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

Percentage Accurate: 99.9% → 99.9%

Time: 5.3s

Alternatives: 10

Speedup: 1.0×

• 21.3% 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: 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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 52.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{y}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+66}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+105}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) y)))
   (if (<= x -1.6e+66)
     t_0
     (if (<= x 1.02e-103) (* (/ z y) -4.0) (if (<= x 1.65e+105) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double tmp;
	if (x <= -1.6e+66) {
		tmp = t_0;
	} else if (x <= 1.02e-103) {
		tmp = (z / y) * -4.0;
	} else if (x <= 1.65e+105) {
		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 = (4.0d0 * x) / y
    if (x <= (-1.6d+66)) then
        tmp = t_0
    else if (x <= 1.02d-103) then
        tmp = (z / y) * (-4.0d0)
    else if (x <= 1.65d+105) 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 = (4.0 * x) / y;
	double tmp;
	if (x <= -1.6e+66) {
		tmp = t_0;
	} else if (x <= 1.02e-103) {
		tmp = (z / y) * -4.0;
	} else if (x <= 1.65e+105) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * x) / y
	tmp = 0
	if x <= -1.6e+66:
		tmp = t_0
	elif x <= 1.02e-103:
		tmp = (z / y) * -4.0
	elif x <= 1.65e+105:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / y)
	tmp = 0.0
	if (x <= -1.6e+66)
		tmp = t_0;
	elseif (x <= 1.02e-103)
		tmp = Float64(Float64(z / y) * -4.0);
	elseif (x <= 1.65e+105)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * x) / y;
	tmp = 0.0;
	if (x <= -1.6e+66)
		tmp = t_0;
	elseif (x <= 1.02e-103)
		tmp = (z / y) * -4.0;
	elseif (x <= 1.65e+105)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -1.6e+66], t$95$0, If[LessEqual[x, 1.02e-103], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[x, 1.65e+105], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e66 or 1.64999999999999999e105 < 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 72.9%

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

      1. associate-*r/ 72.9%

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

   5. Simplified 72.9%

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

   if -1.6e66 < x < 1.01999999999999998e-103

   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 z around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   if 1.01999999999999998e-103 < x < 1.64999999999999999e105

   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 66.4%

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

Alternative 3: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-102}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{+105}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ 4.0 y))))
   (if (<= x -2e+64)
     t_0
     (if (<= x 1.36e-102) (* (/ z y) -4.0) (if (<= x 3.35e+105) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.0 / y);
	double tmp;
	if (x <= -2e+64) {
		tmp = t_0;
	} else if (x <= 1.36e-102) {
		tmp = (z / y) * -4.0;
	} else if (x <= 3.35e+105) {
		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 = x * (4.0d0 / y)
    if (x <= (-2d+64)) then
        tmp = t_0
    else if (x <= 1.36d-102) then
        tmp = (z / y) * (-4.0d0)
    else if (x <= 3.35d+105) 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 = x * (4.0 / y);
	double tmp;
	if (x <= -2e+64) {
		tmp = t_0;
	} else if (x <= 1.36e-102) {
		tmp = (z / y) * -4.0;
	} else if (x <= 3.35e+105) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.0 / y)
	tmp = 0
	if x <= -2e+64:
		tmp = t_0
	elif x <= 1.36e-102:
		tmp = (z / y) * -4.0
	elif x <= 3.35e+105:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.0 / y))
	tmp = 0.0
	if (x <= -2e+64)
		tmp = t_0;
	elseif (x <= 1.36e-102)
		tmp = Float64(Float64(z / y) * -4.0);
	elseif (x <= 3.35e+105)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.0 / y);
	tmp = 0.0;
	if (x <= -2e+64)
		tmp = t_0;
	elseif (x <= 1.36e-102)
		tmp = (z / y) * -4.0;
	elseif (x <= 3.35e+105)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+64], t$95$0, If[LessEqual[x, 1.36e-102], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[x, 3.35e+105], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.00000000000000004e64 or 3.3500000000000002e105 < 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 72.9%

