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

Percentage Accurate: 99.8% → 100.0%

Time: 5.6s

Alternatives: 8

Speedup: 1.2×

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

Specification

Math

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

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: 99.8% 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, 1.2× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{x - y}{z} - 2 \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) / z)) - 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 = (4.0d0 * ((x - y) / z)) - 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 0 100.0%

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

5. Final simplification 100.0%

   \[\leadsto 4 \cdot \frac{x - y}{z} - 2 \]

Alternative 2: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ t_1 := y \cdot \frac{-4}{z}\\ \mathbf{if}\;x \leq -1.26 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-286}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-178}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))) (t_1 (* y (/ -4.0 z))))
   (if (<= x -1.26e+74)
     t_0
     (if (<= x -9e+42)
       t_1
       (if (<= x -2.4e-156)
         -2.0
         (if (<= x -1.55e-188)
           t_1
           (if (<= x 1.1e-286)
             -2.0
             (if (<= x 1.2e-242)
               t_1
               (if (<= x 1.3e-178)
                 -2.0
                 (if (<= x 1.18e-145)
                   t_1
                   (if (<= x 4.1e-75)
                     -2.0
                     (if (<= x 2.4e+64) t_1 t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = y * (-4.0 / z);
	double tmp;
	if (x <= -1.26e+74) {
		tmp = t_0;
	} else if (x <= -9e+42) {
		tmp = t_1;
	} else if (x <= -2.4e-156) {
		tmp = -2.0;
	} else if (x <= -1.55e-188) {
		tmp = t_1;
	} else if (x <= 1.1e-286) {
		tmp = -2.0;
	} else if (x <= 1.2e-242) {
		tmp = t_1;
	} else if (x <= 1.3e-178) {
		tmp = -2.0;
	} else if (x <= 1.18e-145) {
		tmp = t_1;
	} else if (x <= 4.1e-75) {
		tmp = -2.0;
	} else if (x <= 2.4e+64) {
		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 * ((-4.0d0) / z)
    if (x <= (-1.26d+74)) then
        tmp = t_0
    else if (x <= (-9d+42)) then
        tmp = t_1
    else if (x <= (-2.4d-156)) then
        tmp = -2.0d0
    else if (x <= (-1.55d-188)) then
        tmp = t_1
    else if (x <= 1.1d-286) then
        tmp = -2.0d0
    else if (x <= 1.2d-242) then
        tmp = t_1
