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

Percentage Accurate: 99.8% → 100.0%

Time: 8.1s

Alternatives: 11

Speedup: 1.4×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{x - z}{y \cdot 0.25} + 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (/ (- x z) (* y 0.25)) 2.0))

C

double code(double x, double y, double z) {
	return ((x - z) / (y * 0.25)) + 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 = ((x - z) / (y * 0.25d0)) + 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return ((x - z) / (y * 0.25)) + 2.0;
}

Python

def code(x, y, z):
	return ((x - z) / (y * 0.25)) + 2.0

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - z) / Float64(y * 0.25)) + 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - z) / (y * 0.25)) + 2.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - z), $MachinePrecision] / N[(y * 0.25), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

   2. associate-*l/ 99.8%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

   3. +-commutative 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

   4. associate--l+ 99.8%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

   5. +-commutative 99.8%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

   6. distribute-lft-in 99.8%

      \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

   7. associate-+l+ 99.8%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

   8. associate-*l/ 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

   9. *-commutative 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

   10. associate-*l* 99.8%

       \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

   11. metadata-eval 99.8%

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

   12. *-rgt-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + 2} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. clear-num 99.8%

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

   3. div-inv 99.8%

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

   4. metadata-eval 99.8%

      \[\leadsto \left(x - z\right) \cdot \frac{1}{y \cdot \color{blue}{0.25}} + 2 \]

   5. un-div-inv 100.0%

      \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]
7. Add Preprocessing

Alternative 2: 55.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+43}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.058:\\ \;\;\;\;1 + t\_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= y -7e+43)
     2.0
     (if (<= y -7.2e-185)
       t_1
       (if (<= y 1.2e-292)
         t_0
         (if (<= y 2.65e-43) t_1 (if (<= y 0.058) (+ 1.0 t_0) 2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -7e+43) {
		tmp = 2.0;
	} else if (y <= -7.2e-185) {
		tmp = t_1;
	} else if (y <= 1.2e-292) {
		tmp = t_0;
	} else if (y <= 2.65e-43) {
		tmp = t_1;
	} else if (y <= 0.058) {
		tmp = 1.0 + t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (z * (-4.0d0)) / y
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (y <= (-7d+43)) then
        tmp = 2.0d0
    else if (y <= (-7.2d-185)) then
        tmp = t_1
    else if (y <= 1.2d-292) then
        tmp = t_0
    else if (y <= 2.65d-43) then
        tmp = t_1
    else if (y <= 0.058d0) then
        tmp = 1.0d0 + t_0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -7e+43) {
		tmp = 2.0;
	} else if (y <= -7.2e-185) {
		tmp = t_1;
	} else if (y <= 1.2e-292) {
		tmp = t_0;
	} else if (y <= 2.65e-43) {
		tmp = t_1;
	} else if (y <= 0.058) {
		tmp = 1.0 + t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if y <= -7e+43:
		tmp = 2.0
	elif y <= -7.2e-185:
		tmp = t_1
	elif y <= 1.2e-292:
		tmp = t_0
	elif y <= 2.65e-43:
		tmp = t_1
	elif y <= 0.058:
		tmp = 1.0 + t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (y <= -7e+43)
		tmp = 2.0;
	elseif (y <= -7.2e-185)
		tmp = t_1;
	elseif (y <= 1.2e-292)
		tmp = t_0;
	elseif (y <= 2.65e-43)
		tmp = t_1;
	elseif (y <= 0.058)
		tmp = Float64(1.0 + t_0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (y <= -7e+43)
		tmp = 2.0;
	elseif (y <= -7.2e-185)
		tmp = t_1;
	elseif (y <= 1.2e-292)
		tmp = t_0;
	elseif (y <= 2.65e-43)
		tmp = t_1;
	elseif (y <= 0.058)
		tmp = 1.0 + t_0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+43], 2.0, If[LessEqual[y, -7.2e-185], t$95$1, If[LessEqual[y, 1.2e-292], t$95$0, If[LessEqual[y, 2.65e-43], t$95$1, If[LessEqual[y, 0.058], N[(1.0 + t$95$0), $MachinePrecision], 2.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.0000000000000002e43 or 0.0580000000000000029 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.5%

