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

Percentage Accurate: 99.9% → 100.0%

Time: 4.8s

Alternatives: 7

Speedup: 1.4×

• 20.8% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. associate--l+ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around 0 100.0%

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

   1. +-commutative 100.0%

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

6. Simplified 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -11000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-222}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+68}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -4.0 (/ z y)))))
   (if (<= z -2.9e+140)
     t_0
     (if (<= z -8.5e+56)
       2.0
       (if (<= z -11000000000000.0)
         t_0
         (if (<= z 1.25e-222)
           (+ 1.0 (/ (* 4.0 x) y))
           (if (<= z 5e+68) 2.0 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -2.9e+140) {
		tmp = t_0;
	} else if (z <= -8.5e+56) {
		tmp = 2.0;
	} else if (z <= -11000000000000.0) {
		tmp = t_0;
	} else if (z <= 1.25e-222) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else if (z <= 5e+68) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-2.9d+140)) then
        tmp = t_0
    else if (z <= (-8.5d+56)) then
        tmp = 2.0d0
    else if (z <= (-11000000000000.0d0)) then
        tmp = t_0
    else if (z <= 1.25d-222) then
        tmp = 1.0d0 + ((4.0d0 * x) / y)
    else if (z <= 5d+68) then
        tmp = 2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -2.9e+140) {
		tmp = t_0;
	} else if (z <= -8.5e+56) {
		tmp = 2.0;
	} else if (z <= -11000000000000.0) {
		tmp = t_0;
	} else if (z <= 1.25e-222) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else if (z <= 5e+68) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -2.9e+140:
		tmp = t_0
	elif z <= -8.5e+56:
		tmp = 2.0
	elif z <= -11000000000000.0:
		tmp = t_0
	elif z <= 1.25e-222:
		tmp = 1.0 + ((4.0 * x) / y)
	elif z <= 5e+68:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -2.9e+140)
		tmp = t_0;
	elseif (z <= -8.5e+56)
		tmp = 2.0;
	elseif (z <= -11000000000000.0)
		tmp = t_0;
	elseif (z <= 1.25e-222)
		tmp = Float64(1.0 + Float64(Float64(4.0 * x) / y));
	elseif (z <= 5e+68)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -2.9e+140)
		tmp = t_0;
	elseif (z <= -8.5e+56)
		tmp = 2.0;
	elseif (z <= -11000000000000.0)
		tmp = t_0;
	elseif (z <= 1.25e-222)
		tmp = 1.0 + ((4.0 * x) / y);
	elseif (z <= 5e+68)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+140], t$95$0, If[LessEqual[z, -8.5e+56], 2.0, If[LessEqual[z, -11000000000000.0], t$95$0, If[LessEqual[z, 1.25e-222], N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+68], 2.0, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999999e140 or -8.4999999999999998e56 < z < -1.1e13 or 5.0000000000000004e68 < z

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 72.7%

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

      1. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   if -2.8999999999999999e140 < z < -8.4999999999999998e56 or 1.25000000000000002e-222 < z < 5.0000000000000004e68

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 58.8%

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

   if -1.1e13 < z < 1.25000000000000002e-222

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 61.6%

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

      1. associate-*r/ 61.6%

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

      2. *-commutative 61.6%

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

   6. Simplified 61.6%

      \[\leadsto 1 + \color{blue}{\frac{x \cdot 4}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+140}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -11000000000000:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-222}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+68}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 3: 53.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+140} \lor \neg \left(z \leq -9.5 \cdot 10^{+56}\right) \land \left(z \leq -3.8 \cdot 10^{+30} \lor \neg \left(z \leq 1.36 \cdot 10^{+69}\right)\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+140)
         (and (not (<= z -9.5e+56))
              (or (<= z -3.8e+30) (not (<= z 1.36e+69)))))
   (+ 1.0 (* -4.0 (/ z y)))
   2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+140) || (!(z <= -9.5e+56) && ((z <= -3.8e+30) || !(z <= 1.36e+69)))) {
		tmp = 1.0 + (-4.0 * (z / 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 ((z <= (-2.5d+140)) .or. (.not. (z <= (-9.5d+56))) .and. (z <= (-3.8d+30)) .or. (.not. (z <= 1.36d+69))) then
        tmp = 1.0d0 + ((-4.0d0) * (z / 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 ((z <= -2.5e+140) || (!(z <= -9.5e+56) && ((z <= -3.8e+30) || !(z <= 1.36e+69)))) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+140) or (not (z <= -9.5e+56) and ((z <= -3.8e+30) or not (z <= 1.36e+69))):
		tmp = 1.0 + (-4.0 * (z / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+140) || (!(z <= -9.5e+56) && ((z <= -3.8e+30) || !(z <= 1.36e+69))))
		tmp = Float64(1.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e+140) || (~((z <= -9.5e+56)) && ((z <= -3.8e+30) || ~((z <= 1.36e+69)))))
		tmp = 1.0 + (-4.0 * (z / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+140], And[N[Not[LessEqual[z, -9.5e+56]], $MachinePrecision], Or[LessEqual[z, -3.8e+30], N[Not[LessEqual[z, 1.36e+69]], $MachinePrecision]]]], N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000004e140 or -9.4999999999999997e56 < z < -3.8000000000000001e30 or 1.36000000000000006e69 < z

