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

Percentage Accurate: 99.7% → 100.0%

Time: 7.9s

Alternatives: 9

Speedup: 1.2×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 + (3.0 - (4.0 * ((z - x) / 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 + (3.0d0 - (4.0d0 * ((z - x) / y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

3. Taylor expanded in y around 0 100.0%

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

   1. +-commutative 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+200} \lor \neg \left(z \leq -1.4 \cdot 10^{+82}\right) \land \left(z \leq -4.6 \cdot 10^{+57} \lor \neg \left(z \leq 2 \cdot 10^{+159}\right)\right):\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+200)
         (and (not (<= z -1.4e+82)) (or (<= z -4.6e+57) (not (<= z 2e+159)))))
   (+ 1.0 (* (/ z y) -4.0))
   (+ 4.0 (* x (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+200) || (!(z <= -1.4e+82) && ((z <= -4.6e+57) || !(z <= 2e+159)))) {
		tmp = 1.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 + (x * (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 ((z <= (-1.8d+200)) .or. (.not. (z <= (-1.4d+82))) .and. (z <= (-4.6d+57)) .or. (.not. (z <= 2d+159))) then
        tmp = 1.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 4.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+200) || (!(z <= -1.4e+82) && ((z <= -4.6e+57) || !(z <= 2e+159)))) {
		tmp = 1.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+200) or (not (z <= -1.4e+82) and ((z <= -4.6e+57) or not (z <= 2e+159))):
		tmp = 1.0 + ((z / y) * -4.0)
	else:
		tmp = 4.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+200) || (!(z <= -1.4e+82) && ((z <= -4.6e+57) || !(z <= 2e+159))))
		tmp = Float64(1.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(4.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+200) || (~((z <= -1.4e+82)) && ((z <= -4.6e+57) || ~((z <= 2e+159)))))
		tmp = 1.0 + ((z / y) * -4.0);
	else
		tmp = 4.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+200], And[N[Not[LessEqual[z, -1.4e+82]], $MachinePrecision], Or[LessEqual[z, -4.6e+57], N[Not[LessEqual[z, 2e+159]], $MachinePrecision]]]], N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e200 or -1.4e82 < z < -4.5999999999999998e57 or 1.9999999999999999e159 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

   if -1.7999999999999999e200 < z < -1.4e82 or -4.5999999999999998e57 < z < 1.9999999999999999e159

