Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.4% → 99.1%

Time: 9.2s

Alternatives: 16

Speedup: 1.3×

• 23.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

2. Taylor expanded in t around 0 98.7%

   \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
3. Step-by-step derivation

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

4. Simplified 98.7%

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

5. Final simplification 98.7%

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

Alternative 2: 50.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -29000000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 3.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -29000000000000.0)
   (/ x y)
   (if (<= (/ x y) -3.2e-55)
     (/ 2.0 t)
     (if (<= (/ x y) 0.0)
       -2.0
       (if (<= (/ x y) 3.8e-25)
         (/ 2.0 t)
         (if (<= (/ x y) 2.0) -2.0 (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -29000000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -3.2e-55) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 0.0) {
		tmp = -2.0;
	} else if ((x / y) <= 3.8e-25) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-29000000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-3.2d-55)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 0.0d0) then
        tmp = -2.0d0
    else if ((x / y) <= 3.8d-25) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -29000000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -3.2e-55) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 0.0) {
		tmp = -2.0;
	} else if ((x / y) <= 3.8e-25) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -29000000000000.0:
		tmp = x / y
	elif (x / y) <= -3.2e-55:
		tmp = 2.0 / t
	elif (x / y) <= 0.0:
		tmp = -2.0
	elif (x / y) <= 3.8e-25:
		tmp = 2.0 / t
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -29000000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -3.2e-55)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 0.0)
		tmp = -2.0;
	elseif (Float64(x / y) <= 3.8e-25)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -29000000000000.0)
		tmp = x / y;
	elseif ((x / y) <= -3.2e-55)
		tmp = 2.0 / t;
	elseif ((x / y) <= 0.0)
		tmp = -2.0;
	elseif ((x / y) <= 3.8e-25)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -29000000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -3.2e-55], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 3.8e-25], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.9e13 or 2 < (/.f64 x y)

   1. Initial program 77.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in x around inf 71.3%

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

   if -2.9e13 < (/.f64 x y) < -3.2000000000000001e-55 or -0.0 < (/.f64 x y) < 3.7999999999999998e-25

   1. Initial program 94.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 79.4%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 79.4%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 79.4%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   5. Taylor expanded in z around inf 39.2%

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

   if -3.2000000000000001e-55 < (/.f64 x y) < -0.0 or 3.7999999999999998e-25 < (/.f64 x y) < 2

   1. Initial program 81.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 98.8%

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

      2. associate-*r/ 98.8%

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

      3. metadata-eval 98.8%

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

      4. associate-*r/ 98.8%

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

      5. metadata-eval 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in t around inf 47.0%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -29000000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 3.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 92.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \left(t_1 - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))))
   (if (or (<= (/ x y) -5e+20) (not (<= (/ x y) 2e-6)))
     (+ (/ x y) t_1)
     (+ (/ 2.0 t) (- t_1 2.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double tmp;
	if (((x / y) <= -5e+20) || !((x / y) <= 2e-6)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = (2.0 / t) + (t_1 - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    if (((x / y) <= (-5d+20)) .or. (.not. ((x / y) <= 2d-6))) then
        tmp = (x / y) + t_1
    else
        tmp = (2.0d0 / t) + (t_1 - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double tmp;
	if (((x / y) <= -5e+20) || !((x / y) <= 2e-6)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = (2.0 / t) + (t_1 - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	tmp = 0
	if ((x / y) <= -5e+20) or not ((x / y) <= 2e-6):
		tmp = (x / y) + t_1
	else:
		tmp = (2.0 / t) + (t_1 - 2.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	tmp = 0.0
	if ((Float64(x / y) <= -5e+20) || !(Float64(x / y) <= 2e-6))
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = Float64(Float64(2.0 / t) + Float64(t_1 - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	tmp = 0.0;
	if (((x / y) <= -5e+20) || ~(((x / y) <= 2e-6)))
		tmp = (x / y) + t_1;
	else
		tmp = (2.0 / t) + (t_1 - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-6]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + N[(t$95$1 - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e20 or 1.99999999999999991e-6 < (/.f64 x y)