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

   if -7.0000000000000002e43 < y < -7.1999999999999997e-185 or 1.2000000000000001e-292 < y < 2.6500000000000002e-43

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 62.5%

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

   if -7.1999999999999997e-185 < y < 1.2000000000000001e-292

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*l/ 76.2%

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

   6. Simplified 76.2%

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

   if 2.6500000000000002e-43 < y < 0.0580000000000000029

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.8%

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

      1. *-commutative 76.8%

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

   5. Simplified 76.8%

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

Alternative 3: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.058:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= y -3.1e+43)
     2.0
     (if (<= y -7.1e-186)
       t_1
       (if (<= y 1.95e-292)
         t_0
         (if (<= y 1.4e-42) t_1 (if (<= y 0.058) t_0 2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -3.1e+43) {
		tmp = 2.0;
	} else if (y <= -7.1e-186) {
		tmp = t_1;
	} else if (y <= 1.95e-292) {
		tmp = t_0;
	} else if (y <= 1.4e-42) {
		tmp = t_1;
	} else if (y <= 0.058) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (z * (-4.0d0)) / y
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (y <= (-3.1d+43)) then
        tmp = 2.0d0
    else if (y <= (-7.1d-186)) then
        tmp = t_1
    else if (y <= 1.95d-292) then
        tmp = t_0
    else if (y <= 1.4d-42) then
        tmp = t_1
    else if (y <= 0.058d0) then
        tmp = t_0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -3.1e+43) {
		tmp = 2.0;
	} else if (y <= -7.1e-186) {
		tmp = t_1;
	} else if (y <= 1.95e-292) {
		tmp = t_0;
	} else if (y <= 1.4e-42) {
		tmp = t_1;
	} else if (y <= 0.058) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if y <= -3.1e+43:
		tmp = 2.0
	elif y <= -7.1e-186:
		tmp = t_1
	elif y <= 1.95e-292:
		tmp = t_0
	elif y <= 1.4e-42:
		tmp = t_1
	elif y <= 0.058:
		tmp = t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (y <= -3.1e+43)
		tmp = 2.0;
	elseif (y <= -7.1e-186)
		tmp = t_1;
	elseif (y <= 1.95e-292)
		tmp = t_0;
	elseif (y <= 1.4e-42)
		tmp = t_1;
	elseif (y <= 0.058)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (y <= -3.1e+43)
		tmp = 2.0;
	elseif (y <= -7.1e-186)
		tmp = t_1;
	elseif (y <= 1.95e-292)
		tmp = t_0;
	elseif (y <= 1.4e-42)
		tmp = t_1;
	elseif (y <= 0.058)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+43], 2.0, If[LessEqual[y, -7.1e-186], t$95$1, If[LessEqual[y, 1.95e-292], t$95$0, If[LessEqual[y, 1.4e-42], t$95$1, If[LessEqual[y, 0.058], t$95$0, 2.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000002e43 or 0.0580000000000000029 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.5%

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

   if -3.1000000000000002e43 < y < -7.10000000000000014e-186 or 1.95e-292 < y < 1.39999999999999999e-42

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 62.5%

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

   if -7.10000000000000014e-186 < y < 1.95e-292 or 1.39999999999999999e-42 < y < 0.0580000000000000029

