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

Percentage Accurate: 99.8% → 99.8%

Time: 8.1s

Alternatives: 7

Speedup: 1.0×

• 20.9% 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: 99.8% 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: 99.8% 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 57.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{-4}{\frac{y}{z}}\\ t_1 := 1 + \frac{4}{\frac{y}{x}}\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-160}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-200}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-242}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-173}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ -4.0 (/ y z)))) (t_1 (+ 1.0 (/ 4.0 (/ y x)))))
   (if (<= x -5.3e-11)
     t_1
     (if (<= x -5.2e-160)
       t_0
       (if (<= x -6e-200)
         2.0
         (if (<= x 1.2e-242)
           t_0
           (if (<= x 1.45e-173) 2.0 (if (<= x 1.45e-13) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (-4.0 / (y / z));
	double t_1 = 1.0 + (4.0 / (y / x));
	double tmp;
	if (x <= -5.3e-11) {
		tmp = t_1;
	} else if (x <= -5.2e-160) {
		tmp = t_0;
	} else if (x <= -6e-200) {
		tmp = 2.0;
	} else if (x <= 1.2e-242) {
		tmp = t_0;
	} else if (x <= 1.45e-173) {
		tmp = 2.0;
	} else if (x <= 1.45e-13) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((-4.0d0) / (y / z))
    t_1 = 1.0d0 + (4.0d0 / (y / x))
    if (x <= (-5.3d-11)) then
        tmp = t_1
    else if (x <= (-5.2d-160)) then
        tmp = t_0
    else if (x <= (-6d-200)) then
        tmp = 2.0d0
    else if (x <= 1.2d-242) then
        tmp = t_0
    else if (x <= 1.45d-173) then
        tmp = 2.0d0
    else if (x <= 1.45d-13) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (-4.0 / (y / z));
	double t_1 = 1.0 + (4.0 / (y / x));
	double tmp;
	if (x <= -5.3e-11) {
		tmp = t_1;
	} else if (x <= -5.2e-160) {
		tmp = t_0;
	} else if (x <= -6e-200) {
		tmp = 2.0;
	} else if (x <= 1.2e-242) {
		tmp = t_0;
	} else if (x <= 1.45e-173) {
		tmp = 2.0;
	} else if (x <= 1.45e-13) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (-4.0 / (y / z))
	t_1 = 1.0 + (4.0 / (y / x))
	tmp = 0
	if x <= -5.3e-11:
		tmp = t_1
	elif x <= -5.2e-160:
		tmp = t_0
	elif x <= -6e-200:
		tmp = 2.0
	elif x <= 1.2e-242:
		tmp = t_0
	elif x <= 1.45e-173:
		tmp = 2.0
	elif x <= 1.45e-13:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(-4.0 / Float64(y / z)))
	t_1 = Float64(1.0 + Float64(4.0 / Float64(y / x)))
	tmp = 0.0
	if (x <= -5.3e-11)
		tmp = t_1;
	elseif (x <= -5.2e-160)
		tmp = t_0;
	elseif (x <= -6e-200)
		tmp = 2.0;
	elseif (x <= 1.2e-242)
		tmp = t_0;
	elseif (x <= 1.45e-173)
		tmp = 2.0;
	elseif (x <= 1.45e-13)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (-4.0 / (y / z));
	t_1 = 1.0 + (4.0 / (y / x));
	tmp = 0.0;
	if (x <= -5.3e-11)
		tmp = t_1;
	elseif (x <= -5.2e-160)
		tmp = t_0;
	elseif (x <= -6e-200)
		tmp = 2.0;
	elseif (x <= 1.2e-242)
		tmp = t_0;
	elseif (x <= 1.45e-173)
		tmp = 2.0;
	elseif (x <= 1.45e-13)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(-4.0 / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.3e-11], t$95$1, If[LessEqual[x, -5.2e-160], t$95$0, If[LessEqual[x, -6e-200], 2.0, If[LessEqual[x, 1.2e-242], t$95$0, If[LessEqual[x, 1.45e-173], 2.0, If[LessEqual[x, 1.45e-13], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2999999999999998e-11 or 1.4499999999999999e-13 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-/l* 60.8%

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

   5. Simplified 60.8%

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

   if -5.2999999999999998e-11 < x < -5.20000000000000007e-160 or -5.99999999999999989e-200 < x < 1.2e-242 or 1.4499999999999999e-173 < x < 1.4499999999999999e-13

   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 66.4%

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

      1. associate-*r/ 66.4%

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

      2. associate-/l* 66.2%

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

   5. Simplified 66.2%

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

   if -5.20000000000000007e-160 < x < -5.99999999999999989e-200 or 1.2e-242 < x < 1.4499999999999999e-173

