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

Percentage Accurate: 99.8% → 100.0%

Time: 7.8s

Alternatives: 8

Speedup: 1.4×

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

Specification

Math

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

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: 99.8% 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, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

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

   2. +-commutative 99.7%

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

   3. fma-def 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in y around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 54.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+108} \lor \neg \left(x \leq -1.8 \cdot 10^{+43}\right) \land \left(x \leq -0.0062 \lor \neg \left(x \leq 2.5 \cdot 10^{-13}\right)\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.5e+108)
         (and (not (<= x -1.8e+43)) (or (<= x -0.0062) (not (<= x 2.5e-13)))))
   (+ (* 4.0 (/ x y)) 1.0)
   4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e+108) || (!(x <= -1.8e+43) && ((x <= -0.0062) || !(x <= 2.5e-13)))) {
		tmp = (4.0 * (x / y)) + 1.0;
	} 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 <= (-3.5d+108)) .or. (.not. (x <= (-1.8d+43))) .and. (x <= (-0.0062d0)) .or. (.not. (x <= 2.5d-13))) then
        tmp = (4.0d0 * (x / y)) + 1.0d0
    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 <= -3.5e+108) || (!(x <= -1.8e+43) && ((x <= -0.0062) || !(x <= 2.5e-13)))) {
		tmp = (4.0 * (x / y)) + 1.0;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.5e+108) or (not (x <= -1.8e+43) and ((x <= -0.0062) or not (x <= 2.5e-13))):
		tmp = (4.0 * (x / y)) + 1.0
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.5e+108) || (!(x <= -1.8e+43) && ((x <= -0.0062) || !(x <= 2.5e-13))))
		tmp = Float64(Float64(4.0 * Float64(x / y)) + 1.0);
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.5e+108) || (~((x <= -1.8e+43)) && ((x <= -0.0062) || ~((x <= 2.5e-13)))))
		tmp = (4.0 * (x / y)) + 1.0;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e+108], And[N[Not[LessEqual[x, -1.8e+43]], $MachinePrecision], Or[LessEqual[x, -0.0062], N[Not[LessEqual[x, 2.5e-13]], $MachinePrecision]]]], N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000002e108 or -1.80000000000000005e43 < x < -0.00619999999999999978 or 2.49999999999999995e-13 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 70.0%

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

   if -3.5000000000000002e108 < x < -1.80000000000000005e43 or -0.00619999999999999978 < x < 2.49999999999999995e-13

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 51.1%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+108} \lor \neg \left(x \leq -1.8 \cdot 10^{+43}\right) \land \left(x \leq -0.0062 \lor \neg \left(x \leq 2.5 \cdot 10^{-13}\right)\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 3: 57.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y} + 1\\ t_1 := 1 + z \cdot \frac{-4}{y}\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-246}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-220}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 4.0 (/ x y)) 1.0)) (t_1 (+ 1.0 (* z (/ -4.0 y)))))
   (if (<= z -2.45e+25)
     t_1
     (if (<= z 6.2e-246)
       t_0
       (if (<= z 2.9e-220) 4.0 (if (<= z 4.6e+110) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + (z * (-4.0 / y));
	double tmp;
	if (z <= -2.45e+25) {
		tmp = t_1;
	} else if (z <= 6.2e-246) {
		tmp = t_0;
	} else if (z <= 2.9e-220) {
		tmp = 4.0;
	} else if (z <= 4.6e+110) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * (x / y)) + 1.0d0
    t_1 = 1.0d0 + (z * ((-4.0d0) / y))
    if (z <= (-2.45d+25)) then
        tmp = t_1
    else if (z <= 6.2d-246) then
        tmp = t_0
    else if (z <= 2.9d-220) then
        tmp = 4.0d0
    else if (z <= 4.6d+110) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + (z * (-4.0 / y));
	double tmp;
	if (z <= -2.45e+25) {
		tmp = t_1;
	} else if (z <= 6.2e-246) {
		tmp = t_0;
	} else if (z <= 2.9e-220) {
		tmp = 4.0;
	} else if (z <= 4.6e+110) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * (x / y)) + 1.0
	t_1 = 1.0 + (z * (-4.0 / y))
	tmp = 0
	if z <= -2.45e+25:
		tmp = t_1
	elif z <= 6.2e-246:
		tmp = t_0
	elif z <= 2.9e-220:
		tmp = 4.0
	elif z <= 4.6e+110:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(x / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(z * Float64(-4.0 / y)))
	tmp = 0.0
	if (z <= -2.45e+25)
		tmp = t_1;
	elseif (z <= 6.2e-246)
		tmp = t_0;
	elseif (z <= 2.9e-220)
		tmp = 4.0;
	elseif (z <= 4.6e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * (x / y)) + 1.0;
	t_1 = 1.0 + (z * (-4.0 / y));
	tmp = 0.0;
	if (z <= -2.45e+25)
		tmp = t_1;
	elseif (z <= 6.2e-246)
		tmp = t_0;
	elseif (z <= 2.9e-220)
		tmp = 4.0;
	elseif (z <= 4.6e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e+25], t$95$1, If[LessEqual[z, 6.2e-246], t$95$0, If[LessEqual[z, 2.9e-220], 4.0, If[LessEqual[z, 4.6e+110], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45e25 or 4.6e110 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 82.1%

