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

Percentage Accurate: 99.7% → 99.9%

Time: 7.7s

Alternatives: 8

Speedup: 1.2×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 1 + \left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (+ (/ (* 4.0 (- x z)) y) 3.0)))

C

double code(double x, double y, double z) {
	return 1.0 + (((4.0 * (x - z)) / y) + 3.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (((4.0d0 * (x - z)) / y) + 3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (((4.0 * (x - z)) / y) + 3.0);
}

Python

def code(x, y, z):
	return 1.0 + (((4.0 * (x - z)) / y) + 3.0)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(Float64(4.0 * Float64(x - z)) / y) + 3.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (((4.0 * (x - z)) / y) + 3.0);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 100.0%

   \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
4. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   2. associate-*r/ 100.0%

      \[\leadsto 1 + \left(\color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} + 3\right) \]

5. Simplified 100.0%

   \[\leadsto 1 + \color{blue}{\left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right)} \]

6. Final simplification 100.0%

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

Alternative 2: 57.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 4 \cdot \frac{x}{y}\\ t_1 := 1 + \frac{z \cdot -4}{y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-210}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-52}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 4.0 (/ x y)))) (t_1 (+ 1.0 (/ (* z -4.0) y))))
   (if (<= z -4.2e+78)
     t_1
     (if (<= z 9e-210)
       t_0
       (if (<= z 5.4e-52) 4.0 (if (<= z 1.35e+39) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (x / y));
	double t_1 = 1.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -4.2e+78) {
		tmp = t_1;
	} else if (z <= 9e-210) {
		tmp = t_0;
	} else if (z <= 5.4e-52) {
		tmp = 4.0;
	} else if (z <= 1.35e+39) {
		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 * (x / y))
    t_1 = 1.0d0 + ((z * (-4.0d0)) / y)
    if (z <= (-4.2d+78)) then
        tmp = t_1
    else if (z <= 9d-210) then
        tmp = t_0
    else if (z <= 5.4d-52) then
        tmp = 4.0d0
    else if (z <= 1.35d+39) 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 * (x / y));
	double t_1 = 1.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -4.2e+78) {
		tmp = t_1;
	} else if (z <= 9e-210) {
		tmp = t_0;
	} else if (z <= 5.4e-52) {
		tmp = 4.0;
	} else if (z <= 1.35e+39) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (4.0 * (x / y))
	t_1 = 1.0 + ((z * -4.0) / y)
	tmp = 0
	if z <= -4.2e+78:
		tmp = t_1
	elif z <= 9e-210:
		tmp = t_0
	elif z <= 5.4e-52:
		tmp = 4.0
	elif z <= 1.35e+39:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	t_1 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	tmp = 0.0
	if (z <= -4.2e+78)
		tmp = t_1;
	elseif (z <= 9e-210)
		tmp = t_0;
	elseif (z <= 5.4e-52)
		tmp = 4.0;
	elseif (z <= 1.35e+39)
		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 * (x / y));
	t_1 = 1.0 + ((z * -4.0) / y);
	tmp = 0.0;
	if (z <= -4.2e+78)
		tmp = t_1;
	elseif (z <= 9e-210)
		tmp = t_0;
	elseif (z <= 5.4e-52)
		tmp = 4.0;
	elseif (z <= 1.35e+39)
		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[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+78], t$95$1, If[LessEqual[z, 9e-210], t$95$0, If[LessEqual[z, 5.4e-52], 4.0, If[LessEqual[z, 1.35e+39], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000002e78 or 1.35000000000000002e39 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-*l/ 74.2%

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

   5. Simplified 74.2%

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

   if -4.2000000000000002e78 < z < 9.00000000000000039e-210 or 5.40000000000000019e-52 < z < 1.35000000000000002e39