    else if (x <= 1.3d-178) then
        tmp = -2.0d0
    else if (x <= 1.18d-145) then
        tmp = t_1
    else if (x <= 4.1d-75) then
        tmp = -2.0d0
    else if (x <= 2.4d+64) 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 * (-4.0 / z);
	double tmp;
	if (x <= -1.26e+74) {
		tmp = t_0;
	} else if (x <= -9e+42) {
		tmp = t_1;
	} else if (x <= -2.4e-156) {
		tmp = -2.0;
	} else if (x <= -1.55e-188) {
		tmp = t_1;
	} else if (x <= 1.1e-286) {
		tmp = -2.0;
	} else if (x <= 1.2e-242) {
		tmp = t_1;
	} else if (x <= 1.3e-178) {
		tmp = -2.0;
	} else if (x <= 1.18e-145) {
		tmp = t_1;
	} else if (x <= 4.1e-75) {
		tmp = -2.0;
	} else if (x <= 2.4e+64) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	t_1 = y * (-4.0 / z)
	tmp = 0
	if x <= -1.26e+74:
		tmp = t_0
	elif x <= -9e+42:
		tmp = t_1
	elif x <= -2.4e-156:
		tmp = -2.0
	elif x <= -1.55e-188:
		tmp = t_1
	elif x <= 1.1e-286:
		tmp = -2.0
	elif x <= 1.2e-242:
		tmp = t_1
	elif x <= 1.3e-178:
		tmp = -2.0
	elif x <= 1.18e-145:
		tmp = t_1
	elif x <= 4.1e-75:
		tmp = -2.0
	elif x <= 2.4e+64:
		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(y * Float64(-4.0 / z))
	tmp = 0.0
	if (x <= -1.26e+74)
		tmp = t_0;
	elseif (x <= -9e+42)
		tmp = t_1;
	elseif (x <= -2.4e-156)
		tmp = -2.0;
	elseif (x <= -1.55e-188)
		tmp = t_1;
	elseif (x <= 1.1e-286)
		tmp = -2.0;
	elseif (x <= 1.2e-242)
		tmp = t_1;
	elseif (x <= 1.3e-178)
		tmp = -2.0;
	elseif (x <= 1.18e-145)
		tmp = t_1;
	elseif (x <= 4.1e-75)
		tmp = -2.0;
	elseif (x <= 2.4e+64)
		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 * (-4.0 / z);
	tmp = 0.0;
	if (x <= -1.26e+74)
		tmp = t_0;
	elseif (x <= -9e+42)
		tmp = t_1;
	elseif (x <= -2.4e-156)
		tmp = -2.0;
	elseif (x <= -1.55e-188)
		tmp = t_1;
	elseif (x <= 1.1e-286)
		tmp = -2.0;
	elseif (x <= 1.2e-242)
		tmp = t_1;
	elseif (x <= 1.3e-178)
		tmp = -2.0;
	elseif (x <= 1.18e-145)
		tmp = t_1;
	elseif (x <= 4.1e-75)
		tmp = -2.0;
	elseif (x <= 2.4e+64)
		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[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.26e+74], t$95$0, If[LessEqual[x, -9e+42], t$95$1, If[LessEqual[x, -2.4e-156], -2.0, If[LessEqual[x, -1.55e-188], t$95$1, If[LessEqual[x, 1.1e-286], -2.0, If[LessEqual[x, 1.2e-242], t$95$1, If[LessEqual[x, 1.3e-178], -2.0, If[LessEqual[x, 1.18e-145], t$95$1, If[LessEqual[x, 4.1e-75], -2.0, If[LessEqual[x, 2.4e+64], t$95$1, t$95$0]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.26000000000000008e74 or 2.39999999999999999e64 < x