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

   5. Taylor expanded in x around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r/ 72.1%

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

   7. Simplified 72.1%

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

   if -2.45e25 < z < 6.2000000000000001e-246 or 2.8999999999999998e-220 < z < 4.6e110

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 64.3%

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

   if 6.2000000000000001e-246 < z < 2.8999999999999998e-220

   1. Initial program 99.5%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+25}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-220}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+110}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \end{array} \]

Alternative 4: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y} + 1\\ t_1 := 1 + \frac{z \cdot -4}{y}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-246}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-220}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 4.0 (/ x y)) 1.0)) (t_1 (+ 1.0 (/ (* z -4.0) y))))
   (if (<= z -7.5e+24)
     t_1
     (if (<= z 4.3e-246)
       t_0
       (if (<= z 3.45e-220) 4.0 (if (<= z 4.6e+110) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -7.5e+24) {
		tmp = t_1;
	} else if (z <= 4.3e-246) {
		tmp = t_0;
	} else if (z <= 3.45e-220) {
		tmp = 4.0;
	} else if (z <= 4.6e+110) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * (x / y)) + 1.0d0
    t_1 = 1.0d0 + ((z * (-4.0d0)) / y)
    if (z <= (-7.5d+24)) then
        tmp = t_1
    else if (z <= 4.3d-246) then
        tmp = t_0
    else if (z <= 3.45d-220) then
        tmp = 4.0d0
    else if (z <= 4.6d+110) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * (x / y)) + 1.0;
	double t_1 = 1.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -7.5e+24) {
		tmp = t_1;
	} else if (z <= 4.3e-246) {
		tmp = t_0;
	} else if (z <= 3.45e-220) {
		tmp = 4.0;
	} else if (z <= 4.6e+110) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * (x / y)) + 1.0
	t_1 = 1.0 + ((z * -4.0) / y)
	tmp = 0
	if z <= -7.5e+24:
		tmp = t_1
	elif z <= 4.3e-246:
		tmp = t_0
	elif z <= 3.45e-220:
		tmp = 4.0
	elif z <= 4.6e+110:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(x / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	tmp = 0.0
	if (z <= -7.5e+24)
		tmp = t_1;
	elseif (z <= 4.3e-246)
		tmp = t_0;
	elseif (z <= 3.45e-220)
		tmp = 4.0;
	elseif (z <= 4.6e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * (x / y)) + 1.0;
	t_1 = 1.0 + ((z * -4.0) / y);
	tmp = 0.0;
	if (z <= -7.5e+24)
		tmp = t_1;
	elseif (z <= 4.3e-246)
		tmp = t_0;
	elseif (z <= 3.45e-220)
		tmp = 4.0;
	elseif (z <= 4.6e+110)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+24], t$95$1, If[LessEqual[z, 4.3e-246], t$95$0, If[LessEqual[z, 3.45e-220], 4.0, If[LessEqual[z, 4.6e+110], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000014e24 or 4.6e110 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. metadata-eval 72.3%

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

      3. associate-*r* 72.3%

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

      4. neg-mul-1 72.3%

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

      5. associate-*l/ 72.1%

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

      6. *-commutative 72.1%

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

      7. associate-*r/ 72.3%

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

      8. neg-mul-1 72.3%

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

      9. *-commutative 72.3%

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

      10. associate-*l* 72.3%

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

      11. metadata-eval 72.3%

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

   6. Simplified 72.3%

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

   if -7.50000000000000014e24 < z < 4.29999999999999992e-246 or 3.4499999999999999e-220 < z < 4.6e110

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 64.3%

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

   if 4.29999999999999992e-246 < z < 3.4499999999999999e-220

   1. Initial program 99.5%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+24}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-246}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-220}:\\ \;\;\;\;4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+110}:\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \end{array} \]

