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

Percentage Accurate: 99.9% → 100.0%

Time: 5.0s

Alternatives: 9

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 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* 99.7%

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

3. Simplified 99.7%

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

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: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot x}{y}\\ t_1 := -4 \cdot \frac{z}{y} + 1\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+34}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* 4.0 x) y))) (t_1 (+ (* -4.0 (/ z y)) 1.0)))
   (if (<= z -1.45e+152)
     t_1
     (if (<= z -2.25e+21)
       t_0
       (if (<= z -9.5e-149)
         2.0
         (if (<= z -3.4e-182) t_0 (if (<= z 5e+34) 2.0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * x) / y);
	double t_1 = (-4.0 * (z / y)) + 1.0;
	double tmp;
	if (z <= -1.45e+152) {
		tmp = t_1;
	} else if (z <= -2.25e+21) {
		tmp = t_0;
	} else if (z <= -9.5e-149) {
		tmp = 2.0;
	} else if (z <= -3.4e-182) {
		tmp = t_0;
	} else if (z <= 5e+34) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((4.0d0 * x) / y)
    t_1 = ((-4.0d0) * (z / y)) + 1.0d0
    if (z <= (-1.45d+152)) then
        tmp = t_1
    else if (z <= (-2.25d+21)) then
        tmp = t_0
    else if (z <= (-9.5d-149)) then
        tmp = 2.0d0
    else if (z <= (-3.4d-182)) then
        tmp = t_0
    else if (z <= 5d+34) then
        tmp = 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((4.0 * x) / y);
	double t_1 = (-4.0 * (z / y)) + 1.0;
	double tmp;
	if (z <= -1.45e+152) {
		tmp = t_1;
	} else if (z <= -2.25e+21) {
		tmp = t_0;
	} else if (z <= -9.5e-149) {
		tmp = 2.0;
	} else if (z <= -3.4e-182) {
		tmp = t_0;
	} else if (z <= 5e+34) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((4.0 * x) / y)
	t_1 = (-4.0 * (z / y)) + 1.0
	tmp = 0
	if z <= -1.45e+152:
		tmp = t_1
	elif z <= -2.25e+21:
		tmp = t_0
	elif z <= -9.5e-149:
		tmp = 2.0
	elif z <= -3.4e-182:
		tmp = t_0
	elif z <= 5e+34:
		tmp = 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	t_1 = Float64(Float64(-4.0 * Float64(z / y)) + 1.0)
	tmp = 0.0
	if (z <= -1.45e+152)
		tmp = t_1;
	elseif (z <= -2.25e+21)
		tmp = t_0;
	elseif (z <= -9.5e-149)
		tmp = 2.0;
	elseif (z <= -3.4e-182)
		tmp = t_0;
	elseif (z <= 5e+34)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((4.0 * x) / y);
	t_1 = (-4.0 * (z / y)) + 1.0;
	tmp = 0.0;
	if (z <= -1.45e+152)
		tmp = t_1;
	elseif (z <= -2.25e+21)
		tmp = t_0;
	elseif (z <= -9.5e-149)
		tmp = 2.0;
	elseif (z <= -3.4e-182)
		tmp = t_0;
	elseif (z <= 5e+34)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[z, -1.45e+152], t$95$1, If[LessEqual[z, -2.25e+21], t$95$0, If[LessEqual[z, -9.5e-149], 2.0, If[LessEqual[z, -3.4e-182], t$95$0, If[LessEqual[z, 5e+34], 2.0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e152 or 4.9999999999999998e34 < z

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 71.2%

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

      1. *-commutative 71.2%

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

   6. Simplified 71.2%

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

   if -1.4499999999999999e152 < z < -2.25e21 or -9.50000000000000034e-149 < z < -3.39999999999999989e-182

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 62.1%

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

   if -2.25e21 < z < -9.50000000000000034e-149 or -3.39999999999999989e-182 < z < 4.9999999999999998e34

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 62.4%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+152}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+21}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-182}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+34}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \end{array} \]

Alternative 3: 55.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -65 \lor \neg \left(z \leq 7 \cdot 10^{+38}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -65.0) (not (<= z 7e+38))) (+ (* -4.0 (/ z y)) 1.0) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -65.0) || !(z <= 7e+38)) {
		tmp = (-4.0 * (z / 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 ((z <= (-65.0d0)) .or. (.not. (z <= 7d+38))) then
        tmp = ((-4.0d0) * (z / 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 ((z <= -65.0) || !(z <= 7e+38)) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -65.0) or not (z <= 7e+38):
		tmp = (-4.0 * (z / y)) + 1.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -65.0) || !(z <= 7e+38))
		tmp = Float64(Float64(-4.0 * Float64(z / y)) + 1.0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -65.0) || ~((z <= 7e+38)))
		tmp = (-4.0 * (z / y)) + 1.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -65.0], N[Not[LessEqual[z, 7e+38]], $MachinePrecision]], N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -65 or 7.00000000000000003e38 < z

