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

Percentage Accurate: 99.9% → 100.0%

Time: 7.5s

Alternatives: 8

Speedup: 1.4×

• 21.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in y around 0 100.0%

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

   1. +-commutative 100.0%

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

6. Simplified 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 54.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+109} \lor \neg \left(x \leq -1.6 \cdot 10^{+42}\right) \land \left(x \leq -0.0031 \lor \neg \left(x \leq 7.5 \cdot 10^{-16}\right)\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+109)
         (and (not (<= x -1.6e+42)) (or (<= x -0.0031) (not (<= x 7.5e-16)))))
   (+ (* 4.0 (/ x y)) 1.0)
   2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+109) || (!(x <= -1.6e+42) && ((x <= -0.0031) || !(x <= 7.5e-16)))) {
		tmp = (4.0 * (x / y)) + 1.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.8d+109)) .or. (.not. (x <= (-1.6d+42))) .and. (x <= (-0.0031d0)) .or. (.not. (x <= 7.5d-16))) then
        tmp = (4.0d0 * (x / y)) + 1.0d0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+109) || (!(x <= -1.6e+42) && ((x <= -0.0031) || !(x <= 7.5e-16)))) {
		tmp = (4.0 * (x / y)) + 1.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e+109) or (not (x <= -1.6e+42) and ((x <= -0.0031) or not (x <= 7.5e-16))):
		tmp = (4.0 * (x / y)) + 1.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+109) || (!(x <= -1.6e+42) && ((x <= -0.0031) || !(x <= 7.5e-16))))
		tmp = Float64(Float64(4.0 * Float64(x / y)) + 1.0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e+109) || (~((x <= -1.6e+42)) && ((x <= -0.0031) || ~((x <= 7.5e-16)))))
		tmp = (4.0 * (x / y)) + 1.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+109], And[N[Not[LessEqual[x, -1.6e+42]], $MachinePrecision], Or[LessEqual[x, -0.0031], N[Not[LessEqual[x, 7.5e-16]], $MachinePrecision]]]], N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.8e109 or -1.60000000000000001e42 < x < -0.00309999999999999989 or 7.5e-16 < x

   1. Initial program 100.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 70.1%

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

   if -5.8e109 < x < -1.60000000000000001e42 or -0.00309999999999999989 < x < 7.5e-16

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 51.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+109} \lor \neg \left(x \leq -1.6 \cdot 10^{+42}\right) \land \left(x \leq -0.0031 \lor \neg \left(x \leq 7.5 \cdot 10^{-16}\right)\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 3: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y} + 1\\ t_1 := 1 + z \cdot \frac{-4}{y}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-246}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-220}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 4.0 (/ x y)) 1.0)) (t_1 (+ 1.0 (* z (/ -4.0 y)))))
   (if (<= z -1.9e+20)
     t_1
     (if (<= z 4.3e-246)
       t_0
       (if (<= z 4.1e-220) 2.0 (if (<= z 4.3e+110) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + (z * (-4.0 / y));
	double tmp;
	if (z <= -1.9e+20) {
		tmp = t_1;
	} else if (z <= 4.3e-246) {
		tmp = t_0;
	} else if (z <= 4.1e-220) {
		tmp = 2.0;
	} else if (z <= 4.3e+110) {
		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 = (4.0d0 * (x / y)) + 1.0d0
    t_1 = 1.0d0 + (z * ((-4.0d0) / y))
    if (z <= (-1.9d+20)) then
        tmp = t_1
    else if (z <= 4.3d-246) then
        tmp = t_0
    else if (z <= 4.1d-220) then
        tmp = 2.0d0
    else if (z <= 4.3d+110) 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 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + (z * (-4.0 / y));
	double tmp;
	if (z <= -1.9e+20) {
		tmp = t_1;
	} else if (z <= 4.3e-246) {
		tmp = t_0;
	} else if (z <= 4.1e-220) {
		tmp = 2.0;
	} else if (z <= 4.3e+110) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * (x / y)) + 1.0
	t_1 = 1.0 + (z * (-4.0 / y))
	tmp = 0
	if z <= -1.9e+20:
		tmp = t_1
	elif z <= 4.3e-246:
		tmp = t_0
	elif z <= 4.1e-220:
		tmp = 2.0
	elif z <= 4.3e+110:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(x / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(z * Float64(-4.0 / y)))
	tmp = 0.0
	if (z <= -1.9e+20)
		tmp = t_1;
	elseif (z <= 4.3e-246)
		tmp = t_0;
	elseif (z <= 4.1e-220)
		tmp = 2.0;
	elseif (z <= 4.3e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * (x / y)) + 1.0;
	t_1 = 1.0 + (z * (-4.0 / y));
	tmp = 0.0;
	if (z <= -1.9e+20)
		tmp = t_1;
	elseif (z <= 4.3e-246)
		tmp = t_0;
	elseif (z <= 4.1e-220)
		tmp = 2.0;
	elseif (z <= 4.3e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+20], t$95$1, If[LessEqual[z, 4.3e-246], t$95$0, If[LessEqual[z, 4.1e-220], 2.0, If[LessEqual[z, 4.3e+110], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e20 or 4.30000000000000007e110 < z

