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

Percentage Accurate: 99.8% → 100.0%

Time: 6.0s

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 99.2%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
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 z around 0 100.0%

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

6. Final simplification 100.0%

   \[\leadsto 4 \cdot \frac{x - y}{z} - 2 \]
7. Add Preprocessing

Alternative 2: 54.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{4}{z}\\ t_1 := -4 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -6.3 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-145}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-222}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-151}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ 4.0 z))) (t_1 (* -4.0 (/ y z))))
   (if (<= y -6.3e+74)
     t_1
     (if (<= y -6.2e-145)
       -2.0
       (if (<= y 3.8e-222)
         t_0
         (if (<= y 1.26e-151) -2.0 (if (<= y 1.4e+16) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.0 / z);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -6.3e+74) {
		tmp = t_1;
	} else if (y <= -6.2e-145) {
		tmp = -2.0;
	} else if (y <= 3.8e-222) {
		tmp = t_0;
	} else if (y <= 1.26e-151) {
		tmp = -2.0;
	} else if (y <= 1.4e+16) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (4.0d0 / z)
    t_1 = (-4.0d0) * (y / z)
    if (y <= (-6.3d+74)) then
        tmp = t_1
    else if (y <= (-6.2d-145)) then
        tmp = -2.0d0
    else if (y <= 3.8d-222) then
        tmp = t_0
    else if (y <= 1.26d-151) then
        tmp = -2.0d0
    else if (y <= 1.4d+16) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (4.0 / z);
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -6.3e+74) {
		tmp = t_1;
	} else if (y <= -6.2e-145) {
		tmp = -2.0;
	} else if (y <= 3.8e-222) {
		tmp = t_0;
	} else if (y <= 1.26e-151) {
		tmp = -2.0;
	} else if (y <= 1.4e+16) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.0 / z)
	t_1 = -4.0 * (y / z)
	tmp = 0
	if y <= -6.3e+74:
		tmp = t_1
	elif y <= -6.2e-145:
		tmp = -2.0
	elif y <= 3.8e-222:
		tmp = t_0
	elif y <= 1.26e-151:
		tmp = -2.0
	elif y <= 1.4e+16:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.0 / z))
	t_1 = Float64(-4.0 * Float64(y / z))
	tmp = 0.0
	if (y <= -6.3e+74)
		tmp = t_1;
	elseif (y <= -6.2e-145)
		tmp = -2.0;
	elseif (y <= 3.8e-222)
		tmp = t_0;
	elseif (y <= 1.26e-151)
		tmp = -2.0;
	elseif (y <= 1.4e+16)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.0 / z);
	t_1 = -4.0 * (y / z);
	tmp = 0.0;
	if (y <= -6.3e+74)
		tmp = t_1;
	elseif (y <= -6.2e-145)
		tmp = -2.0;
	elseif (y <= 3.8e-222)
		tmp = t_0;
	elseif (y <= 1.26e-151)
		tmp = -2.0;
	elseif (y <= 1.4e+16)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.3e+74], t$95$1, If[LessEqual[y, -6.2e-145], -2.0, If[LessEqual[y, 3.8e-222], t$95$0, If[LessEqual[y, 1.26e-151], -2.0, If[LessEqual[y, 1.4e+16], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.30000000000000016e74 or 1.4e16 < y

   1. Initial program 99.1%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 71.0%

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

   if -6.30000000000000016e74 < y < -6.20000000000000001e-145 or 3.79999999999999997e-222 < y < 1.2600000000000001e-151

   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 59.4%

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

   if -6.20000000000000001e-145 < y < 3.79999999999999997e-222 or 1.2600000000000001e-151 < y < 1.4e16