   1. Initial program 77.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in z around 0 88.6%

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

   if -5e20 < (/.f64 x y) < 1.99999999999999991e-6

   1. Initial program 86.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. metadata-eval 99.2%

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

      4. associate-*r/ 99.2%

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

      5. metadata-eval 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \left(\frac{2}{t \cdot z} - 2\right)\\ \end{array} \]

Alternative 4: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+40} \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+40) (not (<= (/ x y) 1.0)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+40) || !((x / y) <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d+40)) .or. (.not. ((x / y) <= 1.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+40) || !((x / y) <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+40) or not ((x / y) <= 1.0):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+40) || !(Float64(x / y) <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+40) || ~(((x / y) <= 1.0)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+40], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000003e40 or 1 < (/.f64 x y)

   1. Initial program 76.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 97.2%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 97.2%

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

      2. associate-*r/ 97.2%

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

      3. metadata-eval 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in z around inf 80.7%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2\right)} \]
   6. Step-by-step derivation

      1. sub-neg 80.7%

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

      2. associate-*r/ 80.7%

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

      3. metadata-eval 80.7%

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

      4. metadata-eval 80.7%

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

   7. Simplified 80.7%

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

   if -5.00000000000000003e40 < (/.f64 x y) < 1

   1. Initial program 87.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 98.6%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 98.6%

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

      2. associate-*r/ 98.6%

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

      3. metadata-eval 98.6%

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

      4. sub-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. associate-+l+ 98.6%

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

      7. +-commutative 98.6%

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

      8. metadata-eval 98.6%

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

      9. associate-*r/ 98.6%

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

      10. *-commutative 98.6%

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

      11. *-commutative 98.6%

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

      12. associate-/r/ 98.6%

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

      13. associate-/l* 98.6%

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

      14. associate-/r/ 98.6%

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

      15. distribute-lft-in 98.6%

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

      16. associate-*l/ 98.6%

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

      17. *-lft-identity 98.6%

          \[\leadsto -2 + \frac{\color{blue}{2 + \frac{2}{z}}}{t} \]

   7. Simplified 98.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+40} \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]

Alternative 5: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+20) (not (<= (/ x y) 2e-6)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+20) || !((x / y) <= 2e-6)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d+20)) .or. (.not. ((x / y) <= 2d-6))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+20) || !((x / y) <= 2e-6)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+20) or not ((x / y) <= 2e-6):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+20) || !(Float64(x / y) <= 2e-6))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+20) || ~(((x / y) <= 2e-6)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-6]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e20 or 1.99999999999999991e-6 < (/.f64 x y)

   1. Initial program 77.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in z around 0 88.6%

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

   if -5e20 < (/.f64 x y) < 1.99999999999999991e-6

   1. Initial program 86.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. metadata-eval 99.2%

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

      4. sub-neg 99.2%

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

      5. metadata-eval 99.2%

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

      6. associate-+l+ 99.2%

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

      7. +-commutative 99.2%

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

      8. metadata-eval 99.2%

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

      9. associate-*r/ 99.2%

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

      10. *-commutative 99.2%

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

      11. *-commutative 99.2%

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

      12. associate-/r/ 99.2%

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

      13. associate-/l* 99.2%

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

      14. associate-/r/ 99.2%

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

      15. distribute-lft-in 99.2%

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

      16. associate-*l/ 99.2%

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

      17. *-lft-identity 99.2%

          \[\leadsto -2 + \frac{\color{blue}{2 + \frac{2}{z}}}{t} \]

   7. Simplified 99.2%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]

Alternative 6: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+188}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+188)
   (/ x y)
   (if (<= (/ x y) 1.0) (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+188) {
		tmp = x / y;
	} else if ((x / y) <= 1.0) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1d+188)) then
        tmp = x / y
    else if ((x / y) <= 1.0d0) then
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+188) {
		tmp = x / y;
	} else if ((x / y) <= 1.0) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+188:
		tmp = x / y
	elif (x / y) <= 1.0:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+188)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.0)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e+188)
		tmp = x / y;
	elseif ((x / y) <= 1.0)
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+188], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.0], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e188 or 1 < (/.f64 x y)

   1. Initial program 74.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in x around inf 80.3%

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

   if -1e188 < (/.f64 x y) < 1

   1. Initial program 86.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 91.1%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 91.1%

