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

Percentage Accurate: 99.9% → 100.0%

Time: 6.8s

Alternatives: 6

Speedup: 1.4×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 80.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+200} \lor \neg \left(z \leq -8.2 \cdot 10^{+85}\right) \land \left(z \leq -5.9 \cdot 10^{+57} \lor \neg \left(z \leq 3 \cdot 10^{+159}\right)\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+200)
         (and (not (<= z -8.2e+85)) (or (<= z -5.9e+57) (not (<= z 3e+159)))))
   (+ 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 <= -1.5e+200) || (!(z <= -8.2e+85) && ((z <= -5.9e+57) || !(z <= 3e+159)))) {
		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 <= (-1.5d+200)) .or. (.not. (z <= (-8.2d+85))) .and. (z <= (-5.9d+57)) .or. (.not. (z <= 3d+159))) 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 <= -1.5e+200) || (!(z <= -8.2e+85) && ((z <= -5.9e+57) || !(z <= 3e+159)))) {
		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 <= -1.5e+200) or (not (z <= -8.2e+85) and ((z <= -5.9e+57) or not (z <= 3e+159))):
		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 <= -1.5e+200) || (!(z <= -8.2e+85) && ((z <= -5.9e+57) || !(z <= 3e+159))))
		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 <= -1.5e+200) || (~((z <= -8.2e+85)) && ((z <= -5.9e+57) || ~((z <= 3e+159)))))
		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, -1.5e+200], And[N[Not[LessEqual[z, -8.2e+85]], $MachinePrecision], Or[LessEqual[z, -5.9e+57], N[Not[LessEqual[z, 3e+159]], $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 < -1.49999999999999995e200 or -8.19999999999999957e85 < z < -5.90000000000000013e57 or 3.0000000000000002e159 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 91.1%

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

      1. *-commutative 91.1%

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

   5. Simplified 91.1%

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

   if -1.49999999999999995e200 < z < -8.19999999999999957e85 or -5.90000000000000013e57 < z < 3.0000000000000002e159

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around inf 84.6%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+200} \lor \neg \left(z \leq -8.2 \cdot 10^{+85}\right) \land \left(z \leq -5.9 \cdot 10^{+57} \lor \neg \left(z \leq 3 \cdot 10^{+159}\right)\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y} + 1\\ t_1 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-241}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-181}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 4.0 (/ x y)) 1.0)) (t_1 (+ 1.0 (* -4.0 (/ z y)))))
   (if (<= z -2.9e+35)
     t_1
     (if (<= z -1.16e-241)
       t_0
       (if (<= z 4.2e-181) 2.0 (if (<= z 1.8e+159) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -2.9e+35) {
		tmp = t_1;
	} else if (z <= -1.16e-241) {
		tmp = t_0;
	} else if (z <= 4.2e-181) {
		tmp = 2.0;
	} else if (z <= 1.8e+159) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * (x / y)) + 1.0d0
    t_1 = 1.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-2.9d+35)) then
        tmp = t_1
    else if (z <= (-1.16d-241)) then
        tmp = t_0
    else if (z <= 4.2d-181) then
        tmp = 2.0d0
    else if (z <= 1.8d+159) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -2.9e+35) {
		tmp = t_1;
	} else if (z <= -1.16e-241) {
		tmp = t_0;
	} else if (z <= 4.2e-181) {
		tmp = 2.0;
	} else if (z <= 1.8e+159) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * (x / y)) + 1.0
	t_1 = 1.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -2.9e+35:
		tmp = t_1
	elif z <= -1.16e-241:
		tmp = t_0
	elif z <= 4.2e-181:
		tmp = 2.0
	elif z <= 1.8e+159:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(x / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -2.9e+35)
		tmp = t_1;
	elseif (z <= -1.16e-241)
		tmp = t_0;
	elseif (z <= 4.2e-181)
		tmp = 2.0;
	elseif (z <= 1.8e+159)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * (x / y)) + 1.0;
	t_1 = 1.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -2.9e+35)
		tmp = t_1;
	elseif (z <= -1.16e-241)
		tmp = t_0;
	elseif (z <= 4.2e-181)
		tmp = 2.0;
	elseif (z <= 1.8e+159)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+35], t$95$1, If[LessEqual[z, -1.16e-241], t$95$0, If[LessEqual[z, 4.2e-181], 2.0, If[LessEqual[z, 1.8e+159], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999995e35 or 1.80000000000000018e159 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 77.1%