   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 82.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-11}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-160}:\\ \;\;\;\;1 + \frac{-4}{\frac{y}{z}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-200}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-242}:\\ \;\;\;\;1 + \frac{-4}{\frac{y}{z}}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-173}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-13}:\\ \;\;\;\;1 + \frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-131} \lor \neg \left(z \leq 1.25 \cdot 10^{+48}\right):\\ \;\;\;\;1 + \frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e-131) (not (<= z 1.25e+48))) (+ 1.0 (/ -4.0 (/ y z))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-131) || !(z <= 1.25e+48)) {
		tmp = 1.0 + (-4.0 / (y / 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 ((z <= (-2.3d-131)) .or. (.not. (z <= 1.25d+48))) then
        tmp = 1.0d0 + ((-4.0d0) / (y / 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 ((z <= -2.3e-131) || !(z <= 1.25e+48)) {
		tmp = 1.0 + (-4.0 / (y / z));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e-131) or not (z <= 1.25e+48):
		tmp = 1.0 + (-4.0 / (y / z))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e-131) || !(z <= 1.25e+48))
		tmp = Float64(1.0 + Float64(-4.0 / Float64(y / z)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.3e-131) || ~((z <= 1.25e+48)))
		tmp = 1.0 + (-4.0 / (y / z));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e-131], N[Not[LessEqual[z, 1.25e+48]], $MachinePrecision]], N[(1.0 + N[(-4.0 / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000022e-131 or 1.24999999999999993e48 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 65.2%

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

      1. associate-*r/ 65.2%

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

      2. associate-/l* 65.0%

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

   5. Simplified 65.0%

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

   if -2.30000000000000022e-131 < z < 1.24999999999999993e48

   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 45.8%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-131} \lor \neg \left(z \leq 1.25 \cdot 10^{+48}\right):\\ \;\;\;\;1 + \frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+81} \lor \neg \left(z \leq 3.5 \cdot 10^{+86}\right):\\ \;\;\;\;1 + \frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.2e+81) (not (<= z 3.5e+86)))
   (+ 1.0 (/ -4.0 (/ y z)))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+81) || !(z <= 3.5e+86)) {
		tmp = 1.0 + (-4.0 / (y / z));
	} 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 <= (-3.2d+81)) .or. (.not. (z <= 3.5d+86))) then
        tmp = 1.0d0 + ((-4.0d0) / (y / z))
    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 <= -3.2e+81) || !(z <= 3.5e+86)) {
		tmp = 1.0 + (-4.0 / (y / z));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.2e+81) or not (z <= 3.5e+86):
		tmp = 1.0 + (-4.0 / (y / z))
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.2e+81) || !(z <= 3.5e+86))
		tmp = Float64(1.0 + Float64(-4.0 / Float64(y / z)));
	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 <= -3.2e+81) || ~((z <= 3.5e+86)))
		tmp = 1.0 + (-4.0 / (y / z));
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.2e+81], N[Not[LessEqual[z, 3.5e+86]], $MachinePrecision]], N[(1.0 + N[(-4.0 / N[(y / z), $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 < -3.2e81 or 3.50000000000000019e86 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 77.7%

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

      1. associate-*r/ 77.7%

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

      2. associate-/l* 77.5%

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

   5. Simplified 77.5%

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

   if -3.2e81 < z < 3.50000000000000019e86

   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. Add Preprocessing

   5. Taylor expanded in z around 0 86.4%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+81} \lor \neg \left(z \leq 3.5 \cdot 10^{+86}\right):\\ \;\;\;\;1 + \frac{-4}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+79} \lor \neg \left(z \leq 1.46 \cdot 10^{+32}\right):\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e+79) (not (<= z 1.46e+32)))
   (+ 2.0 (/ (* z -4.0) y))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e+79) || !(z <= 1.46e+32)) {
		tmp = 2.0 + ((z * -4.0) / 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 <= (-4d+79)) .or. (.not. (z <= 1.46d+32))) then
        tmp = 2.0d0 + ((z * (-4.0d0)) / 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 <= -4e+79) || !(z <= 1.46e+32)) {
		tmp = 2.0 + ((z * -4.0) / y);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e+79) or not (z <= 1.46e+32):
		tmp = 2.0 + ((z * -4.0) / y)
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e+79) || !(z <= 1.46e+32))
		tmp = Float64(2.0 + Float64(Float64(z * -4.0) / 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 <= -4e+79) || ~((z <= 1.46e+32)))
		tmp = 2.0 + ((z * -4.0) / y);
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e+79], N[Not[LessEqual[z, 1.46e+32]], $MachinePrecision]], N[(2.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999987e79 or 1.46000000000000005e32 < z

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

      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 x around 0 86.2%

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

      1. +-commutative 86.2%

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

      2. associate-*r/ 86.2%

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

   7. Simplified 86.2%

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

   if -3.99999999999999987e79 < z < 1.46000000000000005e32

   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. Add Preprocessing

   5. Taylor expanded in z around 0 89.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+79} \lor \neg \left(z \leq 1.46 \cdot 10^{+32}\right):\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 99.9%

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

   1. associate-*l/ 99.7%

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

   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. Final simplification 99.7%

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

Alternative 7: 34.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 31.4%

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

4. Final simplification 31.4%

   \[\leadsto 2 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))