Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C

Percentage Accurate: 99.9% → 100.0%

Time: 3.4s

Alternatives: 8

Speedup: 1.4×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 2 + \frac{x - z}{y \cdot 0.25} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 2.0 (/ (- x z) (* y 0.25))))

C

double code(double x, double y, double z) {
	return 2.0 + ((x - z) / (y * 0.25));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 + ((x - z) / (y * 0.25d0))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 + ((x - z) / (y * 0.25));
}

Python

def code(x, y, z):
	return 2.0 + ((x - z) / (y * 0.25))

Julia

function code(x, y, z)
	return Float64(2.0 + Float64(Float64(x - z) / Float64(y * 0.25)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 + ((x - z) / (y * 0.25));
end

Wolfram

code[x_, y_, z_] := N[(2.0 + N[(N[(x - z), $MachinePrecision] / N[(y * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

   2. +-commutative 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

   3. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

   4. distribute-lft-in 99.8%

      \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

   5. associate-+r+ 99.8%

      \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

   6. associate-*l/ 99.8%

      \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   7. *-commutative 99.8%

      \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   8. associate-/l* 99.8%

      \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   9. metadata-eval 99.8%

      \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   10. metadata-eval 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   11. associate-/l* 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   12. distribute-rgt-neg-in 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   13. distribute-lft-neg-out 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   14. associate-/l* 99.8%

       \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   15. *-commutative 99.8%

       \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   16. neg-mul-1 99.8%

       \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   17. distribute-lft-neg-out 99.8%

       \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   18. *-inverses 99.8%

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

   19. metadata-eval 99.8%

       \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{2 + \frac{4}{y} \cdot \left(x - z\right)} \]
4. Step-by-step derivation

   1. clear-num 99.8%

      \[\leadsto 2 + \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) \]

   2. div-inv 99.8%

      \[\leadsto 2 + \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) \]

   3. metadata-eval 99.8%

      \[\leadsto 2 + \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) \]

   4. associate-*l/ 100.0%

      \[\leadsto 2 + \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} \]

   5. *-un-lft-identity 100.0%

      \[\leadsto 2 + \frac{\color{blue}{x - z}}{y \cdot 0.25} \]

5. Applied egg-rr 100.0%

   \[\leadsto 2 + \color{blue}{\frac{x - z}{y \cdot 0.25}} \]

6. Final simplification 100.0%

   \[\leadsto 2 + \frac{x - z}{y \cdot 0.25} \]

Alternative 2: 55.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{\frac{y}{-4}}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -27:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-244}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-301}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-147}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 20000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (/ y -4.0))) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= x -27.0)
     t_1
     (if (<= x -1.75e-43)
       t_0
       (if (<= x -1.85e-244)
         2.0
         (if (<= x 1.45e-301)
           t_0
           (if (<= x 7e-147) 2.0 (if (<= x 20000000000000.0) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = z / (y / -4.0);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -27.0) {
		tmp = t_1;
	} else if (x <= -1.75e-43) {
		tmp = t_0;
	} else if (x <= -1.85e-244) {
		tmp = 2.0;
	} else if (x <= 1.45e-301) {
		tmp = t_0;
	} else if (x <= 7e-147) {
		tmp = 2.0;
	} else if (x <= 20000000000000.0) {
		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 = z / (y / (-4.0d0))
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (x <= (-27.0d0)) then
        tmp = t_1
    else if (x <= (-1.75d-43)) then
        tmp = t_0
    else if (x <= (-1.85d-244)) then
        tmp = 2.0d0
    else if (x <= 1.45d-301) then
        tmp = t_0
    else if (x <= 7d-147) then
        tmp = 2.0d0
    else if (x <= 20000000000000.0d0) 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 = z / (y / -4.0);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -27.0) {
		tmp = t_1;
	} else if (x <= -1.75e-43) {
		tmp = t_0;
	} else if (x <= -1.85e-244) {
		tmp = 2.0;
	} else if (x <= 1.45e-301) {
		tmp = t_0;
	} else if (x <= 7e-147) {
		tmp = 2.0;
	} else if (x <= 20000000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (y / -4.0)
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if x <= -27.0:
		tmp = t_1
	elif x <= -1.75e-43:
		tmp = t_0
	elif x <= -1.85e-244:
		tmp = 2.0
	elif x <= 1.45e-301:
		tmp = t_0
	elif x <= 7e-147:
		tmp = 2.0
	elif x <= 20000000000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(y / -4.0))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -27.0)
		tmp = t_1;
	elseif (x <= -1.75e-43)
		tmp = t_0;
	elseif (x <= -1.85e-244)
		tmp = 2.0;
	elseif (x <= 1.45e-301)
		tmp = t_0;
	elseif (x <= 7e-147)
		tmp = 2.0;
	elseif (x <= 20000000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / (y / -4.0);
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (x <= -27.0)
		tmp = t_1;
	elseif (x <= -1.75e-43)
		tmp = t_0;
	elseif (x <= -1.85e-244)
		tmp = 2.0;
	elseif (x <= 1.45e-301)
		tmp = t_0;
	elseif (x <= 7e-147)
		tmp = 2.0;
	elseif (x <= 20000000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / N[(y / -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -27.0], t$95$1, If[LessEqual[x, -1.75e-43], t$95$0, If[LessEqual[x, -1.85e-244], 2.0, If[LessEqual[x, 1.45e-301], t$95$0, If[LessEqual[x, 7e-147], 2.0, If[LessEqual[x, 20000000000000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -27 or 2e13 < x