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

      1. associate-*r/ 72.9%

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

      2. associate-*l/ 72.7%

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

      3. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -2.00000000000000004e64 < x < 1.36000000000000001e-102

   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 z around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   if 1.36000000000000001e-102 < x < 3.3500000000000002e105

   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 66.4%

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

Alternative 4: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-102}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+105}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ 4.0 y))))
   (if (<= x -1.75e+65)
     t_0
     (if (<= x 8e-102) (* z (/ -4.0 y)) (if (<= x 1.45e+105) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.0 / y);
	double tmp;
	if (x <= -1.75e+65) {
		tmp = t_0;
	} else if (x <= 8e-102) {
		tmp = z * (-4.0 / y);
	} else if (x <= 1.45e+105) {
		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 = x * (4.0d0 / y)
    if (x <= (-1.75d+65)) then
        tmp = t_0
    else if (x <= 8d-102) then
        tmp = z * ((-4.0d0) / y)
    else if (x <= 1.45d+105) 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 = x * (4.0 / y);
	double tmp;
	if (x <= -1.75e+65) {
		tmp = t_0;
	} else if (x <= 8e-102) {
		tmp = z * (-4.0 / y);
	} else if (x <= 1.45e+105) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.0 / y)
	tmp = 0
	if x <= -1.75e+65:
		tmp = t_0
	elif x <= 8e-102:
		tmp = z * (-4.0 / y)
	elif x <= 1.45e+105:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.0 / y))
	tmp = 0.0
	if (x <= -1.75e+65)
		tmp = t_0;
	elseif (x <= 8e-102)
		tmp = Float64(z * Float64(-4.0 / y));
	elseif (x <= 1.45e+105)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.0 / y);
	tmp = 0.0;
	if (x <= -1.75e+65)
		tmp = t_0;
	elseif (x <= 8e-102)
		tmp = z * (-4.0 / y);
	elseif (x <= 1.45e+105)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+65], t$95$0, If[LessEqual[x, 8e-102], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+105], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75e65 or 1.45000000000000005e105 < 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 72.9%

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

      1. associate-*r/ 72.9%

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

      2. associate-*l/ 72.7%

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

      3. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -1.75e65 < x < 7.99999999999999946e-102

   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 z around inf 51.1%

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

      1. associate-*r/ 51.1%

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

      2. *-commutative 51.1%

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

      3. associate-/l* 50.9%

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

   5. Simplified 50.9%

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

   if 7.99999999999999946e-102 < x < 1.45000000000000005e105

   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 66.4%

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

Alternative 5: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+21} \lor \neg \left(x \leq 1.11 \cdot 10^{+105}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.2e+21) (not (<= x 1.11e+105)))
   (* 4.0 (/ (- x z) y))
   (+ 2.0 (* (/ z y) -4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+21) || !(x <= 1.11e+105)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0 + ((z / y) * -4.0);
	}
	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 <= (-6.2d+21)) .or. (.not. (x <= 1.11d+105))) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+21) || !(x <= 1.11e+105)) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.2e+21) or not (x <= 1.11e+105):
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0 + ((z / y) * -4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.2e+21) || !(x <= 1.11e+105))
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.2e+21) || ~((x <= 1.11e+105)))
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0 + ((z / y) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e+21], N[Not[LessEqual[x, 1.11e+105]], $MachinePrecision]], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e21 or 1.11e105 < 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 y around 0 84.3%

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

   if -6.2e21 < x < 1.11e105

   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. +-commutative 100.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*r* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-lft-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 90.4%