   1. Initial program 98.8%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 z around 0 64.7%

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

      1. associate-*r/ 64.7%

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

      2. associate-*l/ 64.6%

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

      3. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around inf 60.9%

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

      1. associate-*r/ 60.9%

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

      2. associate-*l/ 60.8%

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

      3. *-commutative 60.8%

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

   10. Simplified 60.8%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-145}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-151}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{z}\\ t_1 := -4 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-145}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-222}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-153}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) z)) (t_1 (* -4.0 (/ y z))))
   (if (<= y -5.8e+74)
     t_1
     (if (<= y -1.8e-145)
       -2.0
       (if (<= y 3e-222)
         t_0
         (if (<= y 1.35e-153) -2.0 (if (<= y 1.3e+24) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / z;
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -5.8e+74) {
		tmp = t_1;
	} else if (y <= -1.8e-145) {
		tmp = -2.0;
	} else if (y <= 3e-222) {
		tmp = t_0;
	} else if (y <= 1.35e-153) {
		tmp = -2.0;
	} else if (y <= 1.3e+24) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * x) / z
    t_1 = (-4.0d0) * (y / z)
    if (y <= (-5.8d+74)) then
        tmp = t_1
    else if (y <= (-1.8d-145)) then
        tmp = -2.0d0
    else if (y <= 3d-222) then
        tmp = t_0
    else if (y <= 1.35d-153) then
        tmp = -2.0d0
    else if (y <= 1.3d+24) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / z;
	double t_1 = -4.0 * (y / z);
	double tmp;
	if (y <= -5.8e+74) {
		tmp = t_1;
	} else if (y <= -1.8e-145) {
		tmp = -2.0;
	} else if (y <= 3e-222) {
		tmp = t_0;
	} else if (y <= 1.35e-153) {
		tmp = -2.0;
	} else if (y <= 1.3e+24) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * x) / z
	t_1 = -4.0 * (y / z)
	tmp = 0
	if y <= -5.8e+74:
		tmp = t_1
	elif y <= -1.8e-145:
		tmp = -2.0
	elif y <= 3e-222:
		tmp = t_0
	elif y <= 1.35e-153:
		tmp = -2.0
	elif y <= 1.3e+24:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / z)
	t_1 = Float64(-4.0 * Float64(y / z))
	tmp = 0.0
	if (y <= -5.8e+74)
		tmp = t_1;
	elseif (y <= -1.8e-145)
		tmp = -2.0;
	elseif (y <= 3e-222)
		tmp = t_0;
	elseif (y <= 1.35e-153)
		tmp = -2.0;
	elseif (y <= 1.3e+24)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * x) / z;
	t_1 = -4.0 * (y / z);
	tmp = 0.0;
	if (y <= -5.8e+74)
		tmp = t_1;
	elseif (y <= -1.8e-145)
		tmp = -2.0;
	elseif (y <= 3e-222)
		tmp = t_0;
	elseif (y <= 1.35e-153)
		tmp = -2.0;
	elseif (y <= 1.3e+24)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+74], t$95$1, If[LessEqual[y, -1.8e-145], -2.0, If[LessEqual[y, 3e-222], t$95$0, If[LessEqual[y, 1.35e-153], -2.0, If[LessEqual[y, 1.3e+24], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000005e74 or 1.2999999999999999e24 < y

   1. Initial program 99.1%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 71.0%

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

   if -5.8000000000000005e74 < y < -1.8e-145 or 3.0000000000000003e-222 < y < 1.35000000000000005e-153

   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 59.4%

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

   if -1.8e-145 < y < 3.0000000000000003e-222 or 1.35000000000000005e-153 < y < 1.2999999999999999e24

