e-241) {
		tmp = x * -3.0;
	} else if (z <= 3.7e-257) {
		tmp = y * 4.0;
	} else if (z <= 2.35e-151) {
		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) * (z * (y - x))
    if (z <= (-0.034d0)) then
        tmp = t_0
    else if (z <= (-5.5d-129)) then
        tmp = y * 4.0d0
    else if (z <= (-1.9d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.9d-208)) then
        tmp = y * 4.0d0
    else if (z <= (-1d-241)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.7d-257) then
        tmp = y * 4.0d0
    else if (z <= 2.35d-151) 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 * (z * (y - x));
	double tmp;
	if (z <= -0.034) {
		tmp = t_0;
	} else if (z <= -5.5e-129) {
		tmp = y * 4.0;
	} else if (z <= -1.9e-148) {
		tmp = x * -3.0;
	} else if (z <= -2.9e-208) {
		tmp = y * 4.0;
	} else if (z <= -1e-241) {
		tmp = x * -3.0;
	} else if (z <= 3.7e-257) {
		tmp = y * 4.0;
	} else if (z <= 2.35e-151) {
		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 * (z * (y - x))
	tmp = 0
	if z <= -0.034:
		tmp = t_0
	elif z <= -5.5e-129:
		tmp = y * 4.0
	elif z <= -1.9e-148:
		tmp = x * -3.0
	elif z <= -2.9e-208:
		tmp = y * 4.0
	elif z <= -1e-241:
		tmp = x * -3.0
	elif z <= 3.7e-257:
		tmp = y * 4.0
	elif z <= 2.35e-151:
		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(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.034)
		tmp = t_0;
	elseif (z <= -5.5e-129)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.9e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.9e-208)
		tmp = Float64(y * 4.0);
	elseif (z <= -1e-241)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.7e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.35e-151)
		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 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.034)
		tmp = t_0;
	elseif (z <= -5.5e-129)
		tmp = y * 4.0;
	elseif (z <= -1.9e-148)
		tmp = x * -3.0;
	elseif (z <= -2.9e-208)
		tmp = y * 4.0;
	elseif (z <= -1e-241)
		tmp = x * -3.0;
	elseif (z <= 3.7e-257)
		tmp = y * 4.0;
	elseif (z <= 2.35e-151)
		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[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.034], t$95$0, If[LessEqual[z, -5.5e-129], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.9e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.9e-208], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1e-241], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.7e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.35e-151], 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 < -0.034000000000000002 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. Step-by-step derivation

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.0%

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

   if -0.034000000000000002 < z < -5.50000000000000023e-129 or -1.90000000000000007e-148 < z < -2.8999999999999999e-208 or -9.9999999999999997e-242 < z < 3.69999999999999984e-257 or 2.35000000000000014e-151 < z < 0.55000000000000004

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 96.8%

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

   5. Taylor expanded in x around 0 64.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

   if -5.50000000000000023e-129 < z < -1.90000000000000007e-148 or -2.8999999999999999e-208 < z < -9.9999999999999997e-242 or 3.69999999999999984e-257 < z < 2.35000000000000014e-151

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.034:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-208}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 6: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-256}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -0.66)
     t_0
     (if (<= z -1e-126)
       (* y 4.0)
       (if (<= z -6e-149)
         (* x -3.0)
         (if (<= z -1.4e-198)
           (* y 4.0)
           (if (<= z -2.25e-241)
             (* x -3.0)
             (if (<= z 2e-256)
               (* y 4.0)
               (if (<= z 5.8e-147)
                 (* x -3.0)
                 (if (<= z 0.68) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -1e-126) {
		tmp = y * 4.0;
	} else if (z <= -6e-149) {
		tmp = x * -3.0;
	} else if (z <= -1.4e-198) {
		tmp = y * 4.0;
	} else if (z <= -2.25e-241) {
		tmp = x * -3.0;
	} else if (z <= 2e-256) {
		tmp = y * 4.0;
	} else if (z <= 5.8e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		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) * (z * y)
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-1d-126)) then
        tmp = y * 4.0d0
    else if (z <= (-6d-149)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.4d-198)) then
        tmp = y * 4.0d0
    else if (z <= (-2.25d-241)) then
        tmp = x * (-3.0d0)
    else if (z <= 2d-256) then
        tmp = y * 4.0d0
    else if (z <= 5.8d-147) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) 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 * (z * y);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -1e-126) {
		tmp = y * 4.0;
	} else if (z <= -6e-149) {
		tmp = x * -3.0;
	} else if (z <= -1.4e-198) {
		tmp = y * 4.0;
	} else if (z <= -2.25e-241) {
		tmp = x * -3.0;
	} else if (z <= 2e-256) {
		tmp = y * 4.0;
	} else if (z <= 5.8e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= -1e-126:
		tmp = y * 4.0
	elif z <= -6e-149:
		tmp = x * -3.0
	elif z <= -1.4e-198:
		tmp = y * 4.0
	elif z <= -2.25e-241:
		tmp = x * -3.0
	elif z <= 2e-256:
		tmp = y * 4.0
	elif z <= 5.8e-147:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -1e-126)
		tmp = Float64(y * 4.0);
	elseif (z <= -6e-149)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.4e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.25e-241)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e-256)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.8e-147)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -1e-126)
		tmp = y * 4.0;
	elseif (z <= -6e-149)
		tmp = x * -3.0;
	elseif (z <= -1.4e-198)
		tmp = y * 4.0;
	elseif (z <= -2.25e-241)
		tmp = x * -3.0;
	elseif (z <= 2e-256)
		tmp = y * 4.0;
	elseif (z <= 5.8e-147)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -1e-126], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -6e-149], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.4e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.25e-241], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e-256], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.8e-147], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 53.4%