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 72.7%

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

      1. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in z around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-*r/ 72.5%

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

   9. Simplified 72.5%

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

   if -1.9e20 < z < 4.29999999999999992e-246 or 4.09999999999999991e-220 < z < 4.30000000000000007e110

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 64.9%

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

   if 4.29999999999999992e-246 < z < 4.09999999999999991e-220

   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* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+20}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-220}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+110}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \end{array} \]

Alternative 4: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y} + 1\\ t_1 := 1 + \frac{z}{y} \cdot -4\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-246}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-219}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 4.0 (/ x y)) 1.0)) (t_1 (+ 1.0 (* (/ z y) -4.0))))
   (if (<= z -1.56e+16)
     t_1
     (if (<= z 9.5e-246)
       t_0
       (if (<= z 1.45e-219) 2.0 (if (<= z 5.4e+110) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + ((z / y) * -4.0);
	double tmp;
	if (z <= -1.56e+16) {
		tmp = t_1;
	} else if (z <= 9.5e-246) {
		tmp = t_0;
	} else if (z <= 1.45e-219) {
		tmp = 2.0;
	} else if (z <= 5.4e+110) {
		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 = (4.0d0 * (x / y)) + 1.0d0
    t_1 = 1.0d0 + ((z / y) * (-4.0d0))
    if (z <= (-1.56d+16)) then
        tmp = t_1
    else if (z <= 9.5d-246) then
        tmp = t_0
    else if (z <= 1.45d-219) then
        tmp = 2.0d0
    else if (z <= 5.4d+110) 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 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + ((z / y) * -4.0);
	double tmp;
	if (z <= -1.56e+16) {
		tmp = t_1;
	} else if (z <= 9.5e-246) {
		tmp = t_0;
	} else if (z <= 1.45e-219) {
		tmp = 2.0;
	} else if (z <= 5.4e+110) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * (x / y)) + 1.0
	t_1 = 1.0 + ((z / y) * -4.0)
	tmp = 0
	if z <= -1.56e+16:
		tmp = t_1
	elif z <= 9.5e-246:
		tmp = t_0
	elif z <= 1.45e-219:
		tmp = 2.0
	elif z <= 5.4e+110:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(x / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(Float64(z / y) * -4.0))
	tmp = 0.0
	if (z <= -1.56e+16)
		tmp = t_1;
	elseif (z <= 9.5e-246)
		tmp = t_0;
	elseif (z <= 1.45e-219)
		tmp = 2.0;
	elseif (z <= 5.4e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * (x / y)) + 1.0;
	t_1 = 1.0 + ((z / y) * -4.0);
	tmp = 0.0;
	if (z <= -1.56e+16)
		tmp = t_1;
	elseif (z <= 9.5e-246)
		tmp = t_0;
	elseif (z <= 1.45e-219)
		tmp = 2.0;
	elseif (z <= 5.4e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.56e+16], t$95$1, If[LessEqual[z, 9.5e-246], t$95$0, If[LessEqual[z, 1.45e-219], 2.0, If[LessEqual[z, 5.4e+110], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.56e16 or 5.40000000000000019e110 < z

