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

Percentage Accurate: 99.9% → 100.0%

Time: 4.7s

Alternatives: 8

Speedup: 0.1×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.9%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

   2. sub-neg 99.7%

      \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

   3. distribute-lft-in 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(x - y\right) + \frac{4}{z} \cdot \left(-z \cdot 0.5\right)} \]

   4. associate-*l/ 98.8%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(x - y\right)}{z}} + \frac{4}{z} \cdot \left(-z \cdot 0.5\right) \]

   5. associate-*r/ 99.9%

      \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z}} + \frac{4}{z} \cdot \left(-z \cdot 0.5\right) \]

   6. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{x - y}{z}, \frac{4}{z} \cdot \left(-z \cdot 0.5\right)\right)} \]

   7. associate-*l/ 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \color{blue}{\frac{4 \cdot \left(-z \cdot 0.5\right)}{z}}\right) \]

   8. *-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{4 \cdot \left(-\color{blue}{0.5 \cdot z}\right)}{z}\right) \]

   9. distribute-rgt-neg-in 100.0%

      \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{4 \cdot \color{blue}{\left(0.5 \cdot \left(-z\right)\right)}}{z}\right) \]

   10. associate-*r* 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{\left(4 \cdot 0.5\right) \cdot \left(-z\right)}}{z}\right) \]

   11. remove-double-neg 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\left(4 \cdot 0.5\right) \cdot \left(-z\right)}{\color{blue}{-\left(-z\right)}}\right) \]

   12. neg-mul-1 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\left(4 \cdot 0.5\right) \cdot \left(-z\right)}{\color{blue}{-1 \cdot \left(-z\right)}}\right) \]

   13. times-frac 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \color{blue}{\frac{4 \cdot 0.5}{-1} \cdot \frac{-z}{-z}}\right) \]

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \frac{\color{blue}{2}}{-1} \cdot \frac{-z}{-z}\right) \]

   15. metadata-eval 100.0%

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

   16. *-inverses 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2 \cdot \color{blue}{1}\right) \]

   17. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, \color{blue}{-2}\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{x - y}{z}, -2\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(4, \frac{x - y}{z}, -2\right) \]