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

   6. Taylor expanded in z around inf 52.6%

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

   if -0.660000000000000031 < z < -9.9999999999999995e-127 or -6.0000000000000003e-149 < z < -1.4e-198 or -2.2499999999999999e-241 < z < 1.99999999999999995e-256 or 5.8000000000000002e-147 < z < 0.680000000000000049

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 96.8%

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

   5. Taylor expanded in x around 0 64.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 64.3%

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

   7. Simplified 64.3%

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

   if -9.9999999999999995e-127 < z < -6.0000000000000003e-149 or -1.4e-198 < z < -2.2499999999999999e-241 or 1.99999999999999995e-256 < z < 5.8000000000000002e-147

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-256}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 7: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.58) (+ (* y 4.0) (* x -3.0)) (+ x (* z (* 6.0 (- x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.58) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	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 <= (-0.58d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.58d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = x + (z * (6.0d0 * (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.58) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.58:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = x + (z * (6.0 * (x - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.58)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(x + Float64(z * Float64(6.0 * Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.58)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = x + (z * (6.0 * (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.58], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 98.7%

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

   if -0.57999999999999996 < z < 0.57999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

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

   5. Taylor expanded in x around 0 97.8%

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

   if 0.57999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.3%

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

      1. neg-mul-1 99.3%

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

   6. Simplified 99.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]

Alternative 8: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+44} \lor \neg \left(x \leq 4.1 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.4e+44) (not (<= x 4.1e+44)))
   (* x (- (* z 6.0) 3.0))
   (* y (+ 4.0 (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.4e+44) || !(x <= 4.1e+44)) {
		tmp = x * ((z * 6.0) - 3.0);
	} else {
		tmp = y * (4.0 + (-6.0 * 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 ((x <= (-5.4d+44)) .or. (.not. (x <= 4.1d+44))) then
        tmp = x * ((z * 6.0d0) - 3.0d0)
    else
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.4e+44) || !(x <= 4.1e+44)) {
		tmp = x * ((z * 6.0) - 3.0);
	} else {
		tmp = y * (4.0 + (-6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.4e+44) or not (x <= 4.1e+44):
		tmp = x * ((z * 6.0) - 3.0)
	else:
		tmp = y * (4.0 + (-6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.4e+44) || !(x <= 4.1e+44))
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	else
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.4e+44) || ~((x <= 4.1e+44)))
		tmp = x * ((z * 6.0) - 3.0);
	else
		tmp = y * (4.0 + (-6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.4e+44], N[Not[LessEqual[x, 4.1e+44]], $MachinePrecision]], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4e44 or 4.09999999999999965e44 < x

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around inf 82.6%

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

   if -5.4e44 < x < 4.09999999999999965e44

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

   7. Simplified 78.4%

      \[\leadsto \color{blue}{y \cdot \left(4 + z \cdot -6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+44} \lor \neg \left(x \leq 4.1 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \]

Alternative 9: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.62\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.62)))
   (* -6.0 (* z (- y x)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.62)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	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 <= (-0.58d0)) .or. (.not. (z <= 0.62d0))) then
        tmp = (-6.0d0) * (z * (y - x))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.62)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.62):
		tmp = -6.0 * (z * (y - x))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.62))
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.62)))
		tmp = -6.0 * (z * (y - x));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.62]], $MachinePrecision]], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.619999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.0%

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

   if -0.57999999999999996 < z < 0.619999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.62\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]

Alternative 10: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.5)))
   (* -6.0 (* z (- y x)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.5)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = (y * 4.0) + (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 ((z <= (-0.58d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = (-6.0d0) * (z * (y - x))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.5)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.5):
		tmp = -6.0 * (z * (y - x))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.5))
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.5)))
		tmp = -6.0 * (z * (y - x));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 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. Step-by-step derivation

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.0%

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

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.8%

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

   5. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]

Alternative 11: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 12: 99.7% 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 99.6%

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

   1. +-commutative 99.6%

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

   2. *-commutative 99.6%

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

   3. associate-*l* 99.5%

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

   4. fma-def 99.5%

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

   5. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. fma-udef 99.5%

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

   2. associate-*r* 99.6%

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

   3. *-commutative 99.6%

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

   4. associate-*l* 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 13: 38.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+15} \lor \neg \left(x \leq 3.1 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.3e+15) (not (<= x 3.1e+44))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e+15) || !(x <= 3.1e+44)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	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 ((x <= (-2.3d+15)) .or. (.not. (x <= 3.1d+44))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e+15) || !(x <= 3.1e+44)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.3e+15) or not (x <= 3.1e+44):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.3e+15) || !(x <= 3.1e+44))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.3e+15) || ~((x <= 3.1e+44)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.3e+15], N[Not[LessEqual[x, 3.1e+44]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e15 or 3.09999999999999996e44 < x

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 54.8%

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

   5. Taylor expanded in x around inf 43.0%

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

      1. *-commutative 43.0%

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

   7. Simplified 43.0%

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

   if -2.3e15 < x < 3.09999999999999996e44

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 51.2%

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

   5. Taylor expanded in x around 0 41.8%

      \[\leadsto \color{blue}{4 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 41.8%

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

   7. Simplified 41.8%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+15} \lor \neg \left(x \leq 3.1 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 14: 26.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

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 * (-3.0d0)
end function

Java

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

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around 0 52.9%

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

5. Taylor expanded in x around inf 26.1%

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

   1. *-commutative 26.1%

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

7. Simplified 26.1%

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

8. Final simplification 26.1%

   \[\leadsto x \cdot -3 \]

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 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in y around inf 51.9%

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

   1. associate-*r* 51.9%

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

6. Simplified 51.9%

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

7. Taylor expanded in x around inf 2.8%

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

8. Final simplification 2.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(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))))