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 60.3%

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

   if 9.00000000000000039e-210 < z < 5.40000000000000019e-52

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.0%

      \[\leadsto 1 + \color{blue}{3} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+78}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-210}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-52}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+39}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+155} \lor \neg \left(y \leq 2.3 \cdot 10^{+86}\right):\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+155) (not (<= y 2.3e+86)))
   (+ 1.0 (+ 3.0 (* z (/ -4.0 y))))
   (+ 1.0 (* (- x z) (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+155) || !(y <= 2.3e+86)) {
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	} else {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.2d+155)) .or. (.not. (y <= 2.3d+86))) then
        tmp = 1.0d0 + (3.0d0 + (z * ((-4.0d0) / y)))
    else
        tmp = 1.0d0 + ((x - z) * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+155) || !(y <= 2.3e+86)) {
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	} else {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e+155) or not (y <= 2.3e+86):
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)))
	else:
		tmp = 1.0 + ((x - z) * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e+155) || !(y <= 2.3e+86))
		tmp = Float64(1.0 + Float64(3.0 + Float64(z * Float64(-4.0 / y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x - z) * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e+155) || ~((y <= 2.3e+86)))
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	else
		tmp = 1.0 + ((x - z) * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e+155], N[Not[LessEqual[y, 2.3e+86]], $MachinePrecision]], N[(1.0 + N[(3.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000015e155 or 2.2999999999999999e86 < y

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.5%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{0.75 \cdot y - z}{y}} \]
   4. Step-by-step derivation

      1. div-sub 88.5%

         \[\leadsto 1 + 4 \cdot \color{blue}{\left(\frac{0.75 \cdot y}{y} - \frac{z}{y}\right)} \]

      2. sub-neg 88.5%

         \[\leadsto 1 + 4 \cdot \color{blue}{\left(\frac{0.75 \cdot y}{y} + \left(-\frac{z}{y}\right)\right)} \]

      3. associate-/l* 88.7%

         \[\leadsto 1 + 4 \cdot \left(\color{blue}{0.75 \cdot \frac{y}{y}} + \left(-\frac{z}{y}\right)\right) \]

      4. *-inverses 88.7%

         \[\leadsto 1 + 4 \cdot \left(0.75 \cdot \color{blue}{1} + \left(-\frac{z}{y}\right)\right) \]

      5. metadata-eval 88.7%

         \[\leadsto 1 + 4 \cdot \left(\color{blue}{0.75} + \left(-\frac{z}{y}\right)\right) \]

      6. distribute-lft-in 88.7%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot 0.75 + 4 \cdot \left(-\frac{z}{y}\right)\right)} \]

      7. metadata-eval 88.7%

         \[\leadsto 1 + \left(\color{blue}{3} + 4 \cdot \left(-\frac{z}{y}\right)\right) \]

      8. distribute-rgt-neg-in 88.7%

         \[\leadsto 1 + \left(3 + \color{blue}{\left(-4 \cdot \frac{z}{y}\right)}\right) \]

      9. *-lft-identity 88.7%

         \[\leadsto 1 + \left(3 + \left(-4 \cdot \frac{\color{blue}{1 \cdot z}}{y}\right)\right) \]

      10. associate-*l/ 88.6%

          \[\leadsto 1 + \left(3 + \left(-4 \cdot \color{blue}{\left(\frac{1}{y} \cdot z\right)}\right)\right) \]

      11. associate-*l* 88.6%

          \[\leadsto 1 + \left(3 + \left(-\color{blue}{\left(4 \cdot \frac{1}{y}\right) \cdot z}\right)\right) \]

      12. *-commutative 88.6%

          \[\leadsto 1 + \left(3 + \left(-\color{blue}{z \cdot \left(4 \cdot \frac{1}{y}\right)}\right)\right) \]

      13. distribute-rgt-neg-in 88.6%

          \[\leadsto 1 + \left(3 + \color{blue}{z \cdot \left(-4 \cdot \frac{1}{y}\right)}\right) \]

      14. associate-*r/ 88.6%

          \[\leadsto 1 + \left(3 + z \cdot \left(-\color{blue}{\frac{4 \cdot 1}{y}}\right)\right) \]

      15. metadata-eval 88.6%

          \[\leadsto 1 + \left(3 + z \cdot \left(-\frac{\color{blue}{4}}{y}\right)\right) \]

