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

Percentage Accurate: 99.8% → 99.8%

Time: 5.0s

Alternatives: 8

Speedup: 1.0×

• 20.8% 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: 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]

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 53.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot -4}{z}\\ t_1 := 4 \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-305}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* y -4.0) z)) (t_1 (* 4.0 (/ x z))))
   (if (<= y -4.8e+69)
     t_0
     (if (<= y -1.3e-10)
       t_1
       (if (<= y -1.65e-305)
         -2.0
         (if (<= y 4e-279)
           t_1
           (if (<= y 7.4e-93) -2.0 (if (<= y 1.58e-25) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * -4.0) / z;
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (y <= -4.8e+69) {
		tmp = t_0;
	} else if (y <= -1.3e-10) {
		tmp = t_1;
	} else if (y <= -1.65e-305) {
		tmp = -2.0;
	} else if (y <= 4e-279) {
		tmp = t_1;
	} else if (y <= 7.4e-93) {
		tmp = -2.0;
	} else if (y <= 1.58e-25) {
		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 = (y * (-4.0d0)) / z
    t_1 = 4.0d0 * (x / z)
    if (y <= (-4.8d+69)) then
        tmp = t_0
    else if (y <= (-1.3d-10)) then
        tmp = t_1
    else if (y <= (-1.65d-305)) then
        tmp = -2.0d0
    else if (y <= 4d-279) then
        tmp = t_1
    else if (y <= 7.4d-93) then
        tmp = -2.0d0
    else if (y <= 1.58d-25) 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 = (y * -4.0) / z;
	double t_1 = 4.0 * (x / z);
	double tmp;
	if (y <= -4.8e+69) {
		tmp = t_0;
	} else if (y <= -1.3e-10) {
		tmp = t_1;
	} else if (y <= -1.65e-305) {
		tmp = -2.0;
	} else if (y <= 4e-279) {
		tmp = t_1;
	} else if (y <= 7.4e-93) {
		tmp = -2.0;
	} else if (y <= 1.58e-25) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * -4.0) / z
	t_1 = 4.0 * (x / z)
	tmp = 0
	if y <= -4.8e+69:
		tmp = t_0
	elif y <= -1.3e-10:
		tmp = t_1
	elif y <= -1.65e-305:
		tmp = -2.0
	elif y <= 4e-279:
		tmp = t_1
	elif y <= 7.4e-93:
		tmp = -2.0
	elif y <= 1.58e-25:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * -4.0) / z)
	t_1 = Float64(4.0 * Float64(x / z))
	tmp = 0.0
	if (y <= -4.8e+69)
		tmp = t_0;
	elseif (y <= -1.3e-10)
		tmp = t_1;
	elseif (y <= -1.65e-305)
		tmp = -2.0;
	elseif (y <= 4e-279)
		tmp = t_1;
	elseif (y <= 7.4e-93)
		tmp = -2.0;
	elseif (y <= 1.58e-25)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * -4.0) / z;
	t_1 = 4.0 * (x / z);
	tmp = 0.0;
	if (y <= -4.8e+69)
		tmp = t_0;
	elseif (y <= -1.3e-10)
		tmp = t_1;
	elseif (y <= -1.65e-305)
		tmp = -2.0;
	elseif (y <= 4e-279)
		tmp = t_1;
	elseif (y <= 7.4e-93)
		tmp = -2.0;
	elseif (y <= 1.58e-25)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * -4.0), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+69], t$95$0, If[LessEqual[y, -1.3e-10], t$95$1, If[LessEqual[y, -1.65e-305], -2.0, If[LessEqual[y, 4e-279], t$95$1, If[LessEqual[y, 7.4e-93], -2.0, If[LessEqual[y, 1.58e-25], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000003e69 or 1.57999999999999989e-25 < y

   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. /-rgt-identity 99.8%

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

      3. metadata-eval 99.8%

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

      4. metadata-eval 99.8%

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

      5. /-rgt-identity 99.8%

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

      6. sub-neg 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-*l/ 68.1%

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

   7. Simplified 68.1%

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

   if -4.8000000000000003e69 < y < -1.29999999999999991e-10 or -1.64999999999999991e-305 < y < 4.00000000000000022e-279 or 7.40000000000000005e-93 < y < 1.57999999999999989e-25

   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. /-rgt-identity 99.6%

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

      3. metadata-eval 99.6%

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

      4. metadata-eval 99.6%

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

      5. /-rgt-identity 99.6%

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

      6. sub-neg 99.6%

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

      7. distribute-rgt-neg-in 99.6%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in x around inf 65.6%

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

   if -1.29999999999999991e-10 < y < -1.64999999999999991e-305 or 4.00000000000000022e-279 < y < 7.40000000000000005e-93