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

      1. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   if -2.89999999999999995e35 < z < -1.16e-241 or 4.20000000000000006e-181 < z < 1.80000000000000018e159

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.3%

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

   if -1.16e-241 < z < 4.20000000000000006e-181

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 63.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-241}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-181}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+55} \lor \neg \left(z \leq 1.8 \cdot 10^{+159}\right):\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.85e+55) (not (<= z 1.8e+159)))
   (+ 2.0 (/ (* z -4.0) y))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.85e+55) || !(z <= 1.8e+159)) {
		tmp = 2.0 + ((z * -4.0) / 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 <= (-1.85d+55)) .or. (.not. (z <= 1.8d+159))) then
        tmp = 2.0d0 + ((z * (-4.0d0)) / 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 <= -1.85e+55) || !(z <= 1.8e+159)) {
		tmp = 2.0 + ((z * -4.0) / y);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.85e+55) or not (z <= 1.8e+159):
		tmp = 2.0 + ((z * -4.0) / y)
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.85e+55) || !(z <= 1.8e+159))
		tmp = Float64(2.0 + Float64(Float64(z * -4.0) / 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 <= -1.85e+55) || ~((z <= 1.8e+159)))
		tmp = 2.0 + ((z * -4.0) / y);
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.85e+55], N[Not[LessEqual[z, 1.8e+159]], $MachinePrecision]], N[(2.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e55 or 1.80000000000000018e159 < 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. +-commutative 98.9%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.25 + \frac{x - z}{y}, 1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.5%

      \[\leadsto \color{blue}{1 + 4 \cdot \left(0.25 - \frac{z}{y}\right)} \]
   6. Step-by-step derivation

      1. sub-neg 84.5%

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

      2. distribute-lft-in 84.5%

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

      3. metadata-eval 84.5%

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

      4. associate-+r+ 84.5%

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

      5. metadata-eval 84.5%

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

      6. neg-mul-1 84.5%

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

      7. associate-*r* 84.5%

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

      8. metadata-eval 84.5%

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

      9. *-commutative 84.5%

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

      10. associate-*l/ 83.4%

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

   7. Simplified 83.4%

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

   if -1.8500000000000001e55 < z < 1.80000000000000018e159

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around inf 87.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+55} \lor \neg \left(z \leq 1.8 \cdot 10^{+159}\right):\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+92}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+44}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e+92) 2.0 (if (<= y 6e+44) (+ (* 4.0 (/ x y)) 1.0) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+92) {
		tmp = 2.0;
	} else if (y <= 6e+44) {
		tmp = (4.0 * (x / y)) + 1.0;
	} 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 <= (-3d+92)) then
        tmp = 2.0d0
    else if (y <= 6d+44) then
        tmp = (4.0d0 * (x / y)) + 1.0d0
    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 <= -3e+92) {
		tmp = 2.0;
	} else if (y <= 6e+44) {
		tmp = (4.0 * (x / y)) + 1.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e+92:
		tmp = 2.0
	elif y <= 6e+44:
		tmp = (4.0 * (x / y)) + 1.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e+92)
		tmp = 2.0;
	elseif (y <= 6e+44)
		tmp = Float64(Float64(4.0 * Float64(x / y)) + 1.0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e+92)
		tmp = 2.0;
	elseif (y <= 6e+44)
		tmp = (4.0 * (x / y)) + 1.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e+92], 2.0, If[LessEqual[y, 6e+44], N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000013e92 or 5.99999999999999974e44 < y

   1. Initial program 98.9%

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

   3. Taylor expanded in y around inf 69.8%

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

   if -3.00000000000000013e92 < y < 5.99999999999999974e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 51.3%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+92}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+44}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 34.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in y around inf 33.5%

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

4. Final simplification 33.5%

   \[\leadsto 2 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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)))