      16. distribute-neg-frac 88.6%

          \[\leadsto 1 + \left(3 + z \cdot \color{blue}{\frac{-4}{y}}\right) \]

      17. metadata-eval 88.6%

          \[\leadsto 1 + \left(3 + z \cdot \frac{\color{blue}{-4}}{y}\right) \]

   5. Simplified 88.6%

      \[\leadsto 1 + \color{blue}{\left(3 + z \cdot \frac{-4}{y}\right)} \]

   if -7.20000000000000015e155 < y < 2.2999999999999999e86

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.5%

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

      1. *-lft-identity 85.5%

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

      2. associate-*l/ 85.2%

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

      3. associate-*r* 85.2%

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

      4. associate-*r/ 85.2%

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

      5. metadata-eval 85.2%

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

   5. Simplified 85.2%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+155} \lor \neg \left(y \leq 2.3 \cdot 10^{+86}\right):\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+78} \lor \neg \left(z \leq 1.3 \cdot 10^{+38}\right):\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.4e+78) (not (<= z 1.3e+38)))
   (+ 1.0 (+ 3.0 (* z (/ -4.0 y))))
   (+ 1.0 (+ 3.0 (* 4.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.4e+78) || !(z <= 1.3e+38)) {
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	} else {
		tmp = 1.0 + (3.0 + (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 <= (-7.4d+78)) .or. (.not. (z <= 1.3d+38))) then
        tmp = 1.0d0 + (3.0d0 + (z * ((-4.0d0) / y)))
    else
        tmp = 1.0d0 + (3.0d0 + (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 <= -7.4e+78) || !(z <= 1.3e+38)) {
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	} else {
		tmp = 1.0 + (3.0 + (4.0 * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.4e+78) or not (z <= 1.3e+38):
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)))
	else:
		tmp = 1.0 + (3.0 + (4.0 * (x / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.4e+78) || !(z <= 1.3e+38))
		tmp = Float64(1.0 + Float64(3.0 + Float64(z * Float64(-4.0 / y))));
	else
		tmp = Float64(1.0 + Float64(3.0 + Float64(4.0 * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.4e+78) || ~((z <= 1.3e+38)))
		tmp = 1.0 + (3.0 + (z * (-4.0 / y)));
	else
		tmp = 1.0 + (3.0 + (4.0 * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.4e+78], N[Not[LessEqual[z, 1.3e+38]], $MachinePrecision]], N[(1.0 + N[(3.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(3.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.39999999999999969e78 or 1.3e38 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.8%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{0.75 \cdot y - z}{y}} \]
   4. Step-by-step derivation

      1. div-sub 91.8%

         \[\leadsto 1 + 4 \cdot \color{blue}{\left(\frac{0.75 \cdot y}{y} - \frac{z}{y}\right)} \]

      2. sub-neg 91.8%

         \[\leadsto 1 + 4 \cdot \color{blue}{\left(\frac{0.75 \cdot y}{y} + \left(-\frac{z}{y}\right)\right)} \]

      3. associate-/l* 91.9%

         \[\leadsto 1 + 4 \cdot \left(\color{blue}{0.75 \cdot \frac{y}{y}} + \left(-\frac{z}{y}\right)\right) \]

      4. *-inverses 91.9%

         \[\leadsto 1 + 4 \cdot \left(0.75 \cdot \color{blue}{1} + \left(-\frac{z}{y}\right)\right) \]

      5. metadata-eval 91.9%

         \[\leadsto 1 + 4 \cdot \left(\color{blue}{0.75} + \left(-\frac{z}{y}\right)\right) \]

      6. distribute-lft-in 91.9%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot 0.75 + 4 \cdot \left(-\frac{z}{y}\right)\right)} \]

      7. metadata-eval 91.9%

         \[\leadsto 1 + \left(\color{blue}{3} + 4 \cdot \left(-\frac{z}{y}\right)\right) \]

      8. distribute-rgt-neg-in 91.9%

         \[\leadsto 1 + \left(3 + \color{blue}{\left(-4 \cdot \frac{z}{y}\right)}\right) \]