   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 inf 71.8%

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

   if -1.26000000000000008e74 < x < -9.00000000000000025e42 or -2.4e-156 < x < -1.5500000000000001e-188 or 1.1e-286 < x < 1.2e-242 or 1.29999999999999999e-178 < x < 1.18000000000000006e-145 or 4.10000000000000002e-75 < x < 2.39999999999999999e64

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 75.6%

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

      1. associate-*r/ 75.6%

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

      2. neg-mul-1 75.6%

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

   6. Simplified 75.6%

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

      1. frac-2neg 75.6%

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

      2. frac-2neg 75.6%

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

      3. metadata-eval 75.6%

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

      4. metadata-eval 75.6%

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

      5. distribute-frac-neg 75.6%

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

      6. remove-double-neg 75.6%

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

      7. frac-2neg 75.6%

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

      8. distribute-frac-neg 75.6%

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

      9. remove-double-neg 75.6%

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

      10. associate-/r/ 75.6%

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

   8. Applied egg-rr 75.6%

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

   9. Taylor expanded in z around 0 75.9%

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

       1. associate-*r/ 75.9%

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

       2. associate-*l/ 75.6%

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

   11. Simplified 75.6%

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

   if -9.00000000000000025e42 < x < -2.4e-156 or -1.5500000000000001e-188 < x < 1.1e-286 or 1.2e-242 < x < 1.29999999999999999e-178 or 1.18000000000000006e-145 < x < 4.10000000000000002e-75