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 84.6%

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

   7. Taylor expanded in x around 0 84.6%

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

      1. associate-*r/ 84.1%

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

   9. Simplified 84.1%

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

   10. Taylor expanded in x around 0 84.6%

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

       1. *-commutative 84.6%

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

       2. associate-*l/ 84.1%

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

       3. associate-*r/ 84.5%

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

   12. Simplified 84.5%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+200} \lor \neg \left(z \leq -1.4 \cdot 10^{+82}\right) \land \left(z \leq -4.6 \cdot 10^{+57} \lor \neg \left(z \leq 2 \cdot 10^{+159}\right)\right):\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z}{y} \cdot -4\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+200}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{+77}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+45} \lor \neg \left(z \leq 2.05 \cdot 10^{+159}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (/ z y) -4.0))))
   (if (<= z -2.8e+200)
     t_0
     (if (<= z -5.9e+77)
       (+ 4.0 (/ (* 4.0 x) y))
       (if (or (<= z -1.9e+45) (not (<= z 2.05e+159)))
         t_0
         (+ 4.0 (* x (/ 4.0 y))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z / y) * -4.0);
	double tmp;
	if (z <= -2.8e+200) {
		tmp = t_0;
	} else if (z <= -5.9e+77) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if ((z <= -1.9e+45) || !(z <= 2.05e+159)) {
		tmp = t_0;
	} else {
		tmp = 4.0 + (x * (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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + ((z / y) * (-4.0d0))
    if (z <= (-2.8d+200)) then
        tmp = t_0
    else if (z <= (-5.9d+77)) then
        tmp = 4.0d0 + ((4.0d0 * x) / y)
    else if ((z <= (-1.9d+45)) .or. (.not. (z <= 2.05d+159))) then
        tmp = t_0
    else
        tmp = 4.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z / y) * -4.0);
	double tmp;
	if (z <= -2.8e+200) {
		tmp = t_0;
	} else if (z <= -5.9e+77) {
		tmp = 4.0 + ((4.0 * x) / y);
	} else if ((z <= -1.9e+45) || !(z <= 2.05e+159)) {
		tmp = t_0;
	} else {
		tmp = 4.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z / y) * -4.0)
	tmp = 0
	if z <= -2.8e+200:
		tmp = t_0
	elif z <= -5.9e+77:
		tmp = 4.0 + ((4.0 * x) / y)
	elif (z <= -1.9e+45) or not (z <= 2.05e+159):
		tmp = t_0
	else:
		tmp = 4.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z / y) * -4.0))
	tmp = 0.0
	if (z <= -2.8e+200)
		tmp = t_0;
	elseif (z <= -5.9e+77)
		tmp = Float64(4.0 + Float64(Float64(4.0 * x) / y));
	elseif ((z <= -1.9e+45) || !(z <= 2.05e+159))
		tmp = t_0;
	else
		tmp = Float64(4.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z / y) * -4.0);
	tmp = 0.0;
	if (z <= -2.8e+200)
		tmp = t_0;
	elseif (z <= -5.9e+77)
		tmp = 4.0 + ((4.0 * x) / y);
	elseif ((z <= -1.9e+45) || ~((z <= 2.05e+159)))
		tmp = t_0;
	else
		tmp = 4.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+200], t$95$0, If[LessEqual[z, -5.9e+77], N[(4.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.9e+45], N[Not[LessEqual[z, 2.05e+159]], $MachinePrecision]], t$95$0, N[(4.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999985e200 or -5.9e77 < z < -1.9000000000000001e45 or 2.05000000000000007e159 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

   if -2.79999999999999985e200 < z < -5.9e77

   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 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 65.1%

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

   7. Taylor expanded in x around 0 65.1%

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

      1. associate-*r/ 65.1%

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

   9. Simplified 65.1%

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

   if -1.9000000000000001e45 < z < 2.05000000000000007e159

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 87.5%

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

   7. Taylor expanded in x around 0 87.5%

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

      1. associate-*r/ 87.0%

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

   9. Simplified 87.0%

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

   10. Taylor expanded in x around 0 87.5%

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

       1. *-commutative 87.5%

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

       2. associate-*l/ 87.0%

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

       3. associate-*r/ 87.5%

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

   12. Simplified 87.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+200}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{+77}:\\ \;\;\;\;4 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+45} \lor \neg \left(z \leq 2.05 \cdot 10^{+159}\right):\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 4 \cdot \frac{x}{y}\\ t_1 := 1 + \frac{z}{y} \cdot -4\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-241}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-180}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 4.0 (/ x y)))) (t_1 (+ 1.0 (* (/ z y) -4.0))))
   (if (<= z -3.35e+50)
     t_1
     (if (<= z -7.5e-241)
       t_0
       (if (<= z 1.1e-180) 4.0 (if (<= z 1.8e+159) 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 / y) * -4.0);
	double tmp;
	if (z <= -3.35e+50) {
		tmp = t_1;
	} else if (z <= -7.5e-241) {
		tmp = t_0;
	} else if (z <= 1.1e-180) {
		tmp = 4.0;
	} else if (z <= 1.8e+159) {
		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 / y) * (-4.0d0))
    if (z <= (-3.35d+50)) then
        tmp = t_1
    else if (z <= (-7.5d-241)) then
        tmp = t_0
    else if (z <= 1.1d-180) then
        tmp = 4.0d0
    else if (z <= 1.8d+159) 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 / y) * -4.0);
	double tmp;
	if (z <= -3.35e+50) {
		tmp = t_1;
	} else if (z <= -7.5e-241) {
		tmp = t_0;
	} else if (z <= 1.1e-180) {
		tmp = 4.0;
	} else if (z <= 1.8e+159) {
		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 / y) * -4.0)
	tmp = 0
	if z <= -3.35e+50:
		tmp = t_1
	elif z <= -7.5e-241:
		tmp = t_0
	elif z <= 1.1e-180:
		tmp = 4.0
	elif z <= 1.8e+159:
		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 / y) * -4.0))
	tmp = 0.0
	if (z <= -3.35e+50)
		tmp = t_1;
	elseif (z <= -7.5e-241)
		tmp = t_0;
	elseif (z <= 1.1e-180)
		tmp = 4.0;
	elseif (z <= 1.8e+159)
		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 / y) * -4.0);
	tmp = 0.0;
	if (z <= -3.35e+50)
		tmp = t_1;
	elseif (z <= -7.5e-241)
		tmp = t_0;
	elseif (z <= 1.1e-180)
		tmp = 4.0;
	elseif (z <= 1.8e+159)
		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 / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.35e+50], t$95$1, If[LessEqual[z, -7.5e-241], t$95$0, If[LessEqual[z, 1.1e-180], 4.0, If[LessEqual[z, 1.8e+159], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3499999999999999e50 or 1.80000000000000018e159 < z