      9. *-lft-identity 91.9%

         \[\leadsto 1 + \left(3 + \left(-4 \cdot \frac{\color{blue}{1 \cdot z}}{y}\right)\right) \]

      10. associate-*l/ 91.6%

          \[\leadsto 1 + \left(3 + \left(-4 \cdot \color{blue}{\left(\frac{1}{y} \cdot z\right)}\right)\right) \]

      11. associate-*l* 91.6%

          \[\leadsto 1 + \left(3 + \left(-\color{blue}{\left(4 \cdot \frac{1}{y}\right) \cdot z}\right)\right) \]

      12. *-commutative 91.6%

          \[\leadsto 1 + \left(3 + \left(-\color{blue}{z \cdot \left(4 \cdot \frac{1}{y}\right)}\right)\right) \]

      13. distribute-rgt-neg-in 91.6%

          \[\leadsto 1 + \left(3 + \color{blue}{z \cdot \left(-4 \cdot \frac{1}{y}\right)}\right) \]

      14. associate-*r/ 91.6%

          \[\leadsto 1 + \left(3 + z \cdot \left(-\color{blue}{\frac{4 \cdot 1}{y}}\right)\right) \]

      15. metadata-eval 91.6%

          \[\leadsto 1 + \left(3 + z \cdot \left(-\frac{\color{blue}{4}}{y}\right)\right) \]

      16. distribute-neg-frac 91.6%

          \[\leadsto 1 + \left(3 + z \cdot \color{blue}{\frac{-4}{y}}\right) \]

      17. metadata-eval 91.6%

          \[\leadsto 1 + \left(3 + z \cdot \frac{\color{blue}{-4}}{y}\right) \]

   5. Simplified 91.6%

      \[\leadsto 1 + \color{blue}{\left(3 + z \cdot \frac{-4}{y}\right)} \]

   if -7.39999999999999969e78 < z < 1.3e38

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

      2. associate-*r/ 100.0%

         \[\leadsto 1 + \left(\color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} + 3\right) \]

   5. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right)} \]

   6. Taylor expanded in x around inf 91.7%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+78} \lor \neg \left(z \leq 1.3 \cdot 10^{+38}\right):\\ \;\;\;\;1 + \left(3 + z \cdot \frac{-4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+77} \lor \neg \left(z \leq 1.08 \cdot 10^{+39}\right):\\ \;\;\;\;1 + \left(3 + \frac{z \cdot -4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.85e+77) (not (<= z 1.08e+39)))
   (+ 1.0 (+ 3.0 (/ (* z -4.0) y)))
   (+ 1.0 (+ 3.0 (* 4.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.85e+77) || !(z <= 1.08e+39)) {
		tmp = 1.0 + (3.0 + ((z * -4.0) / y));
	} else {
		tmp = 1.0 + (3.0 + (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 <= (-1.85d+77)) .or. (.not. (z <= 1.08d+39))) then
        tmp = 1.0d0 + (3.0d0 + ((z * (-4.0d0)) / y))
    else
        tmp = 1.0d0 + (3.0d0 + (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 <= -1.85e+77) || !(z <= 1.08e+39)) {
		tmp = 1.0 + (3.0 + ((z * -4.0) / y));
	} else {
		tmp = 1.0 + (3.0 + (4.0 * (x / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.85e+77) or not (z <= 1.08e+39):
		tmp = 1.0 + (3.0 + ((z * -4.0) / y))
	else:
		tmp = 1.0 + (3.0 + (4.0 * (x / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.85e+77) || !(z <= 1.08e+39))
		tmp = Float64(1.0 + Float64(3.0 + Float64(Float64(z * -4.0) / y)));
	else
		tmp = Float64(1.0 + Float64(3.0 + Float64(4.0 * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.85e+77) || ~((z <= 1.08e+39)))
		tmp = 1.0 + (3.0 + ((z * -4.0) / y));
	else
		tmp = 1.0 + (3.0 + (4.0 * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.85e+77], N[Not[LessEqual[z, 1.08e+39]], $MachinePrecision]], N[(1.0 + N[(3.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(3.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999997e77 or 1.07999999999999998e39 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