Alternative 2: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ t_1 := \frac{y}{z} \cdot -4\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -60:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-308}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-189}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))) (t_1 (* (/ y z) -4.0)))
   (if (<= x -1.65e+43)
     t_0
     (if (<= x -60.0)
       t_1
       (if (<= x -2.8e-31)
         t_0
         (if (<= x 3e-308)
           -2.0
           (if (<= x 1.7e-224)
             t_1
             (if (<= x 2.05e-189) -2.0 (if (<= x 1.55e+53) t_1 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = (y / z) * -4.0;
	double tmp;
	if (x <= -1.65e+43) {
		tmp = t_0;
	} else if (x <= -60.0) {
		tmp = t_1;
	} else if (x <= -2.8e-31) {
		tmp = t_0;
	} else if (x <= 3e-308) {
		tmp = -2.0;
	} else if (x <= 1.7e-224) {
		tmp = t_1;
	} else if (x <= 2.05e-189) {
		tmp = -2.0;
	} else if (x <= 1.55e+53) {
		tmp = t_1;
	} else {
		tmp = t_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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / z)
    t_1 = (y / z) * (-4.0d0)
    if (x <= (-1.65d+43)) then
        tmp = t_0
    else if (x <= (-60.0d0)) then
        tmp = t_1
    else if (x <= (-2.8d-31)) then
        tmp = t_0
    else if (x <= 3d-308) then
        tmp = -2.0d0
    else if (x <= 1.7d-224) then
        tmp = t_1
    else if (x <= 2.05d-189) then
        tmp = -2.0d0
    else if (x <= 1.55d+53) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = (y / z) * -4.0;
	double tmp;
	if (x <= -1.65e+43) {
		tmp = t_0;
	} else if (x <= -60.0) {
		tmp = t_1;
	} else if (x <= -2.8e-31) {
		tmp = t_0;
	} else if (x <= 3e-308) {
		tmp = -2.0;
	} else if (x <= 1.7e-224) {
		tmp = t_1;
	} else if (x <= 2.05e-189) {
		tmp = -2.0;
	} else if (x <= 1.55e+53) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	t_1 = (y / z) * -4.0
	tmp = 0
	if x <= -1.65e+43:
		tmp = t_0
	elif x <= -60.0:
		tmp = t_1
	elif x <= -2.8e-31:
		tmp = t_0
	elif x <= 3e-308:
		tmp = -2.0
	elif x <= 1.7e-224:
		tmp = t_1
	elif x <= 2.05e-189:
		tmp = -2.0
	elif x <= 1.55e+53:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / z))
	t_1 = Float64(Float64(y / z) * -4.0)
	tmp = 0.0
	if (x <= -1.65e+43)
		tmp = t_0;
	elseif (x <= -60.0)
		tmp = t_1;
	elseif (x <= -2.8e-31)
		tmp = t_0;
	elseif (x <= 3e-308)
		tmp = -2.0;
	elseif (x <= 1.7e-224)
		tmp = t_1;
	elseif (x <= 2.05e-189)
		tmp = -2.0;
	elseif (x <= 1.55e+53)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / z);
	t_1 = (y / z) * -4.0;
	tmp = 0.0;
	if (x <= -1.65e+43)
		tmp = t_0;
	elseif (x <= -60.0)
		tmp = t_1;
	elseif (x <= -2.8e-31)
		tmp = t_0;
	elseif (x <= 3e-308)
		tmp = -2.0;
	elseif (x <= 1.7e-224)
		tmp = t_1;
	elseif (x <= 2.05e-189)
		tmp = -2.0;
	elseif (x <= 1.55e+53)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[x, -1.65e+43], t$95$0, If[LessEqual[x, -60.0], t$95$1, If[LessEqual[x, -2.8e-31], t$95$0, If[LessEqual[x, 3e-308], -2.0, If[LessEqual[x, 1.7e-224], t$95$1, If[LessEqual[x, 2.05e-189], -2.0, If[LessEqual[x, 1.55e+53], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6500000000000001e43 or -60 < x < -2.7999999999999999e-31 or 1.5500000000000001e53 < x

   1. Initial program 98.4%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.6%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.6%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in x around inf 66.4%

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

   if -1.6500000000000001e43 < x < -60 or 3.00000000000000022e-308 < x < 1.69999999999999996e-224 or 2.05000000000000015e-189 < x < 1.5500000000000001e53

   1. Initial program 98.6%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in y around inf 61.4%

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

   if -2.7999999999999999e-31 < x < 3.00000000000000022e-308 or 1.69999999999999996e-224 < x < 2.05000000000000015e-189

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around inf 58.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -60:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-308}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-189}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+191} \lor \neg \left(x \leq -5 \cdot 10^{+151} \lor \neg \left(x \leq -6 \cdot 10^{+74}\right) \land x \leq 2.9 \cdot 10^{+181}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e+191)
         (not (or (<= x -5e+151) (and (not (<= x -6e+74)) (<= x 2.9e+181)))))
   (* 4.0 (/ x z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+191) || !((x <= -5e+151) || (!(x <= -6e+74) && (x <= 2.9e+181)))) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / 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 ((x <= (-6.5d+191)) .or. (.not. (x <= (-5d+151)) .or. (.not. (x <= (-6d+74))) .and. (x <= 2.9d+181))) then
        tmp = 4.0d0 * (x / z)
    else
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+191) || !((x <= -5e+151) || (!(x <= -6e+74) && (x <= 2.9e+181)))) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e+191) or not ((x <= -5e+151) or (not (x <= -6e+74) and (x <= 2.9e+181))):
		tmp = 4.0 * (x / z)
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e+191) || !((x <= -5e+151) || (!(x <= -6e+74) && (x <= 2.9e+181))))
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e+191) || ~(((x <= -5e+151) || (~((x <= -6e+74)) && (x <= 2.9e+181)))))
		tmp = 4.0 * (x / z);
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e+191], N[Not[Or[LessEqual[x, -5e+151], And[N[Not[LessEqual[x, -6e+74]], $MachinePrecision], LessEqual[x, 2.9e+181]]]], $MachinePrecision]], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000008e191 or -5.0000000000000002e151 < x < -6e74 or 2.9e181 < x