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 72.7%

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

      1. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   if -1.56e16 < z < 9.5000000000000002e-246 or 1.44999999999999992e-219 < z < 5.40000000000000019e110

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 64.9%

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

   if 9.5000000000000002e-246 < z < 1.44999999999999992e-219

   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* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+16}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-219}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \end{array} \]

Alternative 5: 81.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+98} \lor \neg \left(z \leq 1.12 \cdot 10^{+114}\right):\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e+98) (not (<= z 1.12e+114)))
   (+ 1.0 (* (/ z y) -4.0))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+98) || !(z <= 1.12e+114)) {
		tmp = 1.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (4.0 * (x / 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 ((z <= (-4.2d+98)) .or. (.not. (z <= 1.12d+114))) then
        tmp = 1.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 2.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+98) || !(z <= 1.12e+114)) {
		tmp = 1.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e+98) or not (z <= 1.12e+114):
		tmp = 1.0 + ((z / y) * -4.0)
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e+98) || !(z <= 1.12e+114))
		tmp = Float64(1.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.2e+98) || ~((z <= 1.12e+114)))
		tmp = 1.0 + ((z / y) * -4.0);
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e+98], N[Not[LessEqual[z, 1.12e+114]], $MachinePrecision]], N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000008e98 or 1.11999999999999999e114 < z

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. *-commutative 75.9%

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

   6. Simplified 75.9%

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

   if -4.20000000000000008e98 < z < 1.11999999999999999e114

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 91.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+98} \lor \neg \left(z \leq 1.12 \cdot 10^{+114}\right):\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 85.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+25} \lor \neg \left(z \leq 4.6 \cdot 10^{+110}\right):\\ \;\;\;\;2 - 4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.2e+25) (not (<= z 4.6e+110)))
   (- 2.0 (* 4.0 (/ z y)))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e+25) || !(z <= 4.6e+110)) {
		tmp = 2.0 - (4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / 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 ((z <= (-5.2d+25)) .or. (.not. (z <= 4.6d+110))) then
        tmp = 2.0d0 - (4.0d0 * (z / y))
    else
        tmp = 2.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e+25) || !(z <= 4.6e+110)) {
		tmp = 2.0 - (4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.2e+25) or not (z <= 4.6e+110):
		tmp = 2.0 - (4.0 * (z / y))
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.2e+25) || !(z <= 4.6e+110))
		tmp = Float64(2.0 - Float64(4.0 * Float64(z / y)));
	else
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.2e+25) || ~((z <= 4.6e+110)))
		tmp = 2.0 - (4.0 * (z / y));
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.2e+25], N[Not[LessEqual[z, 4.6e+110]], $MachinePrecision]], N[(2.0 - N[(4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999997e25 or 4.6e110 < z

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 89.5%

         \[\leadsto 4 \cdot \color{blue}{\frac{-1 \cdot z}{y}} + 2 \]

      2. neg-mul-1 89.5%

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

   9. Simplified 89.5%

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

   if -5.1999999999999997e25 < z < 4.6e110

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 93.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+25} \lor \neg \left(z \leq 4.6 \cdot 10^{+110}\right):\\ \;\;\;\;2 - 4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate-*l/ 99.7%

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

   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 99.8%

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

   5. associate-+r+ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 8: 33.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 100.0%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in y around inf 30.5%

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

5. Final simplification 30.5%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023279 
(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)))