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

Percentage Accurate: 99.9% → 100.0%

Time: 5.0s

Alternatives: 8

Speedup: 1.4×

• 20.6% 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

\[\begin{array}{l} \\ 2 + \frac{x - z}{y \cdot 0.25} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 2.0 (/ (- x z) (* y 0.25))))

C

double code(double x, double y, double z) {
	return 2.0 + ((x - z) / (y * 0.25));
}

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) / (y * 0.25d0))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 + ((x - z) / (y * 0.25));
}

Python

def code(x, y, z):
	return 2.0 + ((x - z) / (y * 0.25))

Julia

function code(x, y, z)
	return Float64(2.0 + Float64(Float64(x - z) / Float64(y * 0.25)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 + ((x - z) / (y * 0.25));
end

Wolfram

code[x_, y_, z_] := N[(2.0 + N[(N[(x - z), $MachinePrecision] / N[(y * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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/ 99.4%

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

   2. +-commutative 99.4%

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

   3. associate--l+ 99.4%

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

   4. distribute-lft-in 99.4%

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

   5. associate-+r+ 99.4%

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

3. Simplified 99.4%

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

   1. clear-num 99.4%

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

   2. div-inv 99.4%

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

   3. metadata-eval 99.4%

      \[\leadsto 2 + \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) \]

   4. associate-*l/ 100.0%

      \[\leadsto 2 + \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} \]

   5. *-un-lft-identity 100.0%

      \[\leadsto 2 + \frac{\color{blue}{x - z}}{y \cdot 0.25} \]

6. Applied egg-rr 100.0%

   \[\leadsto 2 + \color{blue}{\frac{x - z}{y \cdot 0.25}} \]

7. Final simplification 100.0%

   \[\leadsto 2 + \frac{x - z}{y \cdot 0.25} \]
8. Add Preprocessing

Alternative 2: 55.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + \frac{x \cdot 4}{y}\\ \mathbf{if}\;x \leq -4.15 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-165}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-238}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-234}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-99}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-26}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (/ (* x 4.0) y))))
   (if (<= x -4.15e-50)
     t_1
     (if (<= x -2.6e-81)
       t_0
       (if (<= x -3.5e-165)
         2.0
         (if (<= x -1.6e-238)
           t_0
           (if (<= x 2e-234)
             2.0
             (if (<= x 6.2e-150)
               t_0
               (if (<= x 4.3e-99) 2.0 (if (<= x 5e-26) t_0 t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + ((x * 4.0) / y);
	double tmp;
	if (x <= -4.15e-50) {
		tmp = t_1;
	} else if (x <= -2.6e-81) {
		tmp = t_0;
	} else if (x <= -3.5e-165) {
		tmp = 2.0;
	} else if (x <= -1.6e-238) {
		tmp = t_0;
	} else if (x <= 2e-234) {
		tmp = 2.0;
	} else if (x <= 6.2e-150) {
		tmp = t_0;
	} else if (x <= 4.3e-99) {
		tmp = 2.0;
	} else if (x <= 5e-26) {
		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 = 1.0d0 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + ((x * 4.0d0) / y)
    if (x <= (-4.15d-50)) then
        tmp = t_1
    else if (x <= (-2.6d-81)) then
        tmp = t_0
    else if (x <= (-3.5d-165)) then
        tmp = 2.0d0
    else if (x <= (-1.6d-238)) then
        tmp = t_0
    else if (x <= 2d-234) then
        tmp = 2.0d0
    else if (x <= 6.2d-150) then
        tmp = t_0
    else if (x <= 4.3d-99) then
        tmp = 2.0d0
    else if (x <= 5d-26) 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 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + ((x * 4.0) / y);
	double tmp;
	if (x <= -4.15e-50) {
		tmp = t_1;
	} else if (x <= -2.6e-81) {
		tmp = t_0;
	} else if (x <= -3.5e-165) {
		tmp = 2.0;
	} else if (x <= -1.6e-238) {
		tmp = t_0;
	} else if (x <= 2e-234) {
		tmp = 2.0;
	} else if (x <= 6.2e-150) {
		tmp = t_0;
	} else if (x <= 4.3e-99) {
		tmp = 2.0;
	} else if (x <= 5e-26) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z * -4.0) / y)
	t_1 = 1.0 + ((x * 4.0) / y)
	tmp = 0
	if x <= -4.15e-50:
		tmp = t_1
	elif x <= -2.6e-81:
		tmp = t_0
	elif x <= -3.5e-165:
		tmp = 2.0
	elif x <= -1.6e-238:
		tmp = t_0
	elif x <= 2e-234:
		tmp = 2.0
	elif x <= 6.2e-150:
		tmp = t_0
	elif x <= 4.3e-99:
		tmp = 2.0
	elif x <= 5e-26:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(Float64(x * 4.0) / y))
	tmp = 0.0
	if (x <= -4.15e-50)
		tmp = t_1;
	elseif (x <= -2.6e-81)
		tmp = t_0;
	elseif (x <= -3.5e-165)
		tmp = 2.0;
	elseif (x <= -1.6e-238)
		tmp = t_0;
	elseif (x <= 2e-234)
		tmp = 2.0;
	elseif (x <= 6.2e-150)
		tmp = t_0;
	elseif (x <= 4.3e-99)
		tmp = 2.0;
	elseif (x <= 5e-26)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z * -4.0) / y);
	t_1 = 1.0 + ((x * 4.0) / y);
	tmp = 0.0;
	if (x <= -4.15e-50)
		tmp = t_1;
	elseif (x <= -2.6e-81)
		tmp = t_0;
	elseif (x <= -3.5e-165)
		tmp = 2.0;
	elseif (x <= -1.6e-238)
		tmp = t_0;
	elseif (x <= 2e-234)
		tmp = 2.0;
	elseif (x <= 6.2e-150)
		tmp = t_0;
	elseif (x <= 4.3e-99)
		tmp = 2.0;
	elseif (x <= 5e-26)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.15e-50], t$95$1, If[LessEqual[x, -2.6e-81], t$95$0, If[LessEqual[x, -3.5e-165], 2.0, If[LessEqual[x, -1.6e-238], t$95$0, If[LessEqual[x, 2e-234], 2.0, If[LessEqual[x, 6.2e-150], t$95$0, If[LessEqual[x, 4.3e-99], 2.0, If[LessEqual[x, 5e-26], t$95$0, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1499999999999998e-50 or 5.00000000000000019e-26 < x