Alternative 5: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;4 - 4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.2e+25)
   (- 4.0 (* 4.0 (/ z y)))
   (if (<= z 8.8e+27) (+ 4.0 (* 4.0 (/ x y))) (+ 1.0 (/ 4.0 (/ y (- x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+25) {
		tmp = 4.0 - (4.0 * (z / y));
	} else if (z <= 8.8e+27) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (4.0 / (y / (x - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.2d+25)) then
        tmp = 4.0d0 - (4.0d0 * (z / y))
    else if (z <= 8.8d+27) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else
        tmp = 1.0d0 + (4.0d0 / (y / (x - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+25) {
		tmp = 4.0 - (4.0 * (z / y));
	} else if (z <= 8.8e+27) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 1.0 + (4.0 / (y / (x - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.2e+25:
		tmp = 4.0 - (4.0 * (z / y))
	elif z <= 8.8e+27:
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = 1.0 + (4.0 / (y / (x - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.2e+25)
		tmp = Float64(4.0 - Float64(4.0 * Float64(z / y)));
	elseif (z <= 8.8e+27)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(1.0 + Float64(4.0 / Float64(y / Float64(x - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.2e+25)
		tmp = 4.0 - (4.0 * (z / y));
	elseif (z <= 8.8e+27)
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = 1.0 + (4.0 / (y / (x - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.2e+25], N[(4.0 - N[(4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+27], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(4.0 / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e25

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 92.6%

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

      1. neg-mul-1 92.6%

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

      2. distribute-neg-frac 92.6%

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

   7. Simplified 92.6%

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

   if -5.1999999999999997e25 < z < 8.7999999999999995e27

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 95.8%

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

   if 8.7999999999999995e27 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 86.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;4 - 4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \end{array} \]

Alternative 6: 81.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+96} \lor \neg \left(z \leq 5.2 \cdot 10^{+112}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9e+96) (not (<= z 5.2e+112)))
   (+ 1.0 (/ (* z -4.0) y))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9e+96) || !(z <= 5.2e+112)) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (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 <= (-9d+96)) .or. (.not. (z <= 5.2d+112))) then
        tmp = 1.0d0 + ((z * (-4.0d0)) / y)
    else
        tmp = 4.0d0 + (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 <= -9e+96) || !(z <= 5.2e+112)) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9e+96) or not (z <= 5.2e+112):
		tmp = 1.0 + ((z * -4.0) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9e+96) || !(z <= 5.2e+112))
		tmp = Float64(1.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9e+96) || ~((z <= 5.2e+112)))
		tmp = 1.0 + ((z * -4.0) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9e+96], N[Not[LessEqual[z, 5.2e+112]], $MachinePrecision]], N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999914e96 or 5.2000000000000001e112 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 75.6%

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

      1. associate-*r/ 75.6%

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

      2. metadata-eval 75.6%

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

      3. associate-*r* 75.6%

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

      4. neg-mul-1 75.6%

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

      5. associate-*l/ 75.4%

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

      6. *-commutative 75.4%

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

      7. associate-*r/ 75.6%

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

      8. neg-mul-1 75.6%

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

      9. *-commutative 75.6%

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

      10. associate-*l* 75.6%

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

      11. metadata-eval 75.6%

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

   6. Simplified 75.6%

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

   if -8.99999999999999914e96 < z < 5.2000000000000001e112

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 91.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+96} \lor \neg \left(z \leq 5.2 \cdot 10^{+112}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 85.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+23} \lor \neg \left(z \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;4 - 4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8e+23) (not (<= z 4.8e+110)))
   (- 4.0 (* 4.0 (/ z y)))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8e+23) || !(z <= 4.8e+110)) {
		tmp = 4.0 - (4.0 * (z / y));
	} else {
		tmp = 4.0 + (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 <= (-8d+23)) .or. (.not. (z <= 4.8d+110))) then
        tmp = 4.0d0 - (4.0d0 * (z / y))
    else
        tmp = 4.0d0 + (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 <= -8e+23) || !(z <= 4.8e+110)) {
		tmp = 4.0 - (4.0 * (z / y));
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8e+23) or not (z <= 4.8e+110):
		tmp = 4.0 - (4.0 * (z / y))
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8e+23) || !(z <= 4.8e+110))
		tmp = Float64(4.0 - Float64(4.0 * Float64(z / y)));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8e+23) || ~((z <= 4.8e+110)))
		tmp = 4.0 - (4.0 * (z / y));
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8e+23], N[Not[LessEqual[z, 4.8e+110]], $MachinePrecision]], N[(4.0 - N[(4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999993e23 or 4.80000000000000025e110 < z

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 89.5%

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

      1. neg-mul-1 89.5%

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

      2. distribute-neg-frac 89.5%

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

   7. Simplified 89.5%

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

   if -7.9999999999999993e23 < z < 4.80000000000000025e110

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 93.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+23} \lor \neg \left(z \leq 4.8 \cdot 10^{+110}\right):\\ \;\;\;\;4 - 4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 8: 33.6% 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. Step-by-step derivation

   1. associate-*l/ 99.7%

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

   2. +-commutative 99.7%

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

   3. fma-def 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in y around inf 30.5%

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

5. Final simplification 30.5%

   \[\leadsto 4 \]

Reproduce

herbie shell --seed 2023279 
(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)))