   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. /-rgt-identity 99.6%

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

      3. metadata-eval 99.6%

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

      4. metadata-eval 99.6%

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

      5. /-rgt-identity 99.6%

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

      6. sub-neg 99.6%

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

      7. distribute-rgt-neg-in 99.6%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in z around inf 62.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-305}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-279}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-25}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -4}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+149} \lor \neg \left(x \leq 2 \cdot 10^{-41}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e+149) (not (<= x 2e-41)))
   (* 4.0 (/ (- x y) z))
   (- (* -4.0 (/ y z)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+149) || !(x <= 2e-41)) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = (-4.0 * (y / z)) - 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 <= (-3.8d+149)) .or. (.not. (x <= 2d-41))) then
        tmp = 4.0d0 * ((x - y) / z)
    else
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+149) || !(x <= 2e-41)) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = (-4.0 * (y / z)) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e+149) or not (x <= 2e-41):
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = (-4.0 * (y / z)) - 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e+149) || !(x <= 2e-41))
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e+149) || ~((x <= 2e-41)))
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = (-4.0 * (y / z)) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e+149], N[Not[LessEqual[x, 2e-41]], $MachinePrecision]], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000001e149 or 2.00000000000000001e-41 < 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. /-rgt-identity 99.7%

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

      3. metadata-eval 99.7%

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

      4. metadata-eval 99.7%

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

      5. /-rgt-identity 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in z around 0 86.3%

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

   if -3.8000000000000001e149 < x < 2.00000000000000001e-41

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. *-lft-identity 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{1 \cdot z}}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      5. metadata-eval 100.0%

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

      6. associate-/l* 99.8%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{--1}{\frac{4}{z}}}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      7. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{x - y}{--1} \cdot \frac{4}{z}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      8. fma-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. /-rgt-identity 99.9%

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

      11. associate-/r/ 99.9%

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

      12. distribute-lft-neg-in 99.9%

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

      13. distribute-frac-neg 99.9%

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

      14. *-commutative 99.9%

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

      15. distribute-lft-neg-in 99.9%

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

      16. associate-/l* 99.9%

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

      17. metadata-eval 99.9%

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

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

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

      20. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 91.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+149} \lor \neg \left(x \leq 2 \cdot 10^{-41}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+87}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+175}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.95e+87) -2.0 (if (<= z 5.8e+175) (* 4.0 (/ (- x y) z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.95e+87) {
		tmp = -2.0;
	} else if (z <= 5.8e+175) {
		tmp = 4.0 * ((x - y) / 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 (z <= (-1.95d+87)) then
        tmp = -2.0d0
    else if (z <= 5.8d+175) then
        tmp = 4.0d0 * ((x - y) / 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 (z <= -1.95e+87) {
		tmp = -2.0;
	} else if (z <= 5.8e+175) {
		tmp = 4.0 * ((x - y) / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.95e+87:
		tmp = -2.0
	elif z <= 5.8e+175:
		tmp = 4.0 * ((x - y) / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.95e+87)
		tmp = -2.0;
	elseif (z <= 5.8e+175)
		tmp = Float64(4.0 * Float64(Float64(x - y) / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.95e+87)
		tmp = -2.0;
	elseif (z <= 5.8e+175)
		tmp = 4.0 * ((x - y) / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.95e+87], -2.0, If[LessEqual[z, 5.8e+175], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e87 or 5.8e175 < 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/ 99.6%

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

      2. /-rgt-identity 99.6%

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

      3. metadata-eval 99.6%

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

      4. metadata-eval 99.6%

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

      5. /-rgt-identity 99.6%

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

      6. sub-neg 99.6%

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

      7. distribute-rgt-neg-in 99.6%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in z around inf 75.3%

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

   if -1.9500000000000001e87 < z < 5.8e175

   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. /-rgt-identity 99.7%

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

      3. metadata-eval 99.7%

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

      4. metadata-eval 99.7%

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

      5. /-rgt-identity 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in z around 0 84.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+87}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+175}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{elif}\;y \leq 2.2:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+84)
   (- (* -4.0 (/ y z)) 2.0)
   (if (<= y 2.2) (- (* 4.0 (/ x z)) 2.0) (* 4.0 (/ (- x y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+84) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else if (y <= 2.2) {
		tmp = (4.0 * (x / z)) - 2.0;
	} 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) :: tmp
    if (y <= (-2d+84)) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    else if (y <= 2.2d0) then
        tmp = (4.0d0 * (x / z)) - 2.0d0
    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 (y <= -2e+84) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else if (y <= 2.2) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else {
		tmp = 4.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+84:
		tmp = (-4.0 * (y / z)) - 2.0
	elif y <= 2.2:
		tmp = (4.0 * (x / z)) - 2.0
	else:
		tmp = 4.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+84)
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	elseif (y <= 2.2)
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	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 (y <= -2e+84)
		tmp = (-4.0 * (y / z)) - 2.0;
	elseif (y <= 2.2)
		tmp = (4.0 * (x / z)) - 2.0;
	else
		tmp = 4.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+84], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[y, 2.2], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000012e84