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in x around inf 69.0%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

   if -27 < x < -1.74999999999999999e-43 or -1.8500000000000001e-244 < x < 1.44999999999999992e-301 or 7.00000000000000007e-147 < x < 2e13

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in z around inf 72.1%

      \[\leadsto 1 + \color{blue}{-4 \cdot \frac{z}{y}} \]
   3. Step-by-step derivation

      1. associate-*r/ 72.1%

         \[\leadsto 1 + \color{blue}{\frac{-4 \cdot z}{y}} \]

   4. Simplified 72.1%

      \[\leadsto 1 + \color{blue}{\frac{-4 \cdot z}{y}} \]

   5. Taylor expanded in z around inf 67.6%

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

      1. associate-*r/ 67.6%

         \[\leadsto \color{blue}{\frac{-4 \cdot z}{y}} \]

      2. *-commutative 67.6%

         \[\leadsto \frac{\color{blue}{z \cdot -4}}{y} \]

      3. associate-/l* 67.6%

         \[\leadsto \color{blue}{\frac{z}{\frac{y}{-4}}} \]

   7. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{z}{\frac{y}{-4}}} \]

   if -1.74999999999999999e-43 < x < -1.8500000000000001e-244 or 1.44999999999999992e-301 < x < 7.00000000000000007e-147

