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

Percentage Accurate: 99.9% → 99.9%

Time: 5.8s

Alternatives: 9

Speedup: 1.0×

• 20.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 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: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-48}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 2.0 (* 4.0 (/ x y)))))
   (if (<= y -8e+91)
     t_0
     (if (<= y -4.8e-48)
       (+ 2.0 (* (/ z y) -4.0))
       (if (<= y 1.65e-31) (* 4.0 (/ (- x z) y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 2.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -8e+91) {
		tmp = t_0;
	} else if (y <= -4.8e-48) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else if (y <= 1.65e-31) {
		tmp = 4.0 * ((x - z) / y);
	} 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 = 2.0d0 + (4.0d0 * (x / y))
    if (y <= (-8d+91)) then
        tmp = t_0
    else if (y <= (-4.8d-48)) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else if (y <= 1.65d-31) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 2.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -8e+91) {
		tmp = t_0;
	} else if (y <= -4.8e-48) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else if (y <= 1.65e-31) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 2.0 + (4.0 * (x / y))
	tmp = 0
	if y <= -8e+91:
		tmp = t_0
	elif y <= -4.8e-48:
		tmp = 2.0 + ((z / y) * -4.0)
	elif y <= 1.65e-31:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(2.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (y <= -8e+91)
		tmp = t_0;
	elseif (y <= -4.8e-48)
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	elseif (y <= 1.65e-31)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 2.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (y <= -8e+91)
		tmp = t_0;
	elseif (y <= -4.8e-48)
		tmp = 2.0 + ((z / y) * -4.0);
	elseif (y <= 1.65e-31)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+91], t$95$0, If[LessEqual[y, -4.8e-48], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-31], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000064e91 or 1.65e-31 < y

   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. +-commutative 99.9%

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

      2. associate-*l/ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-*l/ 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*r* 99.9%

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

      11. metadata-eval 99.9%

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

      12. *-lft-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 91.2%

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

   if -8.00000000000000064e91 < y < -4.8e-48

   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. +-commutative 99.9%

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

      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. Taylor expanded in x around 0 88.6%

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

      1. *-commutative 88.6%

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

   7. Simplified 88.6%

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

   if -4.8e-48 < y < 1.65e-31

   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 95.4%

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

Alternative 3: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-48}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+106}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-48)
   2.0
   (if (<= y -1.75e-85)
     (* (/ z y) -4.0)
     (if (<= y 6.2e+106) (/ (* 4.0 x) y) 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-48) {
		tmp = 2.0;
	} else if (y <= -1.75e-85) {
		tmp = (z / y) * -4.0;
	} else if (y <= 6.2e+106) {
		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 (y <= (-5d-48)) then
        tmp = 2.0d0
    else if (y <= (-1.75d-85)) then
        tmp = (z / y) * (-4.0d0)
    else if (y <= 6.2d+106) 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 (y <= -5e-48) {
		tmp = 2.0;
	} else if (y <= -1.75e-85) {
		tmp = (z / y) * -4.0;
	} else if (y <= 6.2e+106) {
		tmp = (4.0 * x) / y;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-48:
		tmp = 2.0
	elif y <= -1.75e-85:
		tmp = (z / y) * -4.0
	elif y <= 6.2e+106:
		tmp = (4.0 * x) / y
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-48)
		tmp = 2.0;
	elseif (y <= -1.75e-85)
		tmp = Float64(Float64(z / y) * -4.0);
	elseif (y <= 6.2e+106)
		tmp = Float64(Float64(4.0 * x) / y);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-48)
		tmp = 2.0;
	elseif (y <= -1.75e-85)
		tmp = (z / y) * -4.0;
	elseif (y <= 6.2e+106)
		tmp = (4.0 * x) / y;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-48], 2.0, If[LessEqual[y, -1.75e-85], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[y, 6.2e+106], N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999999e-48 or 6.1999999999999999e106 < y