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 62.2%

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

      1. *-commutative 62.2%

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

   6. Simplified 62.2%

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

   if -65 < z < 7.00000000000000003e38

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 60.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -65 \lor \neg \left(z \leq 7 \cdot 10^{+38}\right):\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 4: 81.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+163} \lor \neg \left(x \leq 1.65 \cdot 10^{+154}\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.55e+163) (not (<= x 1.65e+154)))
   (+ 1.0 (/ (* 4.0 x) y))
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.55e+163) || !(x <= 1.65e+154)) {
		tmp = 1.0 + ((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 <= (-2.55d+163)) .or. (.not. (x <= 1.65d+154))) then
        tmp = 1.0d0 + ((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 <= -2.55e+163) || !(x <= 1.65e+154)) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.55e+163) or not (x <= 1.65e+154):
		tmp = 1.0 + ((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 <= -2.55e+163) || !(x <= 1.65e+154))
		tmp = Float64(1.0 + Float64(Float64(4.0 * 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 <= -2.55e+163) || ~((x <= 1.65e+154)))
		tmp = 1.0 + ((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, -2.55e+163], N[Not[LessEqual[x, 1.65e+154]], $MachinePrecision]], N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5500000000000001e163 or 1.65e154 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.5%

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

   if -2.5500000000000001e163 < x < 1.65e154

   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%

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

   3. Simplified 99.8%

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

   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 83.7%

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

      1. neg-mul-1 83.7%

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

      2. distribute-neg-frac 83.7%

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

   9. Simplified 83.7%

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

   10. Taylor expanded in z around 0 83.7%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+163} \lor \neg \left(x \leq 1.65 \cdot 10^{+154}\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 5: 86.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -14000000000 \lor \neg \left(x \leq 2.3 \cdot 10^{+75}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -14000000000.0) (not (<= x 2.3e+75)))
   (+ 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 <= -14000000000.0) || !(x <= 2.3e+75)) {
		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 <= (-14000000000.0d0)) .or. (.not. (x <= 2.3d+75))) 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 <= -14000000000.0) || !(x <= 2.3e+75)) {
		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 <= -14000000000.0) or not (x <= 2.3e+75):
		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 <= -14000000000.0) || !(x <= 2.3e+75))
		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 <= -14000000000.0) || ~((x <= 2.3e+75)))
		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, -14000000000.0], N[Not[LessEqual[x, 2.3e+75]], $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 < -1.4e10 or 2.2999999999999999e75 < 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* 99.7%

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

   3. Simplified 99.7%

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

   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 86.8%

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

   if -1.4e10 < x < 2.2999999999999999e75

   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%

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

   3. Simplified 99.8%

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

   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 91.7%

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

      1. neg-mul-1 91.7%

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

      2. distribute-neg-frac 91.7%

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

   9. Simplified 91.7%

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

   10. Taylor expanded in z around 0 91.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14000000000 \lor \neg \left(x \leq 2.3 \cdot 10^{+75}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 6: 53.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -95 \lor \neg \left(z \leq 1.45 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -95.0) (not (<= z 1.45e+35))) (/ z (/ y -4.0)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -95.0) || !(z <= 1.45e+35)) {
		tmp = z / (y / -4.0);
	} 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 ((z <= (-95.0d0)) .or. (.not. (z <= 1.45d+35))) then
        tmp = z / (y / (-4.0d0))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -95.0) || !(z <= 1.45e+35)) {
		tmp = z / (y / -4.0);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -95.0) or not (z <= 1.45e+35):
		tmp = z / (y / -4.0)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -95.0) || !(z <= 1.45e+35))
		tmp = Float64(z / Float64(y / -4.0));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -95.0) || ~((z <= 1.45e+35)))
		tmp = z / (y / -4.0);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -95.0], N[Not[LessEqual[z, 1.45e+35]], $MachinePrecision]], N[(z / N[(y / -4.0), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -95 or 1.44999999999999997e35 < z

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   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 78.4%

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

      1. neg-mul-1 78.4%

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

      2. distribute-neg-frac 78.4%

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

   9. Simplified 78.4%

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

   10. Taylor expanded in z around 0 78.4%

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

   11. Taylor expanded in z around inf 59.6%

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

       1. *-commutative 59.6%

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

       2. associate-*l/ 59.6%

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

       3. associate-/l* 59.6%

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

   13. Simplified 59.6%

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

   if -95 < z < 1.44999999999999997e35

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 60.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -95 \lor \neg \left(z \leq 1.45 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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%

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

   2. +-commutative 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-lft-in 99.8%

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

   5. associate-+r+ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 8: 8.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 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* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 38.3%

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

   1. *-commutative 38.3%

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

6. Simplified 38.3%

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

7. Taylor expanded in z around 0 9.1%

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

8. Final simplification 9.1%

   \[\leadsto 1 \]

Alternative 9: 34.2% 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 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* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in y around inf 40.4%

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

5. Final simplification 40.4%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023293 
(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)))