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

      1. *-commutative 90.4%

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

   7. Simplified 90.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+21} \lor \neg \left(x \leq 1.11 \cdot 10^{+105}\right):\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+20}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e+20)
   (* 4.0 (/ (- x z) y))
   (if (<= x 6.2e+37) (+ 2.0 (* (/ z y) -4.0)) (+ 2.0 (* x (/ 4.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+20) {
		tmp = 4.0 * ((x - z) / y);
	} else if (x <= 6.2e+37) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (x * (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 <= (-9d+20)) then
        tmp = 4.0d0 * ((x - z) / y)
    else if (x <= 6.2d+37) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 2.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+20) {
		tmp = 4.0 * ((x - z) / y);
	} else if (x <= 6.2e+37) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e+20:
		tmp = 4.0 * ((x - z) / y)
	elif x <= 6.2e+37:
		tmp = 2.0 + ((z / y) * -4.0)
	else:
		tmp = 2.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e+20)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	elseif (x <= 6.2e+37)
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(2.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9e+20)
		tmp = 4.0 * ((x - z) / y);
	elseif (x <= 6.2e+37)
		tmp = 2.0 + ((z / y) * -4.0);
	else
		tmp = 2.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e+20], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+37], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e20

   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 0 83.3%

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

   if -9e20 < x < 6.2000000000000004e37

   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. +-commutative 100.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*r* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-lft-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 92.3%

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

      1. *-commutative 92.3%

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

   7. Simplified 92.3%

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

   if 6.2000000000000004e37 < 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. +-commutative 100.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*r* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-lft-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 93.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+20}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+144}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+99}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+144) 2.0 (if (<= y 1.3e+99) (* 4.0 (/ (- x z) y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+144) {
		tmp = 2.0;
	} else if (y <= 1.3e+99) {
		tmp = 4.0 * ((x - 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 (y <= (-3.1d+144)) then
        tmp = 2.0d0
    else if (y <= 1.3d+99) then
        tmp = 4.0d0 * ((x - 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 (y <= -3.1e+144) {
		tmp = 2.0;
	} else if (y <= 1.3e+99) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e+144:
		tmp = 2.0
	elif y <= 1.3e+99:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+144)
		tmp = 2.0;
	elseif (y <= 1.3e+99)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1e+144)
		tmp = 2.0;
	elseif (y <= 1.3e+99)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e+144], 2.0, If[LessEqual[y, 1.3e+99], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1000000000000002e144 or 1.3e99 < y

   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 75.9%

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

   if -3.1000000000000002e144 < y < 1.3e99

   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 0 85.3%

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

Alternative 8: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+26} \lor \neg \left(x \leq 1.12 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e+26) (not (<= x 1.12e+105))) (* x (/ 4.0 y)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e+26) || !(x <= 1.12e+105)) {
		tmp = 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 <= (-2.7d+26)) .or. (.not. (x <= 1.12d+105))) then
        tmp = 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 <= -2.7e+26) || !(x <= 1.12e+105)) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e+26) or not (x <= 1.12e+105):
		tmp = x * (4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e+26) || !(x <= 1.12e+105))
		tmp = 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 <= -2.7e+26) || ~((x <= 1.12e+105)))
		tmp = x * (4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e+26], N[Not[LessEqual[x, 1.12e+105]], $MachinePrecision]], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e26 or 1.12e105 < 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 69.5%

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

      1. associate-*r/ 69.5%

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

      2. associate-*l/ 69.3%

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

      3. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -2.7e26 < x < 1.12e105

   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 48.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+26} \lor \neg \left(x \leq 1.12 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $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. +-commutative 100.0%

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

   2. associate-*l/ 99.7%

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

   3. +-commutative 99.7%

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

   4. associate--l+ 99.7%

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

   5. +-commutative 99.7%

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

   6. distribute-lft-in 99.7%

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

   7. associate-+l+ 99.8%

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

   8. associate-*l/ 99.8%

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

   9. *-commutative 99.8%

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

   10. associate-*r* 99.8%

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

   11. metadata-eval 99.8%

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

   12. *-lft-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 10: 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. Add Preprocessing

3. Taylor expanded in y around inf 34.8%

   \[\leadsto \color{blue}{2} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024165 
(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)))