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

Percentage Accurate: 99.8% → 99.8%

Time: 4.4s

Alternatives: 8

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

2. Final simplification 100.0%

   \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

Alternative 2: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+35} \lor \neg \left(x - y \leq -100000000000 \lor \neg \left(x - y \leq -1 \cdot 10^{-117}\right) \land x - y \leq 2 \cdot 10^{-124}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- x y) -1e+35)
         (not
          (or (<= (- x y) -100000000000.0)
              (and (not (<= (- x y) -1e-117)) (<= (- x y) 2e-124)))))
   (* (- x y) (/ 4.0 z))
   -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x - y) <= -1e+35) || !(((x - y) <= -100000000000.0) || (!((x - y) <= -1e-117) && ((x - y) <= 2e-124)))) {
		tmp = (x - y) * (4.0 / z);
	} 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 - y) <= (-1d+35)) .or. (.not. ((x - y) <= (-100000000000.0d0)) .or. (.not. ((x - y) <= (-1d-117))) .and. ((x - y) <= 2d-124))) then
        tmp = (x - y) * (4.0d0 / z)
    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 - y) <= -1e+35) || !(((x - y) <= -100000000000.0) || (!((x - y) <= -1e-117) && ((x - y) <= 2e-124)))) {
		tmp = (x - y) * (4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x - y) <= -1e+35) or not (((x - y) <= -100000000000.0) or (not ((x - y) <= -1e-117) and ((x - y) <= 2e-124))):
		tmp = (x - y) * (4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x - y) <= -1e+35) || !((Float64(x - y) <= -100000000000.0) || (!(Float64(x - y) <= -1e-117) && (Float64(x - y) <= 2e-124))))
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x - y) <= -1e+35) || ~((((x - y) <= -100000000000.0) || (~(((x - y) <= -1e-117)) && ((x - y) <= 2e-124)))))
		tmp = (x - y) * (4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x - y), $MachinePrecision], -1e+35], N[Not[Or[LessEqual[N[(x - y), $MachinePrecision], -100000000000.0], And[N[Not[LessEqual[N[(x - y), $MachinePrecision], -1e-117]], $MachinePrecision], LessEqual[N[(x - y), $MachinePrecision], 2e-124]]]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x y) < -9.9999999999999997e34 or -1e11 < (-.f64 x y) < -1.00000000000000003e-117 or 1.99999999999999987e-124 < (-.f64 x y)

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around 0 79.5%

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

   if -9.9999999999999997e34 < (-.f64 x y) < -1e11 or -1.00000000000000003e-117 < (-.f64 x y) < 1.99999999999999987e-124

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around inf 90.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+35} \lor \neg \left(x - y \leq -100000000000 \lor \neg \left(x - y \leq -1 \cdot 10^{-117}\right) \land x - y \leq 2 \cdot 10^{-124}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 3: 53.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{y}{z}\\ t_1 := 4 \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+121}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-180}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -4.0 (/ y z))) (t_1 (* 4.0 (/ x z))))
   (if (<= y -1.9e+121)
     t_0
     (if (<= y -1.4e-271)
       t_1
       (if (<= y 3.2e-180) -2.0 (if (<= y 4.2e+70) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * (y / z);
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (y <= -1.9e+121) {
		tmp = t_0;
	} else if (y <= -1.4e-271) {
		tmp = t_1;
	} else if (y <= 3.2e-180) {
		tmp = -2.0;
	} else if (y <= 4.2e+70) {
		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) * (y / z)
    t_1 = 4.0d0 * (x / z)
    if (y <= (-1.9d+121)) then
        tmp = t_0
    else if (y <= (-1.4d-271)) then
        tmp = t_1
    else if (y <= 3.2d-180) then
        tmp = -2.0d0
    else if (y <= 4.2d+70) 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 * (y / z);
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (y <= -1.9e+121) {
		tmp = t_0;
	} else if (y <= -1.4e-271) {
		tmp = t_1;
	} else if (y <= 3.2e-180) {
		tmp = -2.0;
	} else if (y <= 4.2e+70) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * (y / z)
	t_1 = 4.0 * (x / z)
	tmp = 0
	if y <= -1.9e+121:
		tmp = t_0
	elif y <= -1.4e-271:
		tmp = t_1
	elif y <= 3.2e-180:
		tmp = -2.0
	elif y <= 4.2e+70:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(y / z))
	t_1 = Float64(4.0 * Float64(x / z))
	tmp = 0.0
	if (y <= -1.9e+121)
		tmp = t_0;
	elseif (y <= -1.4e-271)
		tmp = t_1;
	elseif (y <= 3.2e-180)
		tmp = -2.0;
	elseif (y <= 4.2e+70)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * (y / z);
	t_1 = 4.0 * (x / z);
	tmp = 0.0;
	if (y <= -1.9e+121)
		tmp = t_0;
	elseif (y <= -1.4e-271)
		tmp = t_1;
	elseif (y <= 3.2e-180)
		tmp = -2.0;
	elseif (y <= 4.2e+70)
		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[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+121], t$95$0, If[LessEqual[y, -1.4e-271], t$95$1, If[LessEqual[y, 3.2e-180], -2.0, If[LessEqual[y, 4.2e+70], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e121 or 4.20000000000000015e70 < y

