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

Percentage Accurate: 99.8% → 100.0%

Time: 6.7s

Alternatives: 7

Speedup: 1.2×

• 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: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{x - y}{z} - 2 \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - 2.0), $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. cancel-sign-sub-inv 99.7%

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

   3. associate-+l- 99.7%

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

   4. distribute-lft-neg-out 99.7%

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

   5. distribute-rgt-neg-in 99.7%

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

   6. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around 0 100.0%

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

6. Final simplification 100.0%

   \[\leadsto 4 \cdot \frac{x - y}{z} - 2 \]
7. Add Preprocessing

Alternative 2: 53.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+78}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+49}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{-4 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e+78)
   -2.0
   (if (<= z 4.1e+49)
     (* 4.0 (/ x z))
     (if (<= z 9.5e+125) (/ (* -4.0 y) z) -2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+78) {
		tmp = -2.0;
	} else if (z <= 4.1e+49) {
		tmp = 4.0 * (x / z);
	} else if (z <= 9.5e+125) {
		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 (z <= (-4d+78)) then
        tmp = -2.0d0
    else if (z <= 4.1d+49) then
        tmp = 4.0d0 * (x / z)
    else if (z <= 9.5d+125) 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 (z <= -4e+78) {
		tmp = -2.0;
	} else if (z <= 4.1e+49) {
		tmp = 4.0 * (x / z);
	} else if (z <= 9.5e+125) {
		tmp = (-4.0 * y) / z;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+78:
		tmp = -2.0
	elif z <= 4.1e+49:
		tmp = 4.0 * (x / z)
	elif z <= 9.5e+125:
		tmp = (-4.0 * y) / z
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+78)
		tmp = -2.0;
	elseif (z <= 4.1e+49)
		tmp = Float64(4.0 * Float64(x / z));
	elseif (z <= 9.5e+125)
		tmp = Float64(Float64(-4.0 * y) / z);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4e+78)
		tmp = -2.0;
	elseif (z <= 4.1e+49)
		tmp = 4.0 * (x / z);
	elseif (z <= 9.5e+125)
		tmp = (-4.0 * y) / z;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+78], -2.0, If[LessEqual[z, 4.1e+49], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+125], N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision], -2.0]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000003e78 or 9.50000000000000041e125 < 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. associate-*l/ 99.7%

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

      2. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 68.6%

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

   if -4.00000000000000003e78 < z < 4.1e49

   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. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 57.1%

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

   if 4.1e49 < z < 9.50000000000000041e125

   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/ 99.4%

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

      2. cancel-sign-sub-inv 99.4%

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

      3. associate-+l- 99.4%

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

      4. distribute-lft-neg-out 99.4%

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

      5. distribute-rgt-neg-in 99.4%

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

      6. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-*l/ 59.7%

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

   7. Simplified 59.7%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+78}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+49}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{-4 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+69} \lor \neg \left(z \leq 1.1 \cdot 10^{+127}\right):\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e+69) (not (<= z 1.1e+127)))
   (- (* 4.0 (/ x z)) 2.0)
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e+69) || !(z <= 1.1e+127)) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else {
		tmp = 4.0 * ((x - y) / 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 <= (-8.5d+69)) .or. (.not. (z <= 1.1d+127))) then
        tmp = (4.0d0 * (x / z)) - 2.0d0
    else
        tmp = 4.0d0 * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e+69) || !(z <= 1.1e+127)) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e+69) or not (z <= 1.1e+127):
		tmp = (4.0 * (x / z)) - 2.0
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e+69) || !(z <= 1.1e+127))
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e+69) || ~((z <= 1.1e+127)))
		tmp = (4.0 * (x / z)) - 2.0;
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e+69], N[Not[LessEqual[z, 1.1e+127]], $MachinePrecision]], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000002e69 or 1.1000000000000001e127 < 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. associate-*l/ 99.7%

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

      2. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in x around inf 83.9%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{z}} - 2 \]
   7. Step-by-step derivation