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

      2. associate-*r/ 91.1%

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

      3. metadata-eval 91.1%

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

      4. sub-neg 91.1%

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

      5. metadata-eval 91.1%

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

      6. associate-+l+ 91.1%

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

      7. +-commutative 91.1%

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

      8. metadata-eval 91.1%

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

      9. associate-*r/ 91.1%

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

      10. *-commutative 91.1%

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

      11. *-commutative 91.1%

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

      12. associate-/r/ 91.1%

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

      13. associate-/l* 91.0%

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

      14. associate-/r/ 91.0%

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

      15. distribute-lft-in 91.0%

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

      16. associate-*l/ 91.0%

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

      17. *-lft-identity 91.0%

          \[\leadsto -2 + \frac{\color{blue}{2 + \frac{2}{z}}}{t} \]

   7. Simplified 91.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+188}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 7: 64.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+255}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-33} \lor \neg \left(z \leq 8.5 \cdot 10^{-151} \lor \neg \left(z \leq 1.5 \cdot 10^{-107}\right) \land z \leq 1.35 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.6e+255)
   (+ (/ 2.0 t) -2.0)
   (if (or (<= z -1.7e-33)
           (not
            (or (<= z 8.5e-151) (and (not (<= z 1.5e-107)) (<= z 1.35e-48)))))
     (- (/ x y) 2.0)
     (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.6e+255) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.7e-33) || !((z <= 8.5e-151) || (!(z <= 1.5e-107) && (z <= 1.35e-48)))) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8.6d+255)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((z <= (-1.7d-33)) .or. (.not. (z <= 8.5d-151) .or. (.not. (z <= 1.5d-107)) .and. (z <= 1.35d-48))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / (t * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.6e+255) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.7e-33) || !((z <= 8.5e-151) || (!(z <= 1.5e-107) && (z <= 1.35e-48)))) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.6e+255:
		tmp = (2.0 / t) + -2.0
	elif (z <= -1.7e-33) or not ((z <= 8.5e-151) or (not (z <= 1.5e-107) and (z <= 1.35e-48))):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.6e+255)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif ((z <= -1.7e-33) || !((z <= 8.5e-151) || (!(z <= 1.5e-107) && (z <= 1.35e-48))))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.6e+255)
		tmp = (2.0 / t) + -2.0;
	elseif ((z <= -1.7e-33) || ~(((z <= 8.5e-151) || (~((z <= 1.5e-107)) && (z <= 1.35e-48)))))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.6e+255], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[Or[LessEqual[z, -1.7e-33], N[Not[Or[LessEqual[z, 8.5e-151], And[N[Not[LessEqual[z, 1.5e-107]], $MachinePrecision], LessEqual[z, 1.35e-48]]]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5999999999999992e255

   1. Initial program 57.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 83.5%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 83.5%

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

      2. associate-*r/ 83.5%

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

      3. metadata-eval 83.5%

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

      4. associate-*r/ 83.5%

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

      5. metadata-eval 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 83.5%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

      2. associate-*r/ 83.5%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

      3. metadata-eval 83.5%

         \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

      4. metadata-eval 83.5%

         \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

      5. +-commutative 83.5%

         \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   10. Simplified 83.5%

       \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   if -8.5999999999999992e255 < z < -1.7e-33 or 8.49999999999999999e-151 < z < 1.4999999999999999e-107 or 1.35000000000000006e-48 < z

   1. Initial program 73.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 68.4%

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

   if -1.7e-33 < z < 8.49999999999999999e-151 or 1.4999999999999999e-107 < z < 1.35000000000000006e-48

   1. Initial program 97.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 97.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 97.9%

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

      2. associate-*r/ 97.9%

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

      3. metadata-eval 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in z around 0 71.1%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+255}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-33} \lor \neg \left(z \leq 8.5 \cdot 10^{-151} \lor \neg \left(z \leq 1.5 \cdot 10^{-107}\right) \land z \leq 1.35 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]

