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

Percentage Accurate: 99.9% → 99.9%

Time: 5.2s

Alternatives: 8

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. Final simplification 100.0%

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

Alternative 2: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.7 \cdot 10^{-106}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-229}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-146}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-95}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+149}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)) (t_1 (* 4.0 (/ x y))))
   (if (<= x -4.8e+41)
     t_1
     (if (<= x -8.7e-106)
       2.0
       (if (<= x -3e-244)
         t_0
         (if (<= x 9e-229)
           2.0
           (if (<= x 1e-189)
             t_0
             (if (<= x 1.1e-146)
               2.0
               (if (<= x 3.2e-113)
                 t_0
                 (if (<= x 5.2e-95) 2.0 (if (<= x 6.6e+149) t_0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -4.8e+41) {
		tmp = t_1;
	} else if (x <= -8.7e-106) {
		tmp = 2.0;
	} else if (x <= -3e-244) {
		tmp = t_0;
	} else if (x <= 9e-229) {
		tmp = 2.0;
	} else if (x <= 1e-189) {
		tmp = t_0;
	} else if (x <= 1.1e-146) {
		tmp = 2.0;
	} else if (x <= 3.2e-113) {
		tmp = t_0;
	} else if (x <= 5.2e-95) {
		tmp = 2.0;
	} else if (x <= 6.6e+149) {
		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 = (z / y) * (-4.0d0)
    t_1 = 4.0d0 * (x / y)
    if (x <= (-4.8d+41)) then
        tmp = t_1
    else if (x <= (-8.7d-106)) then
        tmp = 2.0d0
    else if (x <= (-3d-244)) then
        tmp = t_0
    else if (x <= 9d-229) then
        tmp = 2.0d0
    else if (x <= 1d-189) then
        tmp = t_0
    else if (x <= 1.1d-146) then
        tmp = 2.0d0
    else if (x <= 3.2d-113) then
        tmp = t_0
    else if (x <= 5.2d-95) then
        tmp = 2.0d0
    else if (x <= 6.6d+149) 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 = (z / y) * -4.0;
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (x <= -4.8e+41) {
		tmp = t_1;
	} else if (x <= -8.7e-106) {
		tmp = 2.0;
	} else if (x <= -3e-244) {
		tmp = t_0;
	} else if (x <= 9e-229) {
		tmp = 2.0;
	} else if (x <= 1e-189) {
		tmp = t_0;
	} else if (x <= 1.1e-146) {
		tmp = 2.0;
	} else if (x <= 3.2e-113) {
		tmp = t_0;
	} else if (x <= 5.2e-95) {
		tmp = 2.0;
	} else if (x <= 6.6e+149) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	t_1 = 4.0 * (x / y)
	tmp = 0
	if x <= -4.8e+41:
		tmp = t_1
	elif x <= -8.7e-106:
		tmp = 2.0
	elif x <= -3e-244:
		tmp = t_0
	elif x <= 9e-229:
		tmp = 2.0
	elif x <= 1e-189:
		tmp = t_0
	elif x <= 1.1e-146:
		tmp = 2.0
	elif x <= 3.2e-113:
		tmp = t_0
	elif x <= 5.2e-95:
		tmp = 2.0
	elif x <= 6.6e+149:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	t_1 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (x <= -4.8e+41)
		tmp = t_1;
	elseif (x <= -8.7e-106)
		tmp = 2.0;
	elseif (x <= -3e-244)
		tmp = t_0;
	elseif (x <= 9e-229)
		tmp = 2.0;
	elseif (x <= 1e-189)
		tmp = t_0;
	elseif (x <= 1.1e-146)
		tmp = 2.0;
	elseif (x <= 3.2e-113)
		tmp = t_0;
	elseif (x <= 5.2e-95)
		tmp = 2.0;
	elseif (x <= 6.6e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	t_1 = 4.0 * (x / y);
	tmp = 0.0;
	if (x <= -4.8e+41)
		tmp = t_1;
	elseif (x <= -8.7e-106)
		tmp = 2.0;
	elseif (x <= -3e-244)
		tmp = t_0;
	elseif (x <= 9e-229)
		tmp = 2.0;
	elseif (x <= 1e-189)
		tmp = t_0;
	elseif (x <= 1.1e-146)
		tmp = 2.0;
	elseif (x <= 3.2e-113)
		tmp = t_0;
	elseif (x <= 5.2e-95)
		tmp = 2.0;
	elseif (x <= 6.6e+149)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+41], t$95$1, If[LessEqual[x, -8.7e-106], 2.0, If[LessEqual[x, -3e-244], t$95$0, If[LessEqual[x, 9e-229], 2.0, If[LessEqual[x, 1e-189], t$95$0, If[LessEqual[x, 1.1e-146], 2.0, If[LessEqual[x, 3.2e-113], t$95$0, If[LessEqual[x, 5.2e-95], 2.0, If[LessEqual[x, 6.6e+149], t$95$0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8000000000000003e41 or 6.6e149 < 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 78.1%