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 74.4%

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

      1. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   if -2.50000000000000004e140 < z < -9.4999999999999997e56 or -3.8000000000000001e30 < z < 1.36000000000000006e69

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 51.3%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+140} \lor \neg \left(z \leq -9.5 \cdot 10^{+56}\right) \land \left(z \leq -3.8 \cdot 10^{+30} \lor \neg \left(z \leq 1.36 \cdot 10^{+69}\right)\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 4: 81.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+145} \lor \neg \left(z \leq 2.9 \cdot 10^{+74}\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e+145) (not (<= z 2.9e+74)))
   (+ 1.0 (* -4.0 (/ z y)))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+145) || !(z <= 2.9e+74)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.2d+145)) .or. (.not. (z <= 2.9d+74))) then
        tmp = 1.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 2.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+145) || !(z <= 2.9e+74)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e+145) or not (z <= 2.9e+74):
		tmp = 1.0 + (-4.0 * (z / y))
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e+145) || !(z <= 2.9e+74))
		tmp = Float64(1.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.2e+145) || ~((z <= 2.9e+74)))
		tmp = 1.0 + (-4.0 * (z / y));
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e+145], N[Not[LessEqual[z, 2.9e+74]], $MachinePrecision]], N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000009e145 or 2.9000000000000002e74 < z

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 75.1%

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

      1. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   if -2.20000000000000009e145 < z < 2.9000000000000002e74

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 87.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+145} \lor \neg \left(z \leq 2.9 \cdot 10^{+74}\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 85.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+111} \lor \neg \left(x \leq 6.4 \cdot 10^{+50}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e+111) (not (<= x 6.4e+50)))
   (+ 2.0 (* 4.0 (/ x y)))
   (+ 2.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+111) || !(x <= 6.4e+50)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8d+111)) .or. (.not. (x <= 6.4d+50))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+111) || !(x <= 6.4e+50)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e+111) or not (x <= 6.4e+50):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e+111) || !(x <= 6.4e+50))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8e+111) || ~((x <= 6.4e+50)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 2.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e+111], N[Not[LessEqual[x, 6.4e+50]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999965e111 or 6.39999999999999966e50 < x

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 86.7%

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

   if -7.99999999999999965e111 < x < 6.39999999999999966e50

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 91.1%

      \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} + 2 \]
   8. Step-by-step derivation

      1. neg-mul-1 91.1%

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

      2. distribute-neg-frac 91.1%

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

   9. Simplified 91.1%

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

       1. associate-*r/ 90.5%

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

       2. neg-mul-1 90.5%

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

       3. associate-*r* 90.5%

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

       4. metadata-eval 90.5%

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

   11. Applied egg-rr 90.5%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+111} \lor \neg \left(x \leq 6.4 \cdot 10^{+50}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \end{array} \]

Alternative 6: 85.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+111} \lor \neg \left(x \leq 8.4 \cdot 10^{+51}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 - 4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+111) (not (<= x 8.4e+51)))
   (+ 2.0 (* 4.0 (/ x y)))
   (- 2.0 (* 4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+111) || !(x <= 8.4e+51)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 - (4.0 * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7d+111)) .or. (.not. (x <= 8.4d+51))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 - (4.0d0 * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+111) || !(x <= 8.4e+51)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 - (4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+111) or not (x <= 8.4e+51):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 - (4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+111) || !(x <= 8.4e+51))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 - Float64(4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e+111) || ~((x <= 8.4e+51)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 2.0 - (4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+111], N[Not[LessEqual[x, 8.4e+51]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 - N[(4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000004e111 or 8.4000000000000005e51 < x

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 86.7%

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

   if -7.0000000000000004e111 < x < 8.4000000000000005e51

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 91.1%

      \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} + 2 \]
   8. Step-by-step derivation

      1. neg-mul-1 91.1%

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

      2. distribute-neg-frac 91.1%

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

   9. Simplified 91.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+111} \lor \neg \left(x \leq 8.4 \cdot 10^{+51}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 - 4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 7: 33.7% 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. Step-by-step derivation

   1. associate-/l* 99.8%

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

   2. associate--l+ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around inf 36.2%

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

5. Final simplification 36.2%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023230 
(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)))