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in y around inf 74.9%

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

   if -1.9e121 < y < -1.3999999999999999e-271 or 3.20000000000000015e-180 < y < 4.20000000000000015e70

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in x around inf 57.8%

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

   if -1.3999999999999999e-271 < y < 3.20000000000000015e-180

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around inf 69.0%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+121}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-271}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-180}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 4: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-54} \lor \neg \left(z \leq 2.05 \cdot 10^{+14}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-54) (not (<= z 2.05e+14)))
   (- (* -4.0 (/ y z)) 2.0)
   (* (- x y) (/ 4.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-54) || !(z <= 2.05e+14)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (x - y) * (4.0 / 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 ((z <= (-4.5d-54)) .or. (.not. (z <= 2.05d+14))) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    else
        tmp = (x - y) * (4.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-54) || !(z <= 2.05e+14)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (x - y) * (4.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-54) or not (z <= 2.05e+14):
		tmp = (-4.0 * (y / z)) - 2.0
	else:
		tmp = (x - y) * (4.0 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-54) || !(z <= 2.05e+14))
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	else
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e-54) || ~((z <= 2.05e+14)))
		tmp = (-4.0 * (y / z)) - 2.0;
	else
		tmp = (x - y) * (4.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-54], N[Not[LessEqual[z, 2.05e+14]], $MachinePrecision]], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e-54 or 2.05e14 < z

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x - y\right) - z \cdot 0.5\right) \cdot 4}}{z} \]

      2. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) - z \cdot 0.5}{\frac{z}{4}}} \]

      3. div-sub 100.0%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}}} \]

      4. *-lft-identity 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{1 \cdot z}}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{\left(--1\right)} \cdot z}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      6. associate-/l* 99.9%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{--1}{\frac{4}{z}}}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      7. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{--1} \cdot \frac{4}{z}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      8. fma-neg 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{--1}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right)} \]

      9. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{\color{blue}{1}}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right) \]

      10. /-rgt-identity 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - y}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right) \]

      11. associate-/r/ 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{4}{z}, -\color{blue}{\frac{z \cdot 0.5}{z} \cdot 4}\right) \]

      12. distribute-rgt-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{4}{z}, \color{blue}{\frac{z \cdot 0.5}{z} \cdot \left(-4\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{4}{z}, -2\right)} \]

   4. Taylor expanded in x around 0 81.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{y}{z} - 2} \]

   if -4.4999999999999998e-54 < z < 2.05e14

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around 0 92.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-54} \lor \neg \left(z \leq 2.05 \cdot 10^{+14}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \]

Alternative 5: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+116} \lor \neg \left(y \leq 1.5 \cdot 10^{+62}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+116) (not (<= y 1.5e+62)))
   (- (* -4.0 (/ y z)) 2.0)
   (- (* 4.0 (/ x z)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+116) || !(y <= 1.5e+62)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (4.0 * (x / z)) - 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 ((y <= (-1.4d+116)) .or. (.not. (y <= 1.5d+62))) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    else
        tmp = (4.0d0 * (x / z)) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+116) || !(y <= 1.5e+62)) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else {
		tmp = (4.0 * (x / z)) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e+116) or not (y <= 1.5e+62):
		tmp = (-4.0 * (y / z)) - 2.0
	else:
		tmp = (4.0 * (x / z)) - 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+116) || !(y <= 1.5e+62))
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	else
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e+116) || ~((y <= 1.5e+62)))
		tmp = (-4.0 * (y / z)) - 2.0;
	else
		tmp = (4.0 * (x / z)) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+116], N[Not[LessEqual[y, 1.5e+62]], $MachinePrecision]], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000002e116 or 1.5e62 < y

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x - y\right) - z \cdot 0.5\right) \cdot 4}}{z} \]

      2. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) - z \cdot 0.5}{\frac{z}{4}}} \]

      3. div-sub 100.0%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}}} \]