Alternative 8: 64.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+256}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-102} \lor \neg \left(z \leq 2.2 \cdot 10^{-44}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -1.28e+256)
     (+ (/ 2.0 t) -2.0)
     (if (<= z -2.15e-33)
       t_1
       (if (<= z 1.18e-150)
         (/ (/ 2.0 z) t)
         (if (or (<= z 2.9e-102) (not (<= z 2.2e-44)))
           t_1
           (/ 2.0 (* t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -1.28e+256) {
		tmp = (2.0 / t) + -2.0;
	} else if (z <= -2.15e-33) {
		tmp = t_1;
	} else if (z <= 1.18e-150) {
		tmp = (2.0 / z) / t;
	} else if ((z <= 2.9e-102) || !(z <= 2.2e-44)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-1.28d+256)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if (z <= (-2.15d-33)) then
        tmp = t_1
    else if (z <= 1.18d-150) then
        tmp = (2.0d0 / z) / t
    else if ((z <= 2.9d-102) .or. (.not. (z <= 2.2d-44))) then
        tmp = t_1
    else
        tmp = 2.0d0 / (t * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -1.28e+256) {
		tmp = (2.0 / t) + -2.0;
	} else if (z <= -2.15e-33) {
		tmp = t_1;
	} else if (z <= 1.18e-150) {
		tmp = (2.0 / z) / t;
	} else if ((z <= 2.9e-102) || !(z <= 2.2e-44)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -1.28e+256:
		tmp = (2.0 / t) + -2.0
	elif z <= -2.15e-33:
		tmp = t_1
	elif z <= 1.18e-150:
		tmp = (2.0 / z) / t
	elif (z <= 2.9e-102) or not (z <= 2.2e-44):
		tmp = t_1
	else:
		tmp = 2.0 / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -1.28e+256)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif (z <= -2.15e-33)
		tmp = t_1;
	elseif (z <= 1.18e-150)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif ((z <= 2.9e-102) || !(z <= 2.2e-44))
		tmp = t_1;
	else
		tmp = Float64(2.0 / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -1.28e+256)
		tmp = (2.0 / t) + -2.0;
	elseif (z <= -2.15e-33)
		tmp = t_1;
	elseif (z <= 1.18e-150)
		tmp = (2.0 / z) / t;
	elseif ((z <= 2.9e-102) || ~((z <= 2.2e-44)))
		tmp = t_1;
	else
		tmp = 2.0 / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -1.28e+256], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[z, -2.15e-33], t$95$1, If[LessEqual[z, 1.18e-150], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 2.9e-102], N[Not[LessEqual[z, 2.2e-44]], $MachinePrecision]], t$95$1, N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2799999999999999e256

   1. Initial program 57.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 83.5%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 83.5%

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

      2. associate-*r/ 83.5%

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

      3. metadata-eval 83.5%

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

      4. associate-*r/ 83.5%

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

      5. metadata-eval 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 83.5%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

      2. associate-*r/ 83.5%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

      3. metadata-eval 83.5%

         \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

      4. metadata-eval 83.5%

         \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

      5. +-commutative 83.5%

         \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   10. Simplified 83.5%

       \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   if -1.2799999999999999e256 < z < -2.15000000000000015e-33 or 1.18e-150 < z < 2.89999999999999986e-102 or 2.20000000000000012e-44 < z

   1. Initial program 73.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 68.4%

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

   if -2.15000000000000015e-33 < z < 1.18e-150

   1. Initial program 97.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 69.7%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 69.7%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 69.7%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   5. Taylor expanded in z around 0 69.7%

      \[\leadsto \frac{\color{blue}{\frac{2}{z}}}{t} \]

   if 2.89999999999999986e-102 < z < 2.20000000000000012e-44

   1. Initial program 100.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 84.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+256}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-102} \lor \neg \left(z \leq 2.2 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]