   1. Initial program 97.4%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.6%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.6%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in x around inf 85.1%

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

   if -6.50000000000000008e191 < x < -5.0000000000000002e151 or -6e74 < x < 2.9e181

   1. Initial program 99.5%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{4 \cdot \frac{-0.5 \cdot z - y}{z}} \]
   5. Step-by-step derivation

      1. div-sub 81.1%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{-0.5 \cdot z}{z} - \frac{y}{z}\right)} \]

      2. *-commutative 81.1%

         \[\leadsto 4 \cdot \left(\frac{\color{blue}{z \cdot -0.5}}{z} - \frac{y}{z}\right) \]

      3. *-lft-identity 81.1%

         \[\leadsto 4 \cdot \left(\frac{\color{blue}{1 \cdot \left(z \cdot -0.5\right)}}{z} - \frac{y}{z}\right) \]

      4. associate-*l/ 81.0%

         \[\leadsto 4 \cdot \left(\color{blue}{\frac{1}{z} \cdot \left(z \cdot -0.5\right)} - \frac{y}{z}\right) \]

      5. associate-*r* 81.0%

         \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{1}{z} \cdot z\right) \cdot -0.5} - \frac{y}{z}\right) \]

      6. lft-mult-inverse 81.1%

         \[\leadsto 4 \cdot \left(\color{blue}{1} \cdot -0.5 - \frac{y}{z}\right) \]

      7. metadata-eval 81.1%

         \[\leadsto 4 \cdot \left(\color{blue}{-0.5} - \frac{y}{z}\right) \]

   6. Simplified 81.1%

      \[\leadsto \color{blue}{4 \cdot \left(-0.5 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+191} \lor \neg \left(x \leq -5 \cdot 10^{+151} \lor \neg \left(x \leq -6 \cdot 10^{+74}\right) \land x \leq 2.9 \cdot 10^{+181}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 4: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+42} \lor \neg \left(z \leq 1.5 \cdot 10^{+197}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.25e+42) (not (<= z 1.5e+197)))
   (* 4.0 (- -0.5 (/ y z)))
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25e+42) || !(z <= 1.5e+197)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = 4.0 * ((x - y) / 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 <= (-1.25d+42)) .or. (.not. (z <= 1.5d+197))) then
        tmp = 4.0d0 * ((-0.5d0) - (y / z))
    else
        tmp = 4.0d0 * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25e+42) || !(z <= 1.5e+197)) {
		tmp = 4.0 * (-0.5 - (y / z));
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.25e+42) or not (z <= 1.5e+197):
		tmp = 4.0 * (-0.5 - (y / z))
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.25e+42) || !(z <= 1.5e+197))
		tmp = Float64(4.0 * Float64(-0.5 - Float64(y / z)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.25e+42) || ~((z <= 1.5e+197)))
		tmp = 4.0 * (-0.5 - (y / z));
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.25e+42], N[Not[LessEqual[z, 1.5e+197]], $MachinePrecision]], N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000002e42 or 1.5000000000000001e197 < z

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in x around 0 84.1%

      \[\leadsto \color{blue}{4 \cdot \frac{-0.5 \cdot z - y}{z}} \]
   5. Step-by-step derivation

      1. div-sub 84.1%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{-0.5 \cdot z}{z} - \frac{y}{z}\right)} \]

      2. *-commutative 84.1%

         \[\leadsto 4 \cdot \left(\frac{\color{blue}{z \cdot -0.5}}{z} - \frac{y}{z}\right) \]

      3. *-lft-identity 84.1%

         \[\leadsto 4 \cdot \left(\frac{\color{blue}{1 \cdot \left(z \cdot -0.5\right)}}{z} - \frac{y}{z}\right) \]