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

   if -4.8000000000000003e41 < x < -8.7000000000000001e-106 or -3.0000000000000001e-244 < x < 9.0000000000000004e-229 or 1.00000000000000007e-189 < x < 1.1e-146 or 3.2000000000000002e-113 < x < 5.20000000000000001e-95

   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 64.7%

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

   if -8.7000000000000001e-106 < x < -3.0000000000000001e-244 or 9.0000000000000004e-229 < x < 1.00000000000000007e-189 or 1.1e-146 < x < 3.2000000000000002e-113 or 5.20000000000000001e-95 < x < 6.6e149

   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 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+41}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -8.7 \cdot 10^{-106}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-244}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-229}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 10^{-189}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-146}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-95}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+41} \lor \neg \left(x \leq 680000\right):\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.2e+41) (not (<= x 680000.0)))
   (* (/ 4.0 y) (- x z))
   (+ 2.0 (* (/ z y) -4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e+41) || !(x <= 680000.0)) {
		tmp = (4.0 / y) * (x - z);
	} 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 <= (-4.2d+41)) .or. (.not. (x <= 680000.0d0))) then
        tmp = (4.0d0 / y) * (x - z)
    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 <= -4.2e+41) || !(x <= 680000.0)) {
		tmp = (4.0 / y) * (x - z);
	} else {
		tmp = 2.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.2e+41) or not (x <= 680000.0):
		tmp = (4.0 / y) * (x - z)
	else:
		tmp = 2.0 + ((z / y) * -4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.2e+41) || !(x <= 680000.0))
		tmp = Float64(Float64(4.0 / y) * Float64(x - z));
	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 <= -4.2e+41) || ~((x <= 680000.0)))
		tmp = (4.0 / y) * (x - z);
	else
		tmp = 2.0 + ((z / y) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.2e+41], N[Not[LessEqual[x, 680000.0]], $MachinePrecision]], N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999999e41 or 6.8e5 < 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 85.4%

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

      1. associate-*r/ 85.4%

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

      2. associate-*l/ 85.2%

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

   5. Simplified 85.2%

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

   if -4.1999999999999999e41 < x < 6.8e5

   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+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 93.3%

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

      1. *-commutative 93.3%

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

   7. Simplified 93.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+41} \lor \neg \left(x \leq 680000\right):\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+225}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e+225) 2.0 (if (<= y 4.6e+112) (* (/ 4.0 y) (- x z)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e+225) {
		tmp = 2.0;
	} else if (y <= 4.6e+112) {
		tmp = (4.0 / y) * (x - z);
	} 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 <= (-1.7d+225)) then
        tmp = 2.0d0
    else if (y <= 4.6d+112) then
        tmp = (4.0d0 / y) * (x - z)
    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 <= -1.7e+225) {
		tmp = 2.0;
	} else if (y <= 4.6e+112) {
		tmp = (4.0 / y) * (x - z);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.7e+225:
		tmp = 2.0
	elif y <= 4.6e+112:
		tmp = (4.0 / y) * (x - z)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e+225)
		tmp = 2.0;
	elseif (y <= 4.6e+112)
		tmp = Float64(Float64(4.0 / y) * Float64(x - z));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.7e+225)
		tmp = 2.0;
	elseif (y <= 4.6e+112)
		tmp = (4.0 / y) * (x - z);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.7e+225], 2.0, If[LessEqual[y, 4.6e+112], N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000009e225 or 4.5999999999999999e112 < 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 80.4%