   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/ 99.6%

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

      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 z around inf 58.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+74}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-286}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-242}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-178}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-75}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{z}\\ t_1 := \frac{y \cdot -4}{z}\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-156}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-286}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-179}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x z))) (t_1 (/ (* y -4.0) z)))
   (if (<= x -1.7e+74)
     t_0
     (if (<= x -2.1e+41)
       t_1
       (if (<= x -1.5e-156)
         -2.0
         (if (<= x -1.15e-185)
           t_1
           (if (<= x 1.15e-286)
             -2.0
             (if (<= x 2e-242)
               t_1
               (if (<= x 9e-179)
                 -2.0
                 (if (<= x 7e-144)
                   (* y (/ -4.0 z))
                   (if (<= x 2.3e-75)
                     -2.0
                     (if (<= x 1.36e+65) t_1 t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / z);
	double t_1 = (y * -4.0) / z;
	double tmp;
	if (x <= -1.7e+74) {
		tmp = t_0;
	} else if (x <= -2.1e+41) {
		tmp = t_1;
	} else if (x <= -1.5e-156) {
		tmp = -2.0;
	} else if (x <= -1.15e-185) {
		tmp = t_1;
	} else if (x <= 1.15e-286) {
		tmp = -2.0;
	} else if (x <= 2e-242) {
		tmp = t_1;
	} else if (x <= 9e-179) {
		tmp = -2.0;
	} else if (x <= 7e-144) {
		tmp = y * (-4.0 / z);
	} else if (x <= 2.3e-75) {
		tmp = -2.0;
	} else if (x <= 1.36e+65) {
		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 * (-4.0d0)) / z
    if (x <= (-1.7d+74)) then
        tmp = t_0
    else if (x <= (-2.1d+41)) then
        tmp = t_1
    else if (x <= (-1.5d-156)) then
        tmp = -2.0d0
    else if (x <= (-1.15d-185)) then
        tmp = t_1
    else if (x <= 1.15d-286) then
        tmp = -2.0d0
    else if (x <= 2d-242) then
        tmp = t_1
    else if (x <= 9d-179) then
        tmp = -2.0d0
    else if (x <= 7d-144) then
        tmp = y * ((-4.0d0) / z)
    else if (x <= 2.3d-75) then
        tmp = -2.0d0
    else if (x <= 1.36d+65) 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 * -4.0) / z;
	double tmp;
	if (x <= -1.7e+74) {
		tmp = t_0;
	} else if (x <= -2.1e+41) {
		tmp = t_1;
	} else if (x <= -1.5e-156) {
		tmp = -2.0;
	} else if (x <= -1.15e-185) {
		tmp = t_1;
	} else if (x <= 1.15e-286) {
		tmp = -2.0;
	} else if (x <= 2e-242) {
		tmp = t_1;
	} else if (x <= 9e-179) {
		tmp = -2.0;
	} else if (x <= 7e-144) {
		tmp = y * (-4.0 / z);
	} else if (x <= 2.3e-75) {
		tmp = -2.0;
	} else if (x <= 1.36e+65) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / z)
	t_1 = (y * -4.0) / z
	tmp = 0
	if x <= -1.7e+74:
		tmp = t_0
	elif x <= -2.1e+41:
		tmp = t_1
	elif x <= -1.5e-156:
		tmp = -2.0
	elif x <= -1.15e-185:
		tmp = t_1
	elif x <= 1.15e-286:
		tmp = -2.0
	elif x <= 2e-242:
		tmp = t_1
	elif x <= 9e-179:
		tmp = -2.0
	elif x <= 7e-144:
		tmp = y * (-4.0 / z)
	elif x <= 2.3e-75:
		tmp = -2.0
	elif x <= 1.36e+65:
		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 * -4.0) / z)
	tmp = 0.0
	if (x <= -1.7e+74)
		tmp = t_0;
	elseif (x <= -2.1e+41)
		tmp = t_1;
	elseif (x <= -1.5e-156)
		tmp = -2.0;
	elseif (x <= -1.15e-185)
		tmp = t_1;
	elseif (x <= 1.15e-286)
		tmp = -2.0;
	elseif (x <= 2e-242)
		tmp = t_1;
	elseif (x <= 9e-179)
		tmp = -2.0;
	elseif (x <= 7e-144)
		tmp = Float64(y * Float64(-4.0 / z));
	elseif (x <= 2.3e-75)
		tmp = -2.0;
	elseif (x <= 1.36e+65)
		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 * -4.0) / z;
	tmp = 0.0;
	if (x <= -1.7e+74)
		tmp = t_0;
	elseif (x <= -2.1e+41)
		tmp = t_1;
	elseif (x <= -1.5e-156)
		tmp = -2.0;
	elseif (x <= -1.15e-185)
		tmp = t_1;
	elseif (x <= 1.15e-286)
		tmp = -2.0;
	elseif (x <= 2e-242)
		tmp = t_1;
	elseif (x <= 9e-179)
		tmp = -2.0;
	elseif (x <= 7e-144)
		tmp = y * (-4.0 / z);
	elseif (x <= 2.3e-75)
		tmp = -2.0;
	elseif (x <= 1.36e+65)
		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 * -4.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.7e+74], t$95$0, If[LessEqual[x, -2.1e+41], t$95$1, If[LessEqual[x, -1.5e-156], -2.0, If[LessEqual[x, -1.15e-185], t$95$1, If[LessEqual[x, 1.15e-286], -2.0, If[LessEqual[x, 2e-242], t$95$1, If[LessEqual[x, 9e-179], -2.0, If[LessEqual[x, 7e-144], N[(y * N[(-4.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-75], -2.0, If[LessEqual[x, 1.36e+65], t$95$1, t$95$0]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.7e74 or 1.3600000000000001e65 < x