      4. associate-*l/ 83.9%

         \[\leadsto 4 \cdot \left(\color{blue}{\frac{1}{z} \cdot \left(z \cdot -0.5\right)} - \frac{y}{z}\right) \]

      5. associate-*r* 83.9%

         \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{1}{z} \cdot z\right) \cdot -0.5} - \frac{y}{z}\right) \]

      6. lft-mult-inverse 84.1%

         \[\leadsto 4 \cdot \left(\color{blue}{1} \cdot -0.5 - \frac{y}{z}\right) \]

      7. metadata-eval 84.1%

         \[\leadsto 4 \cdot \left(\color{blue}{-0.5} - \frac{y}{z}\right) \]

   6. Simplified 84.1%

      \[\leadsto \color{blue}{4 \cdot \left(-0.5 - \frac{y}{z}\right)} \]

   if -1.25000000000000002e42 < z < 1.5000000000000001e197

   1. Initial program 98.4%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.7%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around 0 87.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+42} \lor \neg \left(z \leq 1.5 \cdot 10^{+197}\right):\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 5: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+99} \lor \neg \left(z \leq 5.5 \cdot 10^{-20}\right):\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.6e+99) (not (<= z 5.5e-20)))
   (+ -2.0 (* 4.0 (/ x z)))
   (* 4.0 (/ (- x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e+99) || !(z <= 5.5e-20)) {
		tmp = -2.0 + (4.0 * (x / z));
	} else {
		tmp = 4.0 * ((x - y) / 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 <= (-5.6d+99)) .or. (.not. (z <= 5.5d-20))) then
        tmp = (-2.0d0) + (4.0d0 * (x / z))
    else
        tmp = 4.0d0 * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e+99) || !(z <= 5.5e-20)) {
		tmp = -2.0 + (4.0 * (x / z));
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.6e+99) or not (z <= 5.5e-20):
		tmp = -2.0 + (4.0 * (x / z))
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.6e+99) || !(z <= 5.5e-20))
		tmp = Float64(-2.0 + Float64(4.0 * Float64(x / z)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.6e+99) || ~((z <= 5.5e-20)))
		tmp = -2.0 + (4.0 * (x / z));
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.6e+99], N[Not[LessEqual[z, 5.5e-20]], $MachinePrecision]], N[(-2.0 + N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6e99 or 5.4999999999999996e-20 < z

   1. Initial program 98.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.5%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.5%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.5%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.5%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in y around 0 89.3%

      \[\leadsto \color{blue}{4 \cdot \frac{-0.5 \cdot z + x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto 4 \cdot \frac{\color{blue}{x + -0.5 \cdot z}}{z} \]

      2. metadata-eval 89.3%

         \[\leadsto 4 \cdot \frac{x + \color{blue}{\left(-0.5\right)} \cdot z}{z} \]

      3. cancel-sign-sub-inv 89.3%

         \[\leadsto 4 \cdot \frac{\color{blue}{x - 0.5 \cdot z}}{z} \]

      4. div-sub 89.4%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \frac{0.5 \cdot z}{z}\right)} \]

      5. sub-neg 89.4%

         \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} + \left(-\frac{0.5 \cdot z}{z}\right)\right)} \]

      6. associate-/l* 89.4%

         \[\leadsto 4 \cdot \left(\frac{x}{z} + \left(-\color{blue}{\frac{0.5}{\frac{z}{z}}}\right)\right) \]

      7. *-rgt-identity 89.4%

         \[\leadsto 4 \cdot \left(\frac{x}{z} + \left(-\frac{0.5}{\frac{\color{blue}{z \cdot 1}}{z}}\right)\right) \]

      8. *-commutative 89.4%

         \[\leadsto 4 \cdot \left(\frac{x}{z} + \left(-\frac{0.5}{\frac{\color{blue}{1 \cdot z}}{z}}\right)\right) \]

      9. associate-*l/ 89.2%

         \[\leadsto 4 \cdot \left(\frac{x}{z} + \left(-\frac{0.5}{\color{blue}{\frac{1}{z} \cdot z}}\right)\right) \]