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*l/ 75.8%

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

   6. Simplified 75.8%

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

Alternative 4: 54.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+43}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-291}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.118:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)) (t_1 (* 4.0 (/ x y))))
   (if (<= y -4.8e+43)
     2.0
     (if (<= y -3.4e-185)
       t_1
       (if (<= y 3.1e-291)
         t_0
         (if (<= y 2.15e-42) t_1 (if (<= y 0.118) t_0 2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (y <= -4.8e+43) {
		tmp = 2.0;
	} else if (y <= -3.4e-185) {
		tmp = t_1;
	} else if (y <= 3.1e-291) {
		tmp = t_0;
	} else if (y <= 2.15e-42) {
		tmp = t_1;
	} else if (y <= 0.118) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (z * (-4.0d0)) / y
    t_1 = 4.0d0 * (x / y)
    if (y <= (-4.8d+43)) then
        tmp = 2.0d0
    else if (y <= (-3.4d-185)) then
        tmp = t_1
    else if (y <= 3.1d-291) then
        tmp = t_0
    else if (y <= 2.15d-42) then
        tmp = t_1
    else if (y <= 0.118d0) then
        tmp = t_0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = 4.0 * (x / y);
	double tmp;
	if (y <= -4.8e+43) {
		tmp = 2.0;
	} else if (y <= -3.4e-185) {
		tmp = t_1;
	} else if (y <= 3.1e-291) {
		tmp = t_0;
	} else if (y <= 2.15e-42) {
		tmp = t_1;
	} else if (y <= 0.118) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	t_1 = 4.0 * (x / y)
	tmp = 0
	if y <= -4.8e+43:
		tmp = 2.0
	elif y <= -3.4e-185:
		tmp = t_1
	elif y <= 3.1e-291:
		tmp = t_0
	elif y <= 2.15e-42:
		tmp = t_1
	elif y <= 0.118:
		tmp = t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	t_1 = Float64(4.0 * Float64(x / y))
	tmp = 0.0
	if (y <= -4.8e+43)
		tmp = 2.0;
	elseif (y <= -3.4e-185)
		tmp = t_1;
	elseif (y <= 3.1e-291)
		tmp = t_0;
	elseif (y <= 2.15e-42)
		tmp = t_1;
	elseif (y <= 0.118)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	t_1 = 4.0 * (x / y);
	tmp = 0.0;
	if (y <= -4.8e+43)
		tmp = 2.0;
	elseif (y <= -3.4e-185)
		tmp = t_1;
	elseif (y <= 3.1e-291)
		tmp = t_0;
	elseif (y <= 2.15e-42)
		tmp = t_1;
	elseif (y <= 0.118)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+43], 2.0, If[LessEqual[y, -3.4e-185], t$95$1, If[LessEqual[y, 3.1e-291], t$95$0, If[LessEqual[y, 2.15e-42], t$95$1, If[LessEqual[y, 0.118], t$95$0, 2.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000046e43 or 0.11799999999999999 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.5%

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

   if -4.80000000000000046e43 < y < -3.3999999999999998e-185 or 3.10000000000000011e-291 < y < 2.1500000000000001e-42

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around inf 61.0%

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

   if -3.3999999999999998e-185 < y < 3.10000000000000011e-291 or 2.1500000000000001e-42 < y < 0.11799999999999999