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

   if -1.70000000000000009e225 < y < 4.5999999999999999e112

   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 83.6%

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

      1. associate-*r/ 83.6%

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

      2. associate-*l/ 83.4%

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

   5. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+225}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+52}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq 850:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.12e+52)
   (+ 2.0 (* x (/ 4.0 y)))
   (if (<= x 850.0) (+ 2.0 (* (/ z y) -4.0)) (* (/ 4.0 y) (- x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.12e+52) {
		tmp = 2.0 + (x * (4.0 / y));
	} else if (x <= 850.0) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = (4.0 / y) * (x - z);
	}
	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 <= (-1.12d+52)) then
        tmp = 2.0d0 + (x * (4.0d0 / y))
    else if (x <= 850.0d0) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = (4.0d0 / y) * (x - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.12e+52) {
		tmp = 2.0 + (x * (4.0 / y));
	} else if (x <= 850.0) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = (4.0 / y) * (x - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.12e+52:
		tmp = 2.0 + (x * (4.0 / y))
	elif x <= 850.0:
		tmp = 2.0 + ((z / y) * -4.0)
	else:
		tmp = (4.0 / y) * (x - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.12e+52)
		tmp = Float64(2.0 + Float64(x * Float64(4.0 / y)));
	elseif (x <= 850.0)
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(Float64(4.0 / y) * Float64(x - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.12e+52)
		tmp = 2.0 + (x * (4.0 / y));
	elseif (x <= 850.0)
		tmp = 2.0 + ((z / y) * -4.0);
	else
		tmp = (4.0 / y) * (x - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.12e+52], N[(2.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 850.0], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.12000000000000002e52

   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%

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

      2. +-commutative 99.7%

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

      3. associate--l+ 99.7%

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

      4. distribute-lft-in 99.7%

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

      5. associate-+r+ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. associate-*r/ 93.9%

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

      3. associate-*l/ 93.7%

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

      4. *-commutative 93.7%

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

   7. Simplified 93.7%

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

   if -1.12000000000000002e52 < x < 850

   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+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.7%

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

      1. *-commutative 92.7%

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

   7. Simplified 92.7%

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

   if 850 < 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 89.9%

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

      1. associate-*r/ 89.9%

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

      2. associate-*l/ 89.7%

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

   5. Simplified 89.7%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+52}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq 850:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+41} \lor \neg \left(x \leq 59000\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.75e+41) (not (<= x 59000.0))) (* 4.0 (/ x y)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e+41) || !(x <= 59000.0)) {
		tmp = 4.0 * (x / 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 <= (-1.75d+41)) .or. (.not. (x <= 59000.0d0))) then
        tmp = 4.0d0 * (x / 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 <= -1.75e+41) || !(x <= 59000.0)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.75e+41) or not (x <= 59000.0):
		tmp = 4.0 * (x / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.75e+41) || !(x <= 59000.0))
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.75e+41) || ~((x <= 59000.0)))
		tmp = 4.0 * (x / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.75e+41], N[Not[LessEqual[x, 59000.0]], $MachinePrecision]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e41 or 59000 < 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 69.4%

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

   if -1.75e41 < x < 59000

   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 47.1%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+41} \lor \neg \left(x \leq 59000\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

5. Final simplification 99.8%

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

Alternative 8: 34.3% 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 32.4%

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

4. Final simplification 32.4%

   \[\leadsto 2 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(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)))