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf 60.7%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -27:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-244}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-301}:\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-147}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 20000000000000:\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 3: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-244}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-300}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-278}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3400000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= x -2.1e+27)
     t_1
     (if (<= x -1.75e-43)
       t_0
       (if (<= x -1.1e-244)
         2.0
         (if (<= x 1.95e-300)
           t_0
           (if (<= x 4e-278) 2.0 (if (<= x 3400000000000.0) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -2.1e+27) {
		tmp = t_1;
	} else if (x <= -1.75e-43) {
		tmp = t_0;
	} else if (x <= -1.1e-244) {
		tmp = 2.0;
	} else if (x <= 1.95e-300) {
		tmp = t_0;
	} else if (x <= 4e-278) {
		tmp = 2.0;
	} else if (x <= 3400000000000.0) {
		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 = 1.0d0 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (x <= (-2.1d+27)) then
        tmp = t_1
    else if (x <= (-1.75d-43)) then
        tmp = t_0
    else if (x <= (-1.1d-244)) then
        tmp = 2.0d0
    else if (x <= 1.95d-300) then
        tmp = t_0
    else if (x <= 4d-278) then
        tmp = 2.0d0
    else if (x <= 3400000000000.0d0) 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 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -2.1e+27) {
		tmp = t_1;
	} else if (x <= -1.75e-43) {
		tmp = t_0;
	} else if (x <= -1.1e-244) {
		tmp = 2.0;
	} else if (x <= 1.95e-300) {
		tmp = t_0;
	} else if (x <= 4e-278) {
		tmp = 2.0;
	} else if (x <= 3400000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z * -4.0) / y)
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if x <= -2.1e+27:
		tmp = t_1
	elif x <= -1.75e-43:
		tmp = t_0
	elif x <= -1.1e-244:
		tmp = 2.0
	elif x <= 1.95e-300:
		tmp = t_0
	elif x <= 4e-278:
		tmp = 2.0
	elif x <= 3400000000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -2.1e+27)
		tmp = t_1;
	elseif (x <= -1.75e-43)
		tmp = t_0;
	elseif (x <= -1.1e-244)
		tmp = 2.0;
	elseif (x <= 1.95e-300)
		tmp = t_0;
	elseif (x <= 4e-278)
		tmp = 2.0;
	elseif (x <= 3400000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z * -4.0) / y);
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (x <= -2.1e+27)
		tmp = t_1;
	elseif (x <= -1.75e-43)
		tmp = t_0;
	elseif (x <= -1.1e-244)
		tmp = 2.0;
	elseif (x <= 1.95e-300)
		tmp = t_0;
	elseif (x <= 4e-278)
		tmp = 2.0;
	elseif (x <= 3400000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+27], t$95$1, If[LessEqual[x, -1.75e-43], t$95$0, If[LessEqual[x, -1.1e-244], 2.0, If[LessEqual[x, 1.95e-300], t$95$0, If[LessEqual[x, 4e-278], 2.0, If[LessEqual[x, 3400000000000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.09999999999999995e27 or 3.4e12 < x

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in x around inf 71.4%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

   if -2.09999999999999995e27 < x < -1.74999999999999999e-43 or -1.09999999999999992e-244 < x < 1.9500000000000001e-300 or 3.99999999999999975e-278 < x < 3.4e12

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in z around inf 64.1%

      \[\leadsto 1 + \color{blue}{-4 \cdot \frac{z}{y}} \]
   3. Step-by-step derivation

      1. associate-*r/ 64.1%

         \[\leadsto 1 + \color{blue}{\frac{-4 \cdot z}{y}} \]

   4. Simplified 64.1%

      \[\leadsto 1 + \color{blue}{\frac{-4 \cdot z}{y}} \]

   if -1.74999999999999999e-43 < x < -1.09999999999999992e-244 or 1.9500000000000001e-300 < x < 3.99999999999999975e-278