   1. Initial program 98.8%

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

      1. associate--l- 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 60.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-145}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-222}:\\ \;\;\;\;\frac{4 \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-153}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+24}:\\ \;\;\;\;\frac{4 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0095:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+143}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x y) (/ 4.0 z))))
   (if (<= x -3.5e+70)
     t_0
     (if (<= x 0.0095)
       (- (* -4.0 (/ y z)) 2.0)
       (if (<= x 9e+143) (- (* 4.0 (/ x z)) 2.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) * (4.0 / z);
	double tmp;
	if (x <= -3.5e+70) {
		tmp = t_0;
	} else if (x <= 0.0095) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else if (x <= 9e+143) {
		tmp = (4.0 * (x / z)) - 2.0;
	} 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) :: tmp
    t_0 = (x - y) * (4.0d0 / z)
    if (x <= (-3.5d+70)) then
        tmp = t_0
    else if (x <= 0.0095d0) then
        tmp = ((-4.0d0) * (y / z)) - 2.0d0
    else if (x <= 9d+143) then
        tmp = (4.0d0 * (x / z)) - 2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) * (4.0 / z);
	double tmp;
	if (x <= -3.5e+70) {
		tmp = t_0;
	} else if (x <= 0.0095) {
		tmp = (-4.0 * (y / z)) - 2.0;
	} else if (x <= 9e+143) {
		tmp = (4.0 * (x / z)) - 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) * (4.0 / z)
	tmp = 0
	if x <= -3.5e+70:
		tmp = t_0
	elif x <= 0.0095:
		tmp = (-4.0 * (y / z)) - 2.0
	elif x <= 9e+143:
		tmp = (4.0 * (x / z)) - 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) * Float64(4.0 / z))
	tmp = 0.0
	if (x <= -3.5e+70)
		tmp = t_0;
	elseif (x <= 0.0095)
		tmp = Float64(Float64(-4.0 * Float64(y / z)) - 2.0);
	elseif (x <= 9e+143)
		tmp = Float64(Float64(4.0 * Float64(x / z)) - 2.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) * (4.0 / z);
	tmp = 0.0;
	if (x <= -3.5e+70)
		tmp = t_0;
	elseif (x <= 0.0095)
		tmp = (-4.0 * (y / z)) - 2.0;
	elseif (x <= 9e+143)
		tmp = (4.0 * (x / z)) - 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+70], t$95$0, If[LessEqual[x, 0.0095], N[(N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[x, 9e+143], N[(N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.50000000000000002e70 or 8.9999999999999993e143 < x

   1. Initial program 98.9%

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

      1. associate-*l/ 99.8%

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

      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 z around 0 94.1%

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

      1. associate-*r/ 94.1%

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

      2. associate-*l/ 94.0%

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

      3. *-commutative 94.0%

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

   7. Simplified 94.0%

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

   if -3.50000000000000002e70 < x < 0.00949999999999999976

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      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/ 99.9%

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

      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 91.2%

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

   if 0.00949999999999999976 < x < 8.9999999999999993e143

   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/ 100.0%

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

      8. fma-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. /-rgt-identity 100.0%

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

      11. associate-/r/ 100.0%

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

      12. distribute-lft-neg-in 100.0%

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

      13. distribute-frac-neg 100.0%

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

      14. *-commutative 100.0%

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

      15. distribute-lft-neg-in 100.0%

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

      16. associate-/l* 100.0%

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

      17. metadata-eval 100.0%

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

      18. *-inverses 100.0%

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

      19. metadata-eval 100.0%

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

      20. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 91.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{elif}\;x \leq 0.0095:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+143}:\\ \;\;\;\;4 \cdot \frac{x}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+70} \lor \neg \left(x \leq 1.35 \cdot 10^{+80}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+70) (not (<= x 1.35e+80)))
   (* (- x y) (/ 4.0 z))
   (- (* -4.0 (/ y z)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e+70) || !(x <= 1.35e+80)) {
		tmp = (x - y) * (4.0 / 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 <= (-7d+70)) .or. (.not. (x <= 1.35d+80))) then
        tmp = (x - y) * (4.0d0 / 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 <= -7e+70) || !(x <= 1.35e+80)) {
		tmp = (x - y) * (4.0 / z);
	} else {
		tmp = (-4.0 * (y / z)) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e+70) or not (x <= 1.35e+80):
		tmp = (x - y) * (4.0 / z)
	else:
		tmp = (-4.0 * (y / z)) - 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e+70) || !(x <= 1.35e+80))
		tmp = Float64(Float64(x - y) * Float64(4.0 / 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 <= -7e+70) || ~((x <= 1.35e+80)))
		tmp = (x - y) * (4.0 / z);
	else
		tmp = (-4.0 * (y / z)) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e+70], N[Not[LessEqual[x, 1.35e+80]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(4.0 / 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 < -7.00000000000000005e70 or 1.34999999999999991e80 < x