      1. *-commutative 83.9%

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

   8. Simplified 83.9%

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

   if -8.5000000000000002e69 < z < 1.1000000000000001e127

   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. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 90.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+69} \lor \neg \left(z \leq 1.1 \cdot 10^{+127}\right):\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+158}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+151}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.35e+158) -2.0 (if (<= z 3.1e+151) (* 4.0 (/ (- x y) z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.35e+158) {
		tmp = -2.0;
	} else if (z <= 3.1e+151) {
		tmp = 4.0 * ((x - 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 (z <= (-3.35d+158)) then
        tmp = -2.0d0
    else if (z <= 3.1d+151) then
        tmp = 4.0d0 * ((x - 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 (z <= -3.35e+158) {
		tmp = -2.0;
	} else if (z <= 3.1e+151) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.35e+158:
		tmp = -2.0
	elif z <= 3.1e+151:
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.35e+158)
		tmp = -2.0;
	elseif (z <= 3.1e+151)
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.35e+158)
		tmp = -2.0;
	elseif (z <= 3.1e+151)
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.35e+158], -2.0, If[LessEqual[z, 3.1e+151], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3499999999999998e158 or 3.1000000000000002e151 < 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. associate-*l/ 99.7%

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

      2. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 82.9%

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

   if -3.3499999999999998e158 < z < 3.1000000000000002e151

   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. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 84.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+158}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+151}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+54}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{-4 \cdot y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.25e+54)
   (- (* 4.0 (/ x z)) 2.0)
   (if (<= x 2.05e-22) (- (/ (* -4.0 y) z) 2.0) (* 4.0 (/ (- x y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e+54) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else if (x <= 2.05e-22) {
		tmp = ((-4.0 * y) / z) - 2.0;
	} else {
		tmp = 4.0 * ((x - y) / 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 <= (-2.25d+54)) then
        tmp = (4.0d0 * (x / z)) - 2.0d0
    else if (x <= 2.05d-22) then
        tmp = (((-4.0d0) * y) / z) - 2.0d0
    else
        tmp = 4.0d0 * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e+54) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else if (x <= 2.05e-22) {
		tmp = ((-4.0 * y) / z) - 2.0;
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.25e+54:
		tmp = (4.0 * (x / z)) - 2.0
	elif x <= 2.05e-22:
		tmp = ((-4.0 * y) / z) - 2.0
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.25e+54)
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	elseif (x <= 2.05e-22)
		tmp = Float64(Float64(Float64(-4.0 * y) / z) - 2.0);
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.25e+54)
		tmp = (4.0 * (x / z)) - 2.0;
	elseif (x <= 2.05e-22)
		tmp = ((-4.0 * y) / z) - 2.0;
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.25e+54], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[x, 2.05e-22], N[(N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision] - 2.0), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.24999999999999992e54

   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. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in x around inf 89.6%

      \[\leadsto \color{blue}{4 \cdot \frac{x}{z}} - 2 \]
   7. Step-by-step derivation

      1. *-commutative 89.6%

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

   8. Simplified 89.6%

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

   if -2.24999999999999992e54 < x < 2.05e-22

   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. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in x around 0 92.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{y}{z}} - 2 \]
   7. Step-by-step derivation

      1. associate-*r/ 92.5%

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

   8. Simplified 92.5%

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

   if 2.05e-22 < x

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 88.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+54}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{-4 \cdot y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+78}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+150}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.7e+78) -2.0 (if (<= z 2.9e+150) (* 4.0 (/ x z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.7e+78) {
		tmp = -2.0;
	} else if (z <= 2.9e+150) {
		tmp = 4.0 * (x / 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 (z <= (-1.7d+78)) then
        tmp = -2.0d0
    else if (z <= 2.9d+150) then
        tmp = 4.0d0 * (x / 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 (z <= -1.7e+78) {
		tmp = -2.0;
	} else if (z <= 2.9e+150) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.7e+78:
		tmp = -2.0
	elif z <= 2.9e+150:
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.7e+78)
		tmp = -2.0;
	elseif (z <= 2.9e+150)
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.7e+78)
		tmp = -2.0;
	elseif (z <= 2.9e+150)
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.7e+78], -2.0, If[LessEqual[z, 2.9e+150], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000004e78 or 2.90000000000000011e150 < 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. associate-*l/ 99.7%

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

      2. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 70.1%

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

   if -1.70000000000000004e78 < z < 2.90000000000000011e150

   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. cancel-sign-sub-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 53.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+78}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+150}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 33.9% 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. cancel-sign-sub-inv 99.7%

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

   3. associate-+l- 99.7%

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

   4. distribute-lft-neg-out 99.7%

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

   5. distribute-rgt-neg-in 99.7%

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

   6. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around inf 31.8%

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

6. Final simplification 31.8%

   \[\leadsto -2 \]
7. Add Preprocessing

Developer target: 97.9% 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 2024034 
(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))