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. *-lft-identity 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{1 \cdot z}}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      5. metadata-eval 100.0%

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

      6. associate-/l* 99.8%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{--1}{\frac{4}{z}}}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      7. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{--1} \cdot \frac{4}{z}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      8. fma-neg 99.8%

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

      9. metadata-eval 99.8%

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

      10. /-rgt-identity 99.8%

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

      11. associate-/r/ 99.8%

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

      12. distribute-lft-neg-in 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. *-commutative 99.8%

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

      15. distribute-lft-neg-in 99.8%

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

      16. associate-/l* 99.8%

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

      17. metadata-eval 99.8%

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

      18. *-inverses 99.8%

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

      19. metadata-eval 99.8%

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

      20. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 84.7%

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

   if -2.00000000000000012e84 < y < 2.2000000000000002

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. *-lft-identity 100.0%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{1 \cdot z}}{4}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      5. metadata-eval 100.0%

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

      6. associate-/l* 99.9%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{--1}{\frac{4}{z}}}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      7. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{--1} \cdot \frac{4}{z}} - \frac{z \cdot 0.5}{\frac{z}{4}} \]

      8. fma-neg 99.8%

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

      9. metadata-eval 99.8%

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

      10. /-rgt-identity 99.8%

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

      11. associate-/r/ 99.8%

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

      12. distribute-lft-neg-in 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. *-commutative 99.8%

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

      15. distribute-lft-neg-in 99.8%

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

      16. associate-/l* 99.8%

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

      17. metadata-eval 99.8%

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

      18. *-inverses 99.8%

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

      19. metadata-eval 99.8%

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

      20. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 92.2%

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

   if 2.2000000000000002 < y

   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/ 99.9%

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

      2. /-rgt-identity 99.9%

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

      3. metadata-eval 99.9%

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

      4. metadata-eval 99.9%

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

      5. /-rgt-identity 99.9%

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

      6. sub-neg 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 90.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{elif}\;y \leq 2.2:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+118} \lor \neg \left(x \leq 2 \cdot 10^{-41}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.25e+118) (not (<= x 2e-41))) (* 4.0 (/ x z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.25e+118) || !(x <= 2e-41)) {
		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 <= (-1.25d+118)) .or. (.not. (x <= 2d-41))) 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 <= -1.25e+118) || !(x <= 2e-41)) {
		tmp = 4.0 * (x / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.25e+118) or not (x <= 2e-41):
		tmp = 4.0 * (x / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.25e+118) || !(x <= 2e-41))
		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 <= -1.25e+118) || ~((x <= 2e-41)))
		tmp = 4.0 * (x / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.25e+118], N[Not[LessEqual[x, 2e-41]], $MachinePrecision]], N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999993e118 or 2.00000000000000001e-41 < 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. /-rgt-identity 99.7%

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

      3. metadata-eval 99.7%

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

      4. metadata-eval 99.7%

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

      5. /-rgt-identity 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in x around inf 64.9%

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

   if -1.24999999999999993e118 < x < 2.00000000000000001e-41

   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. /-rgt-identity 99.7%

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

      3. metadata-eval 99.7%

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

      4. metadata-eval 99.7%

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

      5. /-rgt-identity 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. 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. Add Preprocessing

   5. Taylor expanded in z around inf 49.7%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+118} \lor \neg \left(x \leq 2 \cdot 10^{-41}\right):\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 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. /-rgt-identity 99.7%

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

   3. metadata-eval 99.7%

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

   4. metadata-eval 99.7%

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

   5. /-rgt-identity 99.7%

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

   6. sub-neg 99.7%

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

   7. distribute-rgt-neg-in 99.7%

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

   8. 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. Add Preprocessing

5. Final simplification 99.7%

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

Alternative 8: 34.2% 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. /-rgt-identity 99.7%

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

   3. metadata-eval 99.7%

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

   4. metadata-eval 99.7%

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

   5. /-rgt-identity 99.7%

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

   6. sub-neg 99.7%

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

   7. distribute-rgt-neg-in 99.7%

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

   8. 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. Add Preprocessing

5. Taylor expanded in z around inf 33.3%

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

6. Final simplification 33.3%

   \[\leadsto -2 \]
7. Add Preprocessing

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 2024021 
(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))