   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 inf 71.8%

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

   if -1.7e74 < x < -2.1e41 or -1.5e-156 < x < -1.15e-185 or 1.1500000000000001e-286 < x < 2e-242 or 2.3e-75 < x < 1.3600000000000001e65

   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 y around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. associate-*l/ 73.7%

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

   6. Simplified 73.7%

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

   if -2.1e41 < x < -1.5e-156 or -1.15e-185 < x < 1.1500000000000001e-286 or 2e-242 < x < 8.99999999999999984e-179 or 6.9999999999999997e-144 < x < 2.3e-75

   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/ 99.6%

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

      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 z around inf 58.7%

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

   if 8.99999999999999984e-179 < x < 6.9999999999999997e-144

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 89.0%

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

      1. associate-*r/ 89.0%

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

      2. neg-mul-1 89.0%

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

   6. Simplified 89.0%

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

      1. frac-2neg 89.0%

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

      2. frac-2neg 89.0%

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

      3. metadata-eval 89.0%

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

      4. metadata-eval 89.0%

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

      5. distribute-frac-neg 89.0%

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

      6. remove-double-neg 89.0%

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

      7. frac-2neg 89.0%

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

      8. distribute-frac-neg 89.0%

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

      9. remove-double-neg 89.0%

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

      10. associate-/r/ 89.2%

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

   8. Applied egg-rr 89.2%

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

   9. Taylor expanded in z around 0 89.2%

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

       1. associate-*r/ 89.2%

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

       2. associate-*l/ 89.2%

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

   11. Simplified 89.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+74}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-156}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-286}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-242}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-179}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{-4}{z}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{+65}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ t_1 := 4 \cdot \frac{x}{z} + -2\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (- -0.5 (/ y z)))) (t_1 (+ (* 4.0 (/ x z)) -2.0)))
   (if (<= x -6.5e+76)
     t_1
     (if (<= x -3e+15)
       t_0
       (if (<= x -5.6e-55)
         t_1
         (if (<= x 4.1e+18) t_0 (* 4.0 (/ (- x y) z))))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (-0.5 - (y / z));
	double t_1 = (4.0 * (x / z)) + -2.0;
	double tmp;
	if (x <= -6.5e+76) {
		tmp = t_1;
	} else if (x <= -3e+15) {
		tmp = t_0;
	} else if (x <= -5.6e-55) {
		tmp = t_1;
	} else if (x <= 4.1e+18) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * ((-0.5d0) - (y / z))
    t_1 = (4.0d0 * (x / z)) + (-2.0d0)
    if (x <= (-6.5d+76)) then
        tmp = t_1
    else if (x <= (-3d+15)) then
        tmp = t_0
    else if (x <= (-5.6d-55)) then
        tmp = t_1
    else if (x <= 4.1d+18) then
        tmp = t_0
    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 t_0 = 4.0 * (-0.5 - (y / z));
	double t_1 = (4.0 * (x / z)) + -2.0;
	double tmp;
	if (x <= -6.5e+76) {
		tmp = t_1;
	} else if (x <= -3e+15) {
		tmp = t_0;
	} else if (x <= -5.6e-55) {
		tmp = t_1;
	} else if (x <= 4.1e+18) {
		tmp = t_0;
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (-0.5 - (y / z))
	t_1 = (4.0 * (x / z)) + -2.0
	tmp = 0
	if x <= -6.5e+76:
		tmp = t_1
	elif x <= -3e+15:
		tmp = t_0
	elif x <= -5.6e-55:
		tmp = t_1
	elif x <= 4.1e+18:
		tmp = t_0
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(-0.5 - Float64(y / z)))
	t_1 = Float64(Float64(4.0 * Float64(x / z)) + -2.0)
	tmp = 0.0
	if (x <= -6.5e+76)
		tmp = t_1;
	elseif (x <= -3e+15)
		tmp = t_0;
	elseif (x <= -5.6e-55)
		tmp = t_1;
	elseif (x <= 4.1e+18)
		tmp = t_0;
	else
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (-0.5 - (y / z));
	t_1 = (4.0 * (x / z)) + -2.0;
	tmp = 0.0;
	if (x <= -6.5e+76)
		tmp = t_1;
	elseif (x <= -3e+15)
		tmp = t_0;
	elseif (x <= -5.6e-55)
		tmp = t_1;
	elseif (x <= 4.1e+18)
		tmp = t_0;
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(-0.5 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[x, -6.5e+76], t$95$1, If[LessEqual[x, -3e+15], t$95$0, If[LessEqual[x, -5.6e-55], t$95$1, If[LessEqual[x, 4.1e+18], t$95$0, N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5000000000000005e76 or -3e15 < x < -5.59999999999999968e-55