Alternative 9: 79.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -250 \lor \neg \left(t \leq 2.15 \cdot 10^{-16}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -5.2e+60)
     t_1
     (if (<= t -6.8e+16)
       (+ -2.0 (/ (/ 2.0 z) t))
       (if (or (<= t -250.0) (not (<= t 2.15e-16)))
         t_1
         (/ (+ 2.0 (/ 2.0 z)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -5.2e+60) {
		tmp = t_1;
	} else if (t <= -6.8e+16) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else if ((t <= -250.0) || !(t <= 2.15e-16)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-5.2d+60)) then
        tmp = t_1
    else if (t <= (-6.8d+16)) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else if ((t <= (-250.0d0)) .or. (.not. (t <= 2.15d-16))) then
        tmp = t_1
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -5.2e+60) {
		tmp = t_1;
	} else if (t <= -6.8e+16) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else if ((t <= -250.0) || !(t <= 2.15e-16)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -5.2e+60:
		tmp = t_1
	elif t <= -6.8e+16:
		tmp = -2.0 + ((2.0 / z) / t)
	elif (t <= -250.0) or not (t <= 2.15e-16):
		tmp = t_1
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -5.2e+60)
		tmp = t_1;
	elseif (t <= -6.8e+16)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	elseif ((t <= -250.0) || !(t <= 2.15e-16))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -5.2e+60)
		tmp = t_1;
	elseif (t <= -6.8e+16)
		tmp = -2.0 + ((2.0 / z) / t);
	elseif ((t <= -250.0) || ~((t <= 2.15e-16)))
		tmp = t_1;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -5.2e+60], t$95$1, If[LessEqual[t, -6.8e+16], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -250.0], N[Not[LessEqual[t, 2.15e-16]], $MachinePrecision]], t$95$1, N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000016e60 or -6.8e16 < t < -250 or 2.1499999999999999e-16 < t

   1. Initial program 67.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 83.6%

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

   if -5.20000000000000016e60 < t < -6.8e16

   1. Initial program 91.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.6%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. metadata-eval 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in x around 0 81.3%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 81.3%

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

      2. associate-*r/ 81.3%

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

      3. metadata-eval 81.3%

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

      4. sub-neg 81.3%

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

      5. metadata-eval 81.3%

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

      6. associate-+l+ 81.3%

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

      7. +-commutative 81.3%

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

      8. metadata-eval 81.3%

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

      9. associate-*r/ 81.3%

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

      10. *-commutative 81.3%

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

      11. *-commutative 81.3%

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

      12. associate-/r/ 81.3%

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

      13. associate-/l* 81.3%

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

      14. associate-/r/ 81.3%

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

      15. distribute-lft-in 81.3%

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

      16. associate-*l/ 81.4%

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

      17. *-lft-identity 81.4%

          \[\leadsto -2 + \frac{\color{blue}{2 + \frac{2}{z}}}{t} \]

   7. Simplified 81.4%

      \[\leadsto \color{blue}{-2 + \frac{2 + \frac{2}{z}}{t}} \]

   8. Taylor expanded in z around 0 81.4%

      \[\leadsto -2 + \frac{\color{blue}{\frac{2}{z}}}{t} \]

   if -250 < t < 2.1499999999999999e-16

   1. Initial program 97.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 82.3%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 82.3%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 82.3%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -250 \lor \neg \left(t \leq 2.15 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 10: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -190000000 \lor \neg \left(z \leq 2.6 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} + -2\right) + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -190000000.0) (not (<= z 2.6e-32)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (+ (/ x y) -2.0) (/ (/ 2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -190000000.0) || !(z <= 2.6e-32)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((x / y) + -2.0) + ((2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-190000000.0d0)) .or. (.not. (z <= 2.6d-32))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = ((x / y) + (-2.0d0)) + ((2.0d0 / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -190000000.0) || !(z <= 2.6e-32)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((x / y) + -2.0) + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -190000000.0) or not (z <= 2.6e-32):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = ((x / y) + -2.0) + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -190000000.0) || !(z <= 2.6e-32))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(Float64(x / y) + -2.0) + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -190000000.0) || ~((z <= 2.6e-32)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = ((x / y) + -2.0) + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -190000000.0], N[Not[LessEqual[z, 2.6e-32]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e8 or 2.5999999999999997e-32 < z

   1. Initial program 69.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2\right)} \]
   6. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   if -1.9e8 < z < 2.5999999999999997e-32

   1. Initial program 97.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 97.4%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 97.4%

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

      2. associate-*r/ 97.4%

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

      3. metadata-eval 97.4%

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

   4. Simplified 97.4%

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

   5. Taylor expanded in x around 0 97.4%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right)\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 97.4%