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*l/ 75.8%

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

   6. Simplified 75.8%

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

Alternative 5: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+87} \lor \neg \left(z \leq -0.27 \lor \neg \left(z \leq -4.6 \cdot 10^{-30}\right) \land z \leq 1.12 \cdot 10^{+147}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+87)
         (not (or (<= z -0.27) (and (not (<= z -4.6e-30)) (<= z 1.12e+147)))))
   (+ 1.0 (/ (* z -4.0) y))
   (+ 2.0 (* x (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+87) || !((z <= -0.27) || (!(z <= -4.6e-30) && (z <= 1.12e+147)))) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 2.0 + (x * (4.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.8d+87)) .or. (.not. (z <= (-0.27d0)) .or. (.not. (z <= (-4.6d-30))) .and. (z <= 1.12d+147))) then
        tmp = 1.0d0 + ((z * (-4.0d0)) / y)
    else
        tmp = 2.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+87) || !((z <= -0.27) || (!(z <= -4.6e-30) && (z <= 1.12e+147)))) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 2.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+87) or not ((z <= -0.27) or (not (z <= -4.6e-30) and (z <= 1.12e+147))):
		tmp = 1.0 + ((z * -4.0) / y)
	else:
		tmp = 2.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+87) || !((z <= -0.27) || (!(z <= -4.6e-30) && (z <= 1.12e+147))))
		tmp = Float64(1.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = Float64(2.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+87) || ~(((z <= -0.27) || (~((z <= -4.6e-30)) && (z <= 1.12e+147)))))
		tmp = 1.0 + ((z * -4.0) / y);
	else
		tmp = 2.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+87], N[Not[Or[LessEqual[z, -0.27], And[N[Not[LessEqual[z, -4.6e-30]], $MachinePrecision], LessEqual[z, 1.12e+147]]]], $MachinePrecision]], N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999997e87 or -0.27000000000000002 < z < -4.59999999999999968e-30 or 1.12e147 < z

   1. Initial program 98.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.8%

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

      1. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   if -1.79999999999999997e87 < z < -0.27000000000000002 or -4.59999999999999968e-30 < z < 1.12e147

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.9%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 88.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+87} \lor \neg \left(z \leq -0.27 \lor \neg \left(z \leq -4.6 \cdot 10^{-30}\right) \land z \leq 1.12 \cdot 10^{+147}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-15} \lor \neg \left(y \leq 0.48\right):\\ \;\;\;\;2 + \frac{\frac{x}{y}}{0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - z\right) \cdot 4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.95e-15) (not (<= y 0.48)))
   (+ 2.0 (/ (/ x y) 0.25))
   (/ (* (- x z) 4.0) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.95e-15) || !(y <= 0.48)) {
		tmp = 2.0 + ((x / y) / 0.25);
	} else {
		tmp = ((x - z) * 4.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.95d-15)) .or. (.not. (y <= 0.48d0))) then
        tmp = 2.0d0 + ((x / y) / 0.25d0)
    else
        tmp = ((x - z) * 4.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.95e-15) || !(y <= 0.48)) {
		tmp = 2.0 + ((x / y) / 0.25);
	} else {
		tmp = ((x - z) * 4.0) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.95e-15) or not (y <= 0.48):
		tmp = 2.0 + ((x / y) / 0.25)
	else:
		tmp = ((x - z) * 4.0) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.95e-15) || !(y <= 0.48))
		tmp = Float64(2.0 + Float64(Float64(x / y) / 0.25));
	else
		tmp = Float64(Float64(Float64(x - z) * 4.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.95e-15) || ~((y <= 0.48)))
		tmp = 2.0 + ((x / y) / 0.25);
	else
		tmp = ((x - z) * 4.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.95e-15], N[Not[LessEqual[y, 0.48]], $MachinePrecision]], N[(2.0 + N[(N[(x / y), $MachinePrecision] / 0.25), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - z), $MachinePrecision] * 4.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.94999999999999982e-15 or 0.47999999999999998 < y

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.2%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.9%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.9%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.9%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.9%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 88.9%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{x} + 2 \]
   6. Step-by-step derivation

      1. *-commutative 88.9%

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

      2. metadata-eval 88.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{0.25}}}{y} + 2 \]

      3. associate-/r* 88.9%

         \[\leadsto x \cdot \color{blue}{\frac{1}{0.25 \cdot y}} + 2 \]

      4. *-commutative 88.9%

         \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot 0.25}} + 2 \]

      5. div-inv 89.0%

         \[\leadsto \color{blue}{\frac{x}{y \cdot 0.25}} + 2 \]

      6. associate-/r* 89.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{0.25}} + 2 \]