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf 64.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-43}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-244}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-300}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-278}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3400000000000:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 54.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := \frac{z}{\frac{y}{-4}}\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-239}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-147}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))) (t_1 (/ z (/ y -4.0))))
   (if (<= x -1.45e+29)
     t_0
     (if (<= x -2.15e-43)
       t_1
       (if (<= x -3e-239)
         2.0
         (if (<= x 1.4e-303)
           t_1
           (if (<= x 3e-147) 2.0 (if (<= x 1.05e+69) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = z / (y / -4.0);
	double tmp;
	if (x <= -1.45e+29) {
		tmp = t_0;
	} else if (x <= -2.15e-43) {
		tmp = t_1;
	} else if (x <= -3e-239) {
		tmp = 2.0;
	} else if (x <= 1.4e-303) {
		tmp = t_1;
	} else if (x <= 3e-147) {
		tmp = 2.0;
	} else if (x <= 1.05e+69) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / y)
    t_1 = z / (y / (-4.0d0))
    if (x <= (-1.45d+29)) then
        tmp = t_0
    else if (x <= (-2.15d-43)) then
        tmp = t_1
    else if (x <= (-3d-239)) then
        tmp = 2.0d0
    else if (x <= 1.4d-303) then
        tmp = t_1
    else if (x <= 3d-147) then
        tmp = 2.0d0
    else if (x <= 1.05d+69) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = z / (y / -4.0);
	double tmp;
	if (x <= -1.45e+29) {
		tmp = t_0;
	} else if (x <= -2.15e-43) {
		tmp = t_1;
	} else if (x <= -3e-239) {
		tmp = 2.0;
	} else if (x <= 1.4e-303) {
		tmp = t_1;
	} else if (x <= 3e-147) {
		tmp = 2.0;
	} else if (x <= 1.05e+69) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	t_1 = z / (y / -4.0)
	tmp = 0
	if x <= -1.45e+29:
		tmp = t_0
	elif x <= -2.15e-43:
		tmp = t_1
	elif x <= -3e-239:
		tmp = 2.0
	elif x <= 1.4e-303:
		tmp = t_1
	elif x <= 3e-147:
		tmp = 2.0
	elif x <= 1.05e+69:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	t_1 = Float64(z / Float64(y / -4.0))
	tmp = 0.0
	if (x <= -1.45e+29)
		tmp = t_0;
	elseif (x <= -2.15e-43)
		tmp = t_1;
	elseif (x <= -3e-239)
		tmp = 2.0;
	elseif (x <= 1.4e-303)
		tmp = t_1;
	elseif (x <= 3e-147)
		tmp = 2.0;
	elseif (x <= 1.05e+69)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / y);
	t_1 = z / (y / -4.0);
	tmp = 0.0;
	if (x <= -1.45e+29)
		tmp = t_0;
	elseif (x <= -2.15e-43)
		tmp = t_1;
	elseif (x <= -3e-239)
		tmp = 2.0;
	elseif (x <= 1.4e-303)
		tmp = t_1;
	elseif (x <= 3e-147)
		tmp = 2.0;
	elseif (x <= 1.05e+69)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z / N[(y / -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+29], t$95$0, If[LessEqual[x, -2.15e-43], t$95$1, If[LessEqual[x, -3e-239], 2.0, If[LessEqual[x, 1.4e-303], t$95$1, If[LessEqual[x, 3e-147], 2.0, If[LessEqual[x, 1.05e+69], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e29 or 1.05000000000000008e69 < x

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in x around inf 73.5%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

   3. Taylor expanded in x around inf 70.6%

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

   if -1.45e29 < x < -2.14999999999999982e-43 or -2.9999999999999998e-239 < x < 1.4e-303 or 3.0000000000000002e-147 < x < 1.05000000000000008e69

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in z around inf 64.6%

      \[\leadsto 1 + \color{blue}{-4 \cdot \frac{z}{y}} \]
   3. Step-by-step derivation

      1. associate-*r/ 64.6%

         \[\leadsto 1 + \color{blue}{\frac{-4 \cdot z}{y}} \]

   4. Simplified 64.6%

      \[\leadsto 1 + \color{blue}{\frac{-4 \cdot z}{y}} \]

   5. Taylor expanded in z around inf 59.7%

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

      1. associate-*r/ 59.7%

         \[\leadsto \color{blue}{\frac{-4 \cdot z}{y}} \]

      2. *-commutative 59.7%

         \[\leadsto \frac{\color{blue}{z \cdot -4}}{y} \]

      3. associate-/l* 59.7%

         \[\leadsto \color{blue}{\frac{z}{\frac{y}{-4}}} \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{\frac{z}{\frac{y}{-4}}} \]

   if -2.14999999999999982e-43 < x < -2.9999999999999998e-239 or 1.4e-303 < x < 3.0000000000000002e-147

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf 60.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+29}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-239}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-303}:\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-147}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 53.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.75 \cdot 10^{+31} \lor \neg \left(x \leq 58000000000000\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.75e+31) (not (<= x 58000000000000.0))) (* 4.0 (/ x y)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.75e+31) || !(x <= 58000000000000.0)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	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 <= (-3.75d+31)) .or. (.not. (x <= 58000000000000.0d0))) then
        tmp = 4.0d0 * (x / y)
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.75e+31) || !(x <= 58000000000000.0)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.75e+31) or not (x <= 58000000000000.0):
		tmp = 4.0 * (x / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.75e+31) || !(x <= 58000000000000.0))
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.75e+31) || ~((x <= 58000000000000.0)))
		tmp = 4.0 * (x / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.75e+31], N[Not[LessEqual[x, 58000000000000.0]], $MachinePrecision]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.75e31 or 5.8e13 < x