      10. lft-mult-inverse 89.4%

          \[\leadsto 4 \cdot \left(\frac{x}{z} + \left(-\frac{0.5}{\color{blue}{1}}\right)\right) \]

      11. metadata-eval 89.4%

          \[\leadsto 4 \cdot \left(\frac{x}{z} + \left(-\color{blue}{0.5}\right)\right) \]

      12. metadata-eval 89.4%

          \[\leadsto 4 \cdot \left(\frac{x}{z} + \color{blue}{-0.5}\right) \]

      13. distribute-lft-in 89.4%

          \[\leadsto \color{blue}{4 \cdot \frac{x}{z} + 4 \cdot -0.5} \]

      14. metadata-eval 89.4%

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

   6. Simplified 89.4%

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

   if -5.6e99 < z < 5.4999999999999996e-20

   1. Initial program 99.4%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around 0 91.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+99} \lor \neg \left(z \leq 5.5 \cdot 10^{-20}\right):\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 6: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (/ 4.0 z) (+ (- x y) (* z -0.5))))

C

double code(double x, double y, double z) {
	return (4.0 / z) * ((x - y) + (z * -0.5));
}

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 / z) * ((x - y) + (z * (-0.5d0)))
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 / z) * ((x - y) + (z * -0.5));
}

Python

def code(x, y, z):
	return (4.0 / z) * ((x - y) + (z * -0.5))

Julia

function code(x, y, z)
	return Float64(Float64(4.0 / z) * Float64(Float64(x - y) + Float64(z * -0.5)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 / z) * ((x - y) + (z * -0.5));
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 / z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] + N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.9%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

   2. sub-neg 99.7%

      \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

   3. distribute-rgt-neg-in 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

   4. metadata-eval 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

4. Final simplification 99.7%

   \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right) \]

Alternative 7: 53.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+106}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.45e+106) -2.0 (if (<= z 6e-20) (* (/ y z) -4.0) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e+106) {
		tmp = -2.0;
	} else if (z <= 6e-20) {
		tmp = (y / z) * -4.0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.45d+106)) then
        tmp = -2.0d0
    else if (z <= 6d-20) then
        tmp = (y / z) * (-4.0d0)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e+106) {
		tmp = -2.0;
	} else if (z <= 6e-20) {
		tmp = (y / z) * -4.0;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.45e+106:
		tmp = -2.0
	elif z <= 6e-20:
		tmp = (y / z) * -4.0
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.45e+106)
		tmp = -2.0;
	elseif (z <= 6e-20)
		tmp = Float64(Float64(y / z) * -4.0);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.45e+106)
		tmp = -2.0;
	elseif (z <= 6e-20)
		tmp = (y / z) * -4.0;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.45e+106], -2.0, If[LessEqual[z, 6e-20], N[(N[(y / z), $MachinePrecision] * -4.0), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -2.44999999999999999e106 or 6.00000000000000057e-20 < z

   1. Initial program 98.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.5%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.5%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.5%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.5%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in z around inf 65.4%

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

   if -2.44999999999999999e106 < z < 6.00000000000000057e-20

   1. Initial program 99.4%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

      3. distribute-rgt-neg-in 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

      4. metadata-eval 99.8%

         \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

   4. Taylor expanded in y around inf 46.6%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+106}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{z} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 34.0% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := -2.0

Derivation

1. Initial program 98.9%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

   2. sub-neg 99.7%

      \[\leadsto \frac{4}{z} \cdot \color{blue}{\left(\left(x - y\right) + \left(-z \cdot 0.5\right)\right)} \]

   3. distribute-rgt-neg-in 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + \color{blue}{z \cdot \left(-0.5\right)}\right) \]

   4. metadata-eval 99.7%

      \[\leadsto \frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot \color{blue}{-0.5}\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{4}{z} \cdot \left(\left(x - y\right) + z \cdot -0.5\right)} \]

4. Taylor expanded in z around inf 31.1%

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

5. Final simplification 31.1%

   \[\leadsto -2 \]

Developer target: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023208 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))