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

      2. associate-*r/ 97.4%

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

      3. metadata-eval 97.4%

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

      4. sub-neg 97.4%

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

      5. metadata-eval 97.4%

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

      6. associate-+l+ 97.4%

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

      7. associate-+r+ 97.4%

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

      8. associate-+l+ 97.4%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in z around 0 97.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -190000000 \lor \neg \left(z \leq 2.6 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} + -2\right) + \frac{\frac{2}{z}}{t}\\ \end{array} \]

Alternative 11: 69.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+256}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-7} \lor \neg \left(z \leq 2.6 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.22e+256)
   (+ (/ 2.0 t) -2.0)
   (if (or (<= z -1.16e-7) (not (<= z 2.6e-32)))
     (- (/ x y) 2.0)
     (+ -2.0 (/ (/ 2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.22e+256) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.16e-7) || !(z <= 2.6e-32)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + ((2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.22d+256)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((z <= (-1.16d-7)) .or. (.not. (z <= 2.6d-32))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.22e+256) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.16e-7) || !(z <= 2.6e-32)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.22e+256:
		tmp = (2.0 / t) + -2.0
	elif (z <= -1.16e-7) or not (z <= 2.6e-32):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + ((2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.22e+256)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif ((z <= -1.16e-7) || !(z <= 2.6e-32))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.22e+256)
		tmp = (2.0 / t) + -2.0;
	elseif ((z <= -1.16e-7) || ~((z <= 2.6e-32)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + ((2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.22e+256], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[Or[LessEqual[z, -1.16e-7], N[Not[LessEqual[z, 2.6e-32]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999999e256

   1. Initial program 57.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 83.5%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 83.5%

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

      2. associate-*r/ 83.5%

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

      3. metadata-eval 83.5%

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

      4. associate-*r/ 83.5%

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

      5. metadata-eval 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 83.5%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

      2. associate-*r/ 83.5%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

      3. metadata-eval 83.5%

         \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

      4. metadata-eval 83.5%

         \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

      5. +-commutative 83.5%

         \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   10. Simplified 83.5%

       \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   if -1.21999999999999999e256 < z < -1.1600000000000001e-7 or 2.5999999999999997e-32 < z

   1. Initial program 70.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 68.0%

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

   if -1.1600000000000001e-7 < z < 2.5999999999999997e-32

   1. Initial program 97.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 97.3%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 97.3%

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

      2. associate-*r/ 97.3%

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

      3. metadata-eval 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in x around 0 78.7%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 78.7%

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

      2. associate-*r/ 78.7%

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

      3. metadata-eval 78.7%

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

      4. sub-neg 78.7%

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

      5. metadata-eval 78.7%

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

      6. associate-+l+ 78.7%

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

      7. +-commutative 78.7%

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

      8. metadata-eval 78.7%

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

      9. associate-*r/ 78.7%

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

      10. *-commutative 78.7%

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

      11. *-commutative 78.7%

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

      12. associate-/r/ 78.7%

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

      13. associate-/l* 78.7%

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

      14. associate-/r/ 78.7%

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

      15. distribute-lft-in 78.7%

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

      16. associate-*l/ 78.7%

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

      17. *-lft-identity 78.7%

          \[\leadsto -2 + \frac{\color{blue}{2 + \frac{2}{z}}}{t} \]

   7. Simplified 78.7%

      \[\leadsto \color{blue}{-2 + \frac{2 + \frac{2}{z}}{t}} \]

   8. Taylor expanded in z around 0 78.4%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+256}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-7} \lor \neg \left(z \leq 2.6 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \end{array} \]

Alternative 12: 64.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.72 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 7200000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.72e+16) (not (<= (/ x y) 7200000000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.72e+16) || !((x / y) <= 7200000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.72d+16)) .or. (.not. ((x / y) <= 7200000000.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.72e+16) || !((x / y) <= 7200000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.72e+16) or not ((x / y) <= 7200000000.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.72e+16) || !(Float64(x / y) <= 7200000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.72e+16) || ~(((x / y) <= 7200000000.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.72e+16], N[Not[LessEqual[N[(x / y), $MachinePrecision], 7200000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.72e16 or 7.2e9 < (/.f64 x y)