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -3.3499999999999999e50 < z < -7.49999999999999977e-241 or 1.10000000000000007e-180 < z < 1.80000000000000018e159

   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 52.6%

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

   if -7.49999999999999977e-241 < z < 1.10000000000000007e-180

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 95.9%

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

   7. Taylor expanded in x around 0 63.3%

      \[\leadsto \color{blue}{4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+50}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-241}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-180}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+154} \lor \neg \left(x \leq -3.7 \cdot 10^{+81} \lor \neg \left(x \leq -7.5 \cdot 10^{-43}\right) \land x \leq 2.45 \cdot 10^{+94}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e+154)
         (not
          (or (<= x -3.7e+81) (and (not (<= x -7.5e-43)) (<= x 2.45e+94)))))
   (* 4.0 (/ x y))
   4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+154) || !((x <= -3.7e+81) || (!(x <= -7.5e-43) && (x <= 2.45e+94)))) {
		tmp = 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 ((x <= (-3.8d+154)) .or. (.not. (x <= (-3.7d+81)) .or. (.not. (x <= (-7.5d-43))) .and. (x <= 2.45d+94))) then
        tmp = 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 ((x <= -3.8e+154) || !((x <= -3.7e+81) || (!(x <= -7.5e-43) && (x <= 2.45e+94)))) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e+154) or not ((x <= -3.7e+81) or (not (x <= -7.5e-43) and (x <= 2.45e+94))):
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e+154) || !((x <= -3.7e+81) || (!(x <= -7.5e-43) && (x <= 2.45e+94))))
		tmp = 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 ((x <= -3.8e+154) || ~(((x <= -3.7e+81) || (~((x <= -7.5e-43)) && (x <= 2.45e+94)))))
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e+154], N[Not[Or[LessEqual[x, -3.7e+81], And[N[Not[LessEqual[x, -7.5e-43]], $MachinePrecision], LessEqual[x, 2.45e+94]]]], $MachinePrecision]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998e154 or -3.7000000000000001e81 < x < -7.50000000000000068e-43 or 2.4499999999999999e94 < x

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 83.2%

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

   7. Taylor expanded in x around inf 72.4%

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

   if -3.7999999999999998e154 < x < -3.7000000000000001e81 or -7.50000000000000068e-43 < x < 2.4499999999999999e94

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 58.5%

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

   7. Taylor expanded in x around 0 50.5%

      \[\leadsto \color{blue}{4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+154} \lor \neg \left(x \leq -3.7 \cdot 10^{+81} \lor \neg \left(x \leq -7.5 \cdot 10^{-43}\right) \land x \leq 2.45 \cdot 10^{+94}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+33} \lor \neg \left(z \leq 1.25 \cdot 10^{-64}\right):\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e+33) (not (<= z 1.25e-64)))
   (+ 1.0 (* (- x z) (/ 4.0 y)))
   (+ 4.0 (* x (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e+33) || !(z <= 1.25e-64)) {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	} else {
		tmp = 4.0 + (x * (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 ((z <= (-4.4d+33)) .or. (.not. (z <= 1.25d-64))) then
        tmp = 1.0d0 + ((x - z) * (4.0d0 / y))
    else
        tmp = 4.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e+33) || !(z <= 1.25e-64)) {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	} else {
		tmp = 4.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e+33) or not (z <= 1.25e-64):
		tmp = 1.0 + ((x - z) * (4.0 / y))
	else:
		tmp = 4.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e+33) || !(z <= 1.25e-64))
		tmp = Float64(1.0 + Float64(Float64(x - z) * Float64(4.0 / y)));
	else
		tmp = Float64(4.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.4e+33) || ~((z <= 1.25e-64)))
		tmp = 1.0 + ((x - z) * (4.0 / y));
	else
		tmp = 4.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e+33], N[Not[LessEqual[z, 1.25e-64]], $MachinePrecision]], N[(1.0 + N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999988e33 or 1.25000000000000008e-64 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 86.6%