   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 71.4%

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

      1. associate-*r/ 71.4%

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

   5. Simplified 71.4%

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

   if -4.1499999999999998e-50 < x < -2.5999999999999999e-81 or -3.5000000000000002e-165 < x < -1.6000000000000001e-238 or 1.9999999999999999e-234 < x < 6.19999999999999996e-150 or 4.2999999999999999e-99 < x < 5.00000000000000019e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*l/ 71.1%

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

   5. Simplified 71.1%

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

   if -2.5999999999999999e-81 < x < -3.5000000000000002e-165 or -1.6000000000000001e-238 < x < 1.9999999999999999e-234 or 6.19999999999999996e-150 < x < 4.2999999999999999e-99

   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 y around inf 71.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.15 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-81}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-165}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-238}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-234}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-99}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-26}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -200000000 \lor \neg \left(x \leq 2.2 \cdot 10^{-7}\right):\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -200000000.0) (not (<= x 2.2e-7))) (+ 1.0 (* x (/ 4.0 y))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -200000000.0) || !(x <= 2.2e-7)) {
		tmp = 1.0 + (x * (4.0 / 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 ((x <= (-200000000.0d0)) .or. (.not. (x <= 2.2d-7))) then
        tmp = 1.0d0 + (x * (4.0d0 / 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 ((x <= -200000000.0) || !(x <= 2.2e-7)) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -200000000.0) or not (x <= 2.2e-7):
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -200000000.0) || !(x <= 2.2e-7))
		tmp = Float64(1.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -200000000.0) || ~((x <= 2.2e-7)))
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -200000000.0], N[Not[LessEqual[x, 2.2e-7]], $MachinePrecision]], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -2e8 or 2.2000000000000001e-7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.0%

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

      1. associate-*r/ 77.0%

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

      2. associate-*l/ 76.7%

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

      3. *-commutative 76.7%

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

   5. Simplified 76.7%

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

   if -2e8 < x < 2.2000000000000001e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 53.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -200000000 \lor \neg \left(x \leq 2.2 \cdot 10^{-7}\right):\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+16} \lor \neg \left(x \leq 1.45 \cdot 10^{-5}\right):\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e+16) (not (<= x 1.45e-5))) (+ 1.0 (/ 4.0 (/ y x))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e+16) || !(x <= 1.45e-5)) {
		tmp = 1.0 + (4.0 / (y / x));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.45d+16)) .or. (.not. (x <= 1.45d-5))) then
        tmp = 1.0d0 + (4.0d0 / (y / x))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e+16) || !(x <= 1.45e-5)) {
		tmp = 1.0 + (4.0 / (y / x));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45e+16) or not (x <= 1.45e-5):
		tmp = 1.0 + (4.0 / (y / x))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45e+16) || !(x <= 1.45e-5))
		tmp = Float64(1.0 + Float64(4.0 / Float64(y / x)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45e+16) || ~((x <= 1.45e-5)))
		tmp = 1.0 + (4.0 / (y / x));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45e+16], N[Not[LessEqual[x, 1.45e-5]], $MachinePrecision]], N[(1.0 + N[(4.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e16 or 1.45e-5 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.0%