      4. *-lft-identity 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{1 \cdot z}}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{\left(--1\right)} \cdot z}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      6. associate-/l* 99.9%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{--1}{\frac{4}{z}}}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      7. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{x - y}{--1} \cdot \frac{4}{z}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      8. fma-neg 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{--1}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right)} \]

      9. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{\color{blue}{1}}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right) \]

      10. /-rgt-identity 99.7%

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - y}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right) \]

      11. associate-/r/ 99.7%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{4}{z}, -\color{blue}{\frac{z \cdot 0.5}{z} \cdot 4}\right) \]

      12. distribute-rgt-neg-in 99.7%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{4}{z}, \color{blue}{\frac{z \cdot 0.5}{z} \cdot \left(-4\right)}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{4}{z}, -2\right)} \]

   4. Taylor expanded in x around 0 89.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{y}{z} - 2} \]

   if -1.40000000000000002e116 < y < 1.5e62

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x - y\right) - z \cdot 0.5\right) \cdot 4}}{z} \]

      2. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) - z \cdot 0.5}{\frac{z}{4}}} \]

      3. div-sub 100.0%

         \[\leadsto \color{blue}{\frac{x - y}{\frac{z}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}}} \]

      4. *-lft-identity 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{1 \cdot z}}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{\left(--1\right)} \cdot z}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      6. associate-/l* 99.9%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{--1}{\frac{4}{z}}}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      7. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{--1} \cdot \frac{4}{z}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      8. fma-neg 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{--1}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right)} \]

      9. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{\color{blue}{1}}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right) \]

      10. /-rgt-identity 99.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - y}, \frac{4}{z}, -\frac{z \cdot 0.5}{\frac{z}{4}}\right) \]

      11. associate-/r/ 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{4}{z}, -\color{blue}{\frac{z \cdot 0.5}{z} \cdot 4}\right) \]

      12. distribute-rgt-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x - y, \frac{4}{z}, \color{blue}{\frac{z \cdot 0.5}{z} \cdot \left(-4\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, \frac{4}{z}, -2\right)} \]

   4. Taylor expanded in y around 0 88.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+116} \lor \neg \left(y \leq 1.5 \cdot 10^{+62}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \end{array} \]

Alternative 6: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 4.0 z) (+ (- x y) (* z -0.5))))

C

double code(double x, double y, double z) {
	return (4.0 / z) * ((x - y) + (z * -0.5));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 / z) * ((x - y) + (z * (-0.5d0)))
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 / z) * ((x - y) + (z * -0.5));
}

Python

def code(x, y, z):
	return (4.0 / z) * ((x - y) + (z * -0.5))

Julia

function code(x, y, z)
	return Float64(Float64(4.0 / z) * Float64(Float64(x - y) + Float64(z * -0.5)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 / z) * ((x - y) + (z * -0.5));
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 / z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] + N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

   2. sub-neg 99.7%

      \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

   3. distribute-rgt-neg-in 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

   4. metadata-eval 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

4. Final simplification 99.7%

   \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right) \]

Alternative 7: 52.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+48} \lor \neg \left(y \leq 2.05 \cdot 10^{-43}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+48) (not (<= y 2.05e-43))) (* -4.0 (/ y z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+48) || !(y <= 2.05e-43)) {
		tmp = -4.0 * (y / z);
	} 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 ((y <= (-5.5d+48)) .or. (.not. (y <= 2.05d-43))) then
        tmp = (-4.0d0) * (y / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+48) || !(y <= 2.05e-43)) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+48) or not (y <= 2.05e-43):
		tmp = -4.0 * (y / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+48) || !(y <= 2.05e-43))
		tmp = Float64(-4.0 * Float64(y / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.5e+48) || ~((y <= 2.05e-43)))
		tmp = -4.0 * (y / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+48], N[Not[LessEqual[y, 2.05e-43]], $MachinePrecision]], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000002e48 or 2.0499999999999999e-43 < y

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in y around inf 60.2%

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

   if -5.5000000000000002e48 < y < 2.0499999999999999e-43

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around inf 44.2%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+48} \lor \neg \left(y \leq 2.05 \cdot 10^{-43}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 34.7% accurate, 11.0× 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 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

   2. sub-neg 99.7%

      \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

   3. distribute-rgt-neg-in 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

   4. metadata-eval 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

4. Taylor expanded in z around inf 30.1%

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

5. Final simplification 30.1%

   \[\leadsto -2 \]

Developer target: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (4.0 * (x / z)) - (2.0 + (4.0 * (y / 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 = (4.0d0 * (x / z)) - (2.0d0 + (4.0d0 * (y / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))