   7. Applied egg-rr 89.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{0.25}} + 2 \]

   if -2.94999999999999982e-15 < y < 0.47999999999999998

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in y around 0 95.2%

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

      1. associate-*r/ 95.2%

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

   6. Simplified 95.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-15} \lor \neg \left(y \leq 0.48\right):\\ \;\;\;\;2 + \frac{\frac{x}{y}}{0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - z\right) \cdot 4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+63} \lor \neg \left(x \leq 3.5 \cdot 10^{-17}\right):\\ \;\;\;\;2 + \frac{\frac{x}{y}}{0.25}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.4e+63) (not (<= x 3.5e-17)))
   (+ 2.0 (/ (/ x y) 0.25))
   (+ 2.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.4e+63) || !(x <= 3.5e-17)) {
		tmp = 2.0 + ((x / y) / 0.25);
	} else {
		tmp = 2.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-4.4d+63)) .or. (.not. (x <= 3.5d-17))) then
        tmp = 2.0d0 + ((x / y) / 0.25d0)
    else
        tmp = 2.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.4e+63) || !(x <= 3.5e-17)) {
		tmp = 2.0 + ((x / y) / 0.25);
	} else {
		tmp = 2.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.4e+63) or not (x <= 3.5e-17):
		tmp = 2.0 + ((x / y) / 0.25)
	else:
		tmp = 2.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.4e+63) || !(x <= 3.5e-17))
		tmp = Float64(2.0 + Float64(Float64(x / y) / 0.25));
	else
		tmp = Float64(2.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.4e+63) || ~((x <= 3.5e-17)))
		tmp = 2.0 + ((x / y) / 0.25);
	else
		tmp = 2.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.4e+63], N[Not[LessEqual[x, 3.5e-17]], $MachinePrecision]], N[(2.0 + N[(N[(x / y), $MachinePrecision] / 0.25), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3999999999999997e63 or 3.5000000000000002e-17 < x

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.2%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.9%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 87.1%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{x} + 2 \]
   6. Step-by-step derivation

      1. *-commutative 87.1%

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

      2. metadata-eval 87.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{0.25}}}{y} + 2 \]

      3. associate-/r* 87.1%

         \[\leadsto x \cdot \color{blue}{\frac{1}{0.25 \cdot y}} + 2 \]

      4. *-commutative 87.1%

         \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot 0.25}} + 2 \]

      5. div-inv 87.2%

         \[\leadsto \color{blue}{\frac{x}{y \cdot 0.25}} + 2 \]

      6. associate-/r* 87.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{0.25}} + 2 \]

   7. Applied egg-rr 87.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{0.25}} + 2 \]

   if -4.3999999999999997e63 < x < 3.5000000000000002e-17

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + 2} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

         \[\leadsto \left(x - z\right) \cdot \frac{1}{y \cdot \color{blue}{0.25}} + 2 \]

      5. un-div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

   7. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{z}{y}} + 2 \]
   8. Step-by-step derivation

      1. associate-*r/ 89.3%

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

   9. Simplified 89.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+63} \lor \neg \left(x \leq 3.5 \cdot 10^{-17}\right):\\ \;\;\;\;2 + \frac{\frac{x}{y}}{0.25}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+64} \lor \neg \left(x \leq 6.2 \cdot 10^{-19}\right):\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.02e+64) (not (<= x 6.2e-19)))
   (+ 2.0 (* x (/ 4.0 y)))
   (+ 2.0 (/ (* z -4.0) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e+64) || !(x <= 6.2e-19)) {
		tmp = 2.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.02d+64)) .or. (.not. (x <= 6.2d-19))) then
        tmp = 2.0d0 + (x * (4.0d0 / y))
    else
        tmp = 2.0d0 + ((z * (-4.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e+64) || !(x <= 6.2e-19)) {
		tmp = 2.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0 + ((z * -4.0) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.02e+64) or not (x <= 6.2e-19):
		tmp = 2.0 + (x * (4.0 / y))
	else:
		tmp = 2.0 + ((z * -4.0) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.02e+64) || !(x <= 6.2e-19))
		tmp = Float64(2.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = Float64(2.0 + Float64(Float64(z * -4.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.02e+64) || ~((x <= 6.2e-19)))
		tmp = 2.0 + (x * (4.0 / y));
	else
		tmp = 2.0 + ((z * -4.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.02e+64], N[Not[LessEqual[x, 6.2e-19]], $MachinePrecision]], N[(2.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999996e64 or 6.1999999999999998e-19 < x