   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 72.0%

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

   if -4.9999999999999999e-48 < y < -1.74999999999999989e-85

   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 86.2%

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

      1. *-commutative 86.2%

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

   5. Simplified 86.2%

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

   if -1.74999999999999989e-85 < y < 6.1999999999999999e106

   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 55.4%

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

      1. associate-*r/ 55.4%

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

   5. Simplified 55.4%

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

Alternative 4: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-50}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e-50)
   2.0
   (if (<= y -3.9e-85)
     (* (/ z y) -4.0)
     (if (<= y 1.4e+108) (* x (/ 4.0 y)) 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-50) {
		tmp = 2.0;
	} else if (y <= -3.9e-85) {
		tmp = (z / y) * -4.0;
	} else if (y <= 1.4e+108) {
		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 (y <= (-4.8d-50)) then
        tmp = 2.0d0
    else if (y <= (-3.9d-85)) then
        tmp = (z / y) * (-4.0d0)
    else if (y <= 1.4d+108) 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 (y <= -4.8e-50) {
		tmp = 2.0;
	} else if (y <= -3.9e-85) {
		tmp = (z / y) * -4.0;
	} else if (y <= 1.4e+108) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e-50:
		tmp = 2.0
	elif y <= -3.9e-85:
		tmp = (z / y) * -4.0
	elif y <= 1.4e+108:
		tmp = x * (4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e-50)
		tmp = 2.0;
	elseif (y <= -3.9e-85)
		tmp = Float64(Float64(z / y) * -4.0);
	elseif (y <= 1.4e+108)
		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 (y <= -4.8e-50)
		tmp = 2.0;
	elseif (y <= -3.9e-85)
		tmp = (z / y) * -4.0;
	elseif (y <= 1.4e+108)
		tmp = x * (4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e-50], 2.0, If[LessEqual[y, -3.9e-85], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[y, 1.4e+108], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000004e-50 or 1.3999999999999999e108 < y

   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 72.0%

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

   if -4.80000000000000004e-50 < y < -3.89999999999999988e-85

   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 86.2%

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

      1. *-commutative 86.2%

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

   5. Simplified 86.2%

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

   if -3.89999999999999988e-85 < y < 1.3999999999999999e108

   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 55.4%

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

      1. associate-*r/ 55.4%

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

      2. associate-*l/ 55.3%

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

      3. *-commutative 55.3%

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

   5. Simplified 55.3%

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

Alternative 5: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-50} \lor \neg \left(y \leq 1.15 \cdot 10^{-30}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e-50) (not (<= y 1.15e-30)))
   (+ 2.0 (* 4.0 (/ x y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e-50) || !(y <= 1.15e-30)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - 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 ((y <= (-7d-50)) .or. (.not. (y <= 1.15d-30))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e-50) || !(y <= 1.15e-30)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e-50) or not (y <= 1.15e-30):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e-50) || !(y <= 1.15e-30))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7e-50) || ~((y <= 1.15e-30)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e-50], N[Not[LessEqual[y, 1.15e-30]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999993e-50 or 1.14999999999999992e-30 < y

   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. +-commutative 99.9%

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

      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 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-*l/ 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*r* 99.9%

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

      11. metadata-eval 99.9%

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

      12. *-lft-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 86.6%

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

   if -6.99999999999999993e-50 < y < 1.14999999999999992e-30

   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 95.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-50} \lor \neg \left(y \leq 1.15 \cdot 10^{-30}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -480000000000:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+108}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -480000000000.0)
   2.0
   (if (<= y 1.6e+108) (* 4.0 (/ (- x z) y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -480000000000.0) {
		tmp = 2.0;
	} else if (y <= 1.6e+108) {
		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 <= (-480000000000.0d0)) then
        tmp = 2.0d0
    else if (y <= 1.6d+108) 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 <= -480000000000.0) {
		tmp = 2.0;
	} else if (y <= 1.6e+108) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -480000000000.0:
		tmp = 2.0
	elif y <= 1.6e+108:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -480000000000.0)
		tmp = 2.0;
	elseif (y <= 1.6e+108)
		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 <= -480000000000.0)
		tmp = 2.0;
	elseif (y <= 1.6e+108)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -480000000000.0], 2.0, If[LessEqual[y, 1.6e+108], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e11 or 1.6e108 < y

   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 74.0%

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

   if -4.8e11 < y < 1.6e108

   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 88.3%

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

Alternative 7: 52.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-50}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e-50) 2.0 (if (<= y 2.55e+108) (* x (/ 4.0 y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e-50) {
		tmp = 2.0;
	} else if (y <= 2.55e+108) {
		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 (y <= (-7.5d-50)) then
        tmp = 2.0d0
    else if (y <= 2.55d+108) 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 (y <= -7.5e-50) {
		tmp = 2.0;
	} else if (y <= 2.55e+108) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e-50:
		tmp = 2.0
	elif y <= 2.55e+108:
		tmp = x * (4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e-50)
		tmp = 2.0;
	elseif (y <= 2.55e+108)
		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 (y <= -7.5e-50)
		tmp = 2.0;
	elseif (y <= 2.55e+108)
		tmp = x * (4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e-50], 2.0, If[LessEqual[y, 2.55e+108], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e-50 or 2.54999999999999984e108 < y

   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 72.0%

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

   if -7.5e-50 < y < 2.54999999999999984e108

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.4%

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

      1. associate-*r/ 53.4%

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

      2. associate-*l/ 53.3%

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

      3. *-commutative 53.3%

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

   5. Simplified 53.3%

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

Alternative 8: 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/ 99.8%

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

   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. Add Preprocessing

Alternative 9: 34.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 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 41.1%

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

Reproduce

herbie shell --seed 2024170 
(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)))