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

      1. associate-*r/ 77.0%

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

      2. associate-*l/ 76.7%

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

      3. *-commutative 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in x around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. associate-/l* 76.9%

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

   8. Simplified 76.9%

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

   if -1.45e16 < x < 1.45e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 53.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+16} \lor \neg \left(x \leq 1.45 \cdot 10^{-5}\right):\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -430000000000 \lor \neg \left(x \leq 5.2 \cdot 10^{-6}\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -430000000000.0) (not (<= x 5.2e-6)))
   (+ 1.0 (/ (* x 4.0) y))
   2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -430000000000.0) || !(x <= 5.2e-6)) {
		tmp = 1.0 + ((x * 4.0) / 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 ((x <= (-430000000000.0d0)) .or. (.not. (x <= 5.2d-6))) then
        tmp = 1.0d0 + ((x * 4.0d0) / 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 ((x <= -430000000000.0) || !(x <= 5.2e-6)) {
		tmp = 1.0 + ((x * 4.0) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -430000000000.0) or not (x <= 5.2e-6):
		tmp = 1.0 + ((x * 4.0) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -430000000000.0) || !(x <= 5.2e-6))
		tmp = Float64(1.0 + Float64(Float64(x * 4.0) / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -430000000000.0) || ~((x <= 5.2e-6)))
		tmp = 1.0 + ((x * 4.0) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -430000000000.0], N[Not[LessEqual[x, 5.2e-6]], $MachinePrecision]], N[(1.0 + N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e11 or 5.20000000000000019e-6 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.0%

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

      1. associate-*r/ 77.0%

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

   5. Simplified 77.0%

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

   if -4.3e11 < x < 5.20000000000000019e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 53.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -430000000000 \lor \neg \left(x \leq 5.2 \cdot 10^{-6}\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -350000000000 \lor \neg \left(x \leq 8.8 \cdot 10^{+179}\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -350000000000.0) (not (<= x 8.8e+179)))
   (+ 1.0 (/ (* x 4.0) y))
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -350000000000.0) || !(x <= 8.8e+179)) {
		tmp = 1.0 + ((x * 4.0) / 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 <= (-350000000000.0d0)) .or. (.not. (x <= 8.8d+179))) then
        tmp = 1.0d0 + ((x * 4.0d0) / 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 <= -350000000000.0) || !(x <= 8.8e+179)) {
		tmp = 1.0 + ((x * 4.0) / y);
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -350000000000.0) or not (x <= 8.8e+179):
		tmp = 1.0 + ((x * 4.0) / y)
	else:
		tmp = 2.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -350000000000.0) || !(x <= 8.8e+179))
		tmp = Float64(1.0 + Float64(Float64(x * 4.0) / 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 <= -350000000000.0) || ~((x <= 8.8e+179)))
		tmp = 1.0 + ((x * 4.0) / y);
	else
		tmp = 2.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -350000000000.0], N[Not[LessEqual[x, 8.8e+179]], $MachinePrecision]], N[(1.0 + N[(N[(x * 4.0), $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 < -3.5e11 or 8.8000000000000002e179 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 84.1%

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

      1. associate-*r/ 84.1%

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

   5. Simplified 84.1%

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

   if -3.5e11 < x < 8.8000000000000002e179

   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/ 99.2%

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

      2. +-commutative 99.2%

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

      3. associate--l+ 99.2%

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

      4. distribute-lft-in 99.2%

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

      5. associate-+r+ 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.2%

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

      2. div-inv 99.2%

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

      3. metadata-eval 99.2%

         \[\leadsto 2 + \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) \]

      4. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} \]

      5. *-un-lft-identity 100.0%

         \[\leadsto 2 + \frac{\color{blue}{x - z}}{y \cdot 0.25} \]

   6. Applied egg-rr 100.0%

      \[\leadsto 2 + \color{blue}{\frac{x - z}{y \cdot 0.25}} \]

   7. Taylor expanded in x around 0 87.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350000000000 \lor \neg \left(x \leq 8.8 \cdot 10^{+179}\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

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 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/ 99.4%

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

   2. +-commutative 99.4%

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

   3. associate--l+ 99.4%

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

   4. distribute-lft-in 99.4%

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

   5. associate-+r+ 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 8: 34.7% 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 99.9%

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

3. Taylor expanded in y around inf 34.5%

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

4. Final simplification 34.5%

   \[\leadsto 2 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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)))