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in x around inf 71.4%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

   3. Taylor expanded in x around inf 68.4%

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

   if -3.75e31 < x < 5.8e13

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

   2. Taylor expanded in y around inf 48.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.75 \cdot 10^{+31} \lor \neg \left(x \leq 58000000000000\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 6: 99.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 2 + \left(x - z\right) \cdot \frac{4}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 2.0 (* (- x z) (/ 4.0 y))))

C

double code(double x, double y, double z) {
	return 2.0 + ((x - z) * (4.0 / y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 + ((x - z) * (4.0d0 / y))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 + ((x - z) * (4.0 / y));
}

Python

def code(x, y, z):
	return 2.0 + ((x - z) * (4.0 / y))

Julia

function code(x, y, z)
	return Float64(2.0 + Float64(Float64(x - z) * Float64(4.0 / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 + ((x - z) * (4.0 / y));
end

Wolfram

code[x_, y_, z_] := N[(2.0 + N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

   2. +-commutative 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) \]

   3. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} \]

   4. distribute-lft-in 99.8%

      \[\leadsto 1 + \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + \frac{4}{y} \cdot \left(x - z\right)\right)} \]

   5. associate-+r+ 99.8%

      \[\leadsto \color{blue}{\left(1 + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right) + \frac{4}{y} \cdot \left(x - z\right)} \]

   6. associate-*l/ 99.8%

      \[\leadsto \left(1 + \color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   7. *-commutative 99.8%

      \[\leadsto \left(1 + \frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   8. associate-/l* 99.8%

      \[\leadsto \left(1 + \color{blue}{\frac{y \cdot 0.25}{\frac{y}{4}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   9. metadata-eval 99.8%

      \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\color{blue}{\frac{-1}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   10. metadata-eval 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{y}{\frac{-1}{\color{blue}{-0.25}}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   11. associate-/l* 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\color{blue}{\frac{y \cdot \left(-0.25\right)}{-1}}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   12. distribute-rgt-neg-in 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{-y \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   13. distribute-lft-neg-out 99.8%

       \[\leadsto \left(1 + \frac{y \cdot 0.25}{\frac{\color{blue}{\left(-y\right) \cdot 0.25}}{-1}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   14. associate-/l* 99.8%

       \[\leadsto \left(1 + \color{blue}{\frac{\left(y \cdot 0.25\right) \cdot -1}{\left(-y\right) \cdot 0.25}}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   15. *-commutative 99.8%

       \[\leadsto \left(1 + \frac{\color{blue}{-1 \cdot \left(y \cdot 0.25\right)}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   16. neg-mul-1 99.8%

       \[\leadsto \left(1 + \frac{\color{blue}{-y \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   17. distribute-lft-neg-out 99.8%

       \[\leadsto \left(1 + \frac{\color{blue}{\left(-y\right) \cdot 0.25}}{\left(-y\right) \cdot 0.25}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   18. *-inverses 99.8%

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

   19. metadata-eval 99.8%

       \[\leadsto \color{blue}{2} + \frac{4}{y} \cdot \left(x - z\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{2 + \frac{4}{y} \cdot \left(x - z\right)} \]

4. Final simplification 99.8%

   \[\leadsto 2 + \left(x - z\right) \cdot \frac{4}{y} \]

Alternative 7: 8.1% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

2. Taylor expanded in x around inf 42.4%

   \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

3. Taylor expanded in x around 0 8.2%

   \[\leadsto \color{blue}{1} \]

4. Final simplification 8.2%

   \[\leadsto 1 \]

Alternative 8: 33.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

double code(double x, double y, double z) {
	return 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

2. Taylor expanded in y around inf 34.9%

   \[\leadsto \color{blue}{2} \]

3. Final simplification 34.9%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))