   1. Initial program 99.1%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 z around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. associate-*l/ 89.5%

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

      3. *-commutative 89.5%

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

   7. Simplified 89.5%

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

   if -7.00000000000000005e70 < x < 1.34999999999999991e80

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      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/ 99.9%

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

      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 89.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+70} \lor \neg \left(x \leq 1.35 \cdot 10^{+80}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+99}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.9e+99) -2.0 (if (<= z 1.15e+91) (* (- x y) (/ 4.0 z)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.9e+99) {
		tmp = -2.0;
	} else if (z <= 1.15e+91) {
		tmp = (x - y) * (4.0 / 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 <= (-3.9d+99)) then
        tmp = -2.0d0
    else if (z <= 1.15d+91) then
        tmp = (x - y) * (4.0d0 / 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 <= -3.9e+99) {
		tmp = -2.0;
	} else if (z <= 1.15e+91) {
		tmp = (x - y) * (4.0 / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.9e+99:
		tmp = -2.0
	elif z <= 1.15e+91:
		tmp = (x - y) * (4.0 / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.9e+99)
		tmp = -2.0;
	elseif (z <= 1.15e+91)
		tmp = Float64(Float64(x - y) * Float64(4.0 / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.9e+99)
		tmp = -2.0;
	elseif (z <= 1.15e+91)
		tmp = (x - y) * (4.0 / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.9e+99], -2.0, If[LessEqual[z, 1.15e+91], N[(N[(x - y), $MachinePrecision] * N[(4.0 / z), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999995e99 or 1.14999999999999996e91 < z

   1. Initial program 97.6%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 z around inf 70.8%

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

   if -3.89999999999999995e99 < z < 1.14999999999999996e91

   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 z around 0 88.9%

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

      1. associate-*r/ 88.9%

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

      2. associate-*l/ 88.7%

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

      3. *-commutative 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+99}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{4}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+74} \lor \neg \left(y \leq 4.1 \cdot 10^{-26}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+74) (not (<= y 4.1e-26))) (* -4.0 (/ y z)) -2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+74) || !(y <= 4.1e-26)) {
		tmp = -4.0 * (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 ((y <= (-5.8d+74)) .or. (.not. (y <= 4.1d-26))) then
        tmp = (-4.0d0) * (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 ((y <= -5.8e+74) || !(y <= 4.1e-26)) {
		tmp = -4.0 * (y / z);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+74) or not (y <= 4.1e-26):
		tmp = -4.0 * (y / z)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+74) || !(y <= 4.1e-26))
		tmp = Float64(-4.0 * Float64(y / z));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e+74) || ~((y <= 4.1e-26)))
		tmp = -4.0 * (y / z);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e+74], N[Not[LessEqual[y, 4.1e-26]], $MachinePrecision]], N[(-4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000005e74 or 4.0999999999999999e-26 < y

   1. Initial program 99.2%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 69.0%

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

   if -5.8000000000000005e74 < y < 4.0999999999999999e-26

   1. Initial program 99.3%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   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 48.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+74} \lor \neg \left(y \leq 4.1 \cdot 10^{-26}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.8% 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 99.2%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
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 z around inf 31.9%

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

6. Final simplification 31.9%

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

Developer target: 98.1% 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 2024036 
(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))