   1. Initial program 77.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in x around inf 71.3%

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

   if -1.72e16 < (/.f64 x y) < 7.2e9

   1. Initial program 87.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. metadata-eval 99.2%

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

      4. associate-*r/ 99.2%

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

      5. metadata-eval 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in z around inf 60.1%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 60.1%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

      2. associate-*r/ 60.1%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

      3. metadata-eval 60.1%

         \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

      4. metadata-eval 60.1%

         \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

      5. +-commutative 60.1%

         \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   10. Simplified 60.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.72 \cdot 10^{+16} \lor \neg \left(\frac{x}{y} \leq 7200000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 13: 64.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.05 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.05e+17)
   (/ x y)
   (if (<= (/ x y) 8.2e-19) (+ (/ 2.0 t) -2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.05e+17) {
		tmp = x / y;
	} else if ((x / y) <= 8.2e-19) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2.05d+17)) then
        tmp = x / y
    else if ((x / y) <= 8.2d-19) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.05e+17) {
		tmp = x / y;
	} else if ((x / y) <= 8.2e-19) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.05e+17:
		tmp = x / y
	elif (x / y) <= 8.2e-19:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.05e+17)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 8.2e-19)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.05e+17)
		tmp = x / y;
	elseif ((x / y) <= 8.2e-19)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.05e+17], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 8.2e-19], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.05e17

   1. Initial program 77.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in x around inf 64.8%

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

   if -2.05e17 < (/.f64 x y) < 8.1999999999999997e-19

   1. Initial program 87.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 60.9%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   9. Step-by-step derivation

      1. sub-neg 60.9%

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

      2. associate-*r/ 60.9%

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

      3. metadata-eval 60.9%

         \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

      4. metadata-eval 60.9%

         \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

      5. +-commutative 60.9%

         \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   10. Simplified 60.9%

       \[\leadsto \color{blue}{-2 + \frac{2}{t}} \]

   if 8.1999999999999997e-19 < (/.f64 x y)

   1. Initial program 76.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around inf 75.9%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.05 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 14: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

2. Taylor expanded in t around 0 98.7%

   \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
3. Step-by-step derivation

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

4. Simplified 98.7%

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

5. Taylor expanded in x around 0 98.7%

   \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right)\right) - 2} \]
6. Step-by-step derivation

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

   4. sub-neg 98.7%

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

   5. metadata-eval 98.7%

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

   6. associate-+l+ 98.7%

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

   7. associate-+r+ 98.7%

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

   8. associate-+l+ 98.7%

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

7. Simplified 98.7%

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

8. Final simplification 98.7%

   \[\leadsto \frac{2 + \frac{2}{z}}{t} + \left(\frac{x}{y} + -2\right) \]

Alternative 15: 37.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-9}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.5e-9) -2.0 (if (<= t 1.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e-9) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.5d-9)) then
        tmp = -2.0d0
    else if (t <= 1.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e-9) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.5e-9:
		tmp = -2.0
	elif t <= 1.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.5e-9)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.5e-9)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.5e-9], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4999999999999996e-9 or 1 < t

   1. Initial program 69.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 59.1%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   6. Step-by-step derivation

      1. associate--l+ 59.1%

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

      2. associate-*r/ 59.1%

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

      3. metadata-eval 59.1%

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

      4. associate-*r/ 59.1%

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

      5. metadata-eval 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in t around inf 36.9%

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

   if -5.4999999999999996e-9 < t < 1

   1. Initial program 97.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

   2. Taylor expanded in t around 0 80.1%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   3. Step-by-step derivation

      1. associate-*r/ 80.1%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 80.1%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   4. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   5. Taylor expanded in z around inf 37.9%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-9}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 16: 20.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]

2. Taylor expanded in t around 0 98.7%

   \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
3. Step-by-step derivation

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

4. Simplified 98.7%

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

5. Taylor expanded in x around 0 69.2%

   \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
6. Step-by-step derivation

   1. associate--l+ 69.2%

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

   2. associate-*r/ 69.2%

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

   3. metadata-eval 69.2%

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

   4. associate-*r/ 69.2%

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

   5. metadata-eval 69.2%

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

7. Simplified 69.2%

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

8. Taylor expanded in t around inf 20.5%

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

9. Final simplification 20.5%

   \[\leadsto -2 \]

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))