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

      1. *-commutative 86.6%

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

      2. *-rgt-identity 86.6%

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

      3. associate-*r/ 86.4%

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

      4. associate-*l* 86.4%

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

      5. associate-*l/ 86.4%

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

      6. metadata-eval 86.4%

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

   5. Simplified 86.4%

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

   if -4.39999999999999988e33 < z < 1.25000000000000008e-64

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 92.8%

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

   7. Taylor expanded in x around 0 92.8%

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

      1. associate-*r/ 92.1%

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

   9. Simplified 92.1%

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

   10. Taylor expanded in x around 0 92.8%

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

       1. *-commutative 92.8%

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

       2. associate-*l/ 92.1%

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

       3. associate-*r/ 92.8%

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

   12. Simplified 92.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+33} \lor \neg \left(z \leq 1.25 \cdot 10^{-64}\right):\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+54} \lor \neg \left(z \leq 1.25 \cdot 10^{-64}\right):\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+54) (not (<= z 1.25e-64)))
   (+ 1.0 (* (- x 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 <= -6e+54) || !(z <= 1.25e-64)) {
		tmp = 1.0 + ((x - 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 <= (-6d+54)) .or. (.not. (z <= 1.25d-64))) then
        tmp = 1.0d0 + ((x - 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 <= -6e+54) || !(z <= 1.25e-64)) {
		tmp = 1.0 + ((x - 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 <= -6e+54) or not (z <= 1.25e-64):
		tmp = 1.0 + ((x - 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 <= -6e+54) || !(z <= 1.25e-64))
		tmp = Float64(1.0 + Float64(Float64(x - 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 <= -6e+54) || ~((z <= 1.25e-64)))
		tmp = 1.0 + ((x - 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, -6e+54], N[Not[LessEqual[z, 1.25e-64]], $MachinePrecision]], N[(1.0 + N[(N[(x - z), $MachinePrecision] * N[(4.0 / 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 < -5.9999999999999998e54 or 1.25000000000000008e-64 < z

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 86.6%

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

      1. *-commutative 86.6%

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

      2. *-rgt-identity 86.6%

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

      3. associate-*r/ 86.4%

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

      4. associate-*l* 86.4%

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

      5. associate-*l/ 86.4%

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

      6. metadata-eval 86.4%

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

   5. Simplified 86.4%

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

   if -5.9999999999999998e54 < z < 1.25000000000000008e-64

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 92.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+54} \lor \neg \left(z \leq 1.25 \cdot 10^{-64}\right):\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + 4 \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+95}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+44}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.8e+95) 4.0 (if (<= y 3.1e+44) (+ 1.0 (* 4.0 (/ x y))) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.8e+95) {
		tmp = 4.0;
	} else if (y <= 3.1e+44) {
		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 <= (-7.8d+95)) then
        tmp = 4.0d0
    else if (y <= 3.1d+44) 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 <= -7.8e+95) {
		tmp = 4.0;
	} else if (y <= 3.1e+44) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.8e+95:
		tmp = 4.0
	elif y <= 3.1e+44:
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.8e+95)
		tmp = 4.0;
	elseif (y <= 3.1e+44)
		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 <= -7.8e+95)
		tmp = 4.0;
	elseif (y <= 3.1e+44)
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.8e+95], 4.0, If[LessEqual[y, 3.1e+44], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7999999999999994e95 or 3.09999999999999996e44 < y

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 85.7%

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

   7. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{4} \]

   if -7.7999999999999994e95 < y < 3.09999999999999996e44

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 51.1%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+95}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+44}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.4% 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 99.2%

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

3. Taylor expanded in y around 0 100.0%

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

   1. +-commutative 100.0%

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

5. Simplified 100.0%

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

6. Taylor expanded in x around inf 69.6%

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

7. Taylor expanded in x around 0 33.5%

   \[\leadsto \color{blue}{4} \]

8. Final simplification 33.5%

   \[\leadsto 4 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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)))