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.2%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.9%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.9%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 87.1%

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

   if -1.01999999999999996e64 < x < 6.1999999999999998e-19

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

      3. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

      4. associate--l+ 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

      5. +-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

      6. distribute-lft-in 99.8%

         \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

      8. associate-*l/ 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

      9. *-commutative 99.8%

         \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

      10. associate-*l* 99.8%

          \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + 2} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

         \[\leadsto \left(x - z\right) \cdot \frac{1}{y \cdot \color{blue}{0.25}} + 2 \]

      5. un-div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

   7. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{z}{y}} + 2 \]
   8. Step-by-step derivation

      1. associate-*r/ 89.3%

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

   9. Simplified 89.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+64} \lor \neg \left(x \leq 6.2 \cdot 10^{-19}\right):\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+43}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+88}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+43) 2.0 (if (<= y 1.25e+88) (* 4.0 (/ x y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+43) {
		tmp = 2.0;
	} else if (y <= 1.25e+88) {
		tmp = 4.0 * (x / y);
	} 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 <= (-3.4d+43)) then
        tmp = 2.0d0
    else if (y <= 1.25d+88) then
        tmp = 4.0d0 * (x / y)
    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 <= -3.4e+43) {
		tmp = 2.0;
	} else if (y <= 1.25e+88) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+43:
		tmp = 2.0
	elif y <= 1.25e+88:
		tmp = 4.0 * (x / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+43)
		tmp = 2.0;
	elseif (y <= 1.25e+88)
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+43)
		tmp = 2.0;
	elseif (y <= 1.25e+88)
		tmp = 4.0 * (x / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+43], 2.0, If[LessEqual[y, 1.25e+88], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000012e43 or 1.24999999999999999e88 < y

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.9%

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

   if -3.40000000000000012e43 < y < 1.24999999999999999e88

   1. Initial program 99.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.4%

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

   4. Taylor expanded in x around inf 51.6%

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

Alternative 10: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} + 1} \]

   2. associate-*l/ 99.8%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} + 1 \]

   3. +-commutative 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.25 + x\right)} - z\right) + 1 \]

   4. associate--l+ 99.8%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(y \cdot 0.25 + \left(x - z\right)\right)} + 1 \]

   5. +-commutative 99.8%

      \[\leadsto \frac{4}{y} \cdot \color{blue}{\left(\left(x - z\right) + y \cdot 0.25\right)} + 1 \]

   6. distribute-lft-in 99.8%

      \[\leadsto \color{blue}{\left(\frac{4}{y} \cdot \left(x - z\right) + \frac{4}{y} \cdot \left(y \cdot 0.25\right)\right)} + 1 \]

   7. associate-+l+ 99.8%

      \[\leadsto \color{blue}{\frac{4}{y} \cdot \left(x - z\right) + \left(\frac{4}{y} \cdot \left(y \cdot 0.25\right) + 1\right)} \]

   8. associate-*l/ 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\color{blue}{\frac{4 \cdot \left(y \cdot 0.25\right)}{y}} + 1\right) \]

   9. *-commutative 99.8%

      \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{\left(y \cdot 0.25\right) \cdot 4}}{y} + 1\right) \]

   10. associate-*l* 99.8%

       \[\leadsto \frac{4}{y} \cdot \left(x - z\right) + \left(\frac{\color{blue}{y \cdot \left(0.25 \cdot 4\right)}}{y} + 1\right) \]

   11. metadata-eval 99.8%

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

   12. *-rgt-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 11: 35.0% accurate, 13.0× 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 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 34.4%

   \[\leadsto \color{blue}{2} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))