   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/ 99.8%

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

      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 0 95.9%

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

      1. +-commutative 95.9%

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

      2. metadata-eval 95.9%

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

      3. cancel-sign-sub-inv 95.9%

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

      4. div-sub 95.9%

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

      5. associate-/l* 95.9%

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

      6. *-lft-identity 95.9%

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

      7. associate-*l/ 95.9%

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

      8. lft-mult-inverse 95.9%

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

      9. metadata-eval 95.9%

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

      10. sub-neg 95.9%

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

      11. metadata-eval 95.9%

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

      12. distribute-lft-in 95.9%

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

      13. metadata-eval 95.9%

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

   6. Simplified 95.9%

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

   if -6.5000000000000005e76 < x < -3e15 or -5.59999999999999968e-55 < x < 4.1e18

   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 97.5%

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

      1. div-sub 97.6%

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

      2. associate-/l* 97.6%

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

      3. *-lft-identity 97.6%

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

      4. associate-*l/ 97.4%

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

      5. lft-mult-inverse 97.6%

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

      6. metadata-eval 97.6%

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

   6. Simplified 97.6%

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

   if 4.1e18 < x

   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 0 83.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+76}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+15}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;4 \cdot \frac{x}{z} + -2\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+18}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 5: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+88} \lor \neg \left(x \leq 1.3 \cdot 10^{+201}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.1e+88) (not (<= x 1.3e+201)))
   (* 4.0 (/ x z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e+88) || !(x <= 1.3e+201)) {
		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 <= (-3.1d+88)) .or. (.not. (x <= 1.3d+201))) 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 <= -3.1e+88) || !(x <= 1.3e+201)) {
		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 <= -3.1e+88) or not (x <= 1.3e+201):
		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 <= -3.1e+88) || !(x <= 1.3e+201))
		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 <= -3.1e+88) || ~((x <= 1.3e+201)))
		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, -3.1e+88], N[Not[LessEqual[x, 1.3e+201]], $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 < -3.1000000000000001e88 or 1.29999999999999993e201 < x

   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/ 99.8%

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

      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 x around inf 88.2%

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

   if -3.1000000000000001e88 < x < 1.29999999999999993e201

   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 87.0%

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

      1. div-sub 87.1%

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

      2. associate-/l* 87.1%

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

      3. *-lft-identity 87.1%

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

      4. associate-*l/ 86.9%

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

      5. lft-mult-inverse 87.1%

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

      6. metadata-eval 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+88} \lor \neg \left(x \leq 1.3 \cdot 10^{+201}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 6: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+88} \lor \neg \left(x \leq 1.26 \cdot 10^{+17}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.75e+88) (not (<= x 1.26e+17)))
   (* 4.0 (/ (- x y) z))
   (* 4.0 (- -0.5 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.75e+88) || !(x <= 1.26e+17)) {
		tmp = 4.0 * ((x - y) / 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 <= (-2.75d+88)) .or. (.not. (x <= 1.26d+17))) then
        tmp = 4.0d0 * ((x - y) / 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 <= -2.75e+88) || !(x <= 1.26e+17)) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = 4.0 * (-0.5 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.75e+88) or not (x <= 1.26e+17):
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = 4.0 * (-0.5 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.75e+88) || !(x <= 1.26e+17))
		tmp = Float64(4.0 * Float64(Float64(x - y) / 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 <= -2.75e+88) || ~((x <= 1.26e+17)))
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = 4.0 * (-0.5 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.75e+88], N[Not[LessEqual[x, 1.26e+17]], $MachinePrecision]], N[(4.0 * N[(N[(x - y), $MachinePrecision] / 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 < -2.75e88 or 1.26e17 < x

   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 0 86.3%

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

   if -2.75e88 < x < 1.26e17

   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 93.4%

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

      1. div-sub 93.5%

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

      2. associate-/l* 93.5%

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

      3. *-lft-identity 93.5%

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

      4. associate-*l/ 93.3%

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

      5. lft-mult-inverse 93.5%

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

      6. metadata-eval 93.5%

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

   6. Simplified 93.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+88} \lor \neg \left(x \leq 1.26 \cdot 10^{+17}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \left(-0.5 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 7: 54.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+88} \lor \neg \left(x \leq 2.8 \cdot 10^{+16}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.75e+88) (not (<= x 2.8e+16))) (* 4.0 (/ x z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.75e+88) || !(x <= 2.8e+16)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.75d+88)) .or. (.not. (x <= 2.8d+16))) then
        tmp = 4.0d0 * (x / z)
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.75e+88) || !(x <= 2.8e+16)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.75e+88) or not (x <= 2.8e+16):
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.75e+88) || !(x <= 2.8e+16))
		tmp = Float64(4.0 * Float64(x / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.75e+88) || ~((x <= 2.8e+16)))
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.75e+88], N[Not[LessEqual[x, 2.8e+16]], $MachinePrecision]], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if x < -2.75e88 or 2.8e16 < x

   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 inf 69.0%

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

   if -2.75e88 < x < 2.8e16

   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 45.5%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+88} \lor \neg \left(x \leq 2.8 \cdot 10^{+16}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 8: 34.6% 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 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 33.1%

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

5. Final simplification 33.1%

   \[\leadsto -2 \]

Developer target: 97.7% 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 2023171 
(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))