      2. associate-*r/ 100.0%

         \[\leadsto 1 + \left(\color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} + 3\right) \]

   5. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right)} \]

   6. Taylor expanded in x around 0 91.9%

      \[\leadsto 1 + \left(\color{blue}{-4 \cdot \frac{z}{y}} + 3\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 91.9%

         \[\leadsto 1 + \left(\color{blue}{\frac{-4 \cdot z}{y}} + 3\right) \]

   8. Simplified 91.9%

      \[\leadsto 1 + \left(\color{blue}{\frac{-4 \cdot z}{y}} + 3\right) \]

   if -1.84999999999999997e77 < z < 1.07999999999999998e39

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

      2. associate-*r/ 100.0%

         \[\leadsto 1 + \left(\color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} + 3\right) \]

   5. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(\frac{4 \cdot \left(x - z\right)}{y} + 3\right)} \]

   6. Taylor expanded in x around inf 91.7%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+77} \lor \neg \left(z \leq 1.08 \cdot 10^{+39}\right):\\ \;\;\;\;1 + \left(3 + \frac{z \cdot -4}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+161}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+161)
   4.0
   (if (<= y 3.6e+177) (+ 1.0 (* (- x z) (/ 4.0 y))) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+161) {
		tmp = 4.0;
	} else if (y <= 3.6e+177) {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d+161)) then
        tmp = 4.0d0
    else if (y <= 3.6d+177) then
        tmp = 1.0d0 + ((x - z) * (4.0d0 / y))
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+161) {
		tmp = 4.0;
	} else if (y <= 3.6e+177) {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+161:
		tmp = 4.0
	elif y <= 3.6e+177:
		tmp = 1.0 + ((x - z) * (4.0 / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+161)
		tmp = 4.0;
	elseif (y <= 3.6e+177)
		tmp = Float64(1.0 + Float64(Float64(x - z) * Float64(4.0 / y)));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+161)
		tmp = 4.0;
	elseif (y <= 3.6e+177)
		tmp = 1.0 + ((x - z) * (4.0 / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+161], 4.0, If[LessEqual[y, 3.6e+177], N[(1.0 + N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999984e161 or 3.60000000000000003e177 < y

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.9%

      \[\leadsto 1 + \color{blue}{3} \]

   if -8.99999999999999984e161 < y < 3.60000000000000003e177

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.7%

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

      1. *-lft-identity 83.7%

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

      2. associate-*l/ 83.4%

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

      3. associate-*r* 83.4%

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

      4. associate-*r/ 83.4%

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

      5. metadata-eval 83.4%

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

   5. Simplified 83.4%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+161}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+156}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+86}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+156) 4.0 (if (<= y 6.2e+86) (+ 1.0 (* 4.0 (/ x y))) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+156) {
		tmp = 4.0;
	} else if (y <= 6.2e+86) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.7d+156)) then
        tmp = 4.0d0
    else if (y <= 6.2d+86) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+156) {
		tmp = 4.0;
	} else if (y <= 6.2e+86) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+156:
		tmp = 4.0
	elif y <= 6.2e+86:
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+156)
		tmp = 4.0;
	elseif (y <= 6.2e+86)
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+156)
		tmp = 4.0;
	elseif (y <= 6.2e+86)
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+156], 4.0, If[LessEqual[y, 6.2e+86], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e156 or 6.2000000000000004e86 < y

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.2%

      \[\leadsto 1 + \color{blue}{3} \]

   if -2.7e156 < y < 6.2000000000000004e86

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 46.4%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+156}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+86}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 4.0)

C

double code(double x, double y, double z) {
	return 4.0;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return 4.0;
}

Python

def code(x, y, z):
	return 4.0

Julia

function code(x, y, z)
	return 4.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0;
end

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 34.4%

   \[\leadsto 1 + \color{blue}{3} \]

4. Final simplification 34.4%

   \[\leadsto 4 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))