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

Percentage Accurate: 86.6% → 99.2%

Time: 9.5s

Alternatives: 12

Speedup: 1.3×

• 23.2% 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: 86.6% 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: 99.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

2. Taylor expanded in t around 0 99.2%

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

   1. sub-neg 99.2%

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

   2. metadata-eval 99.2%

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

   3. +-commutative 99.2%

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

   4. associate-+r+ 99.2%

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

   5. metadata-eval 99.2%

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

   6. associate-*r/ 99.2%

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

   7. +-commutative 99.2%

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

   8. associate-*r/ 99.2%

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

   9. metadata-eval 99.2%

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

   10. associate-*r/ 99.2%

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

   11. metadata-eval 99.2%

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

   12. associate-/r* 99.2%

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

4. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;\frac{x}{y} \leq -550000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5500000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.9 \cdot 10^{+125}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+168}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= (/ x y) -550000.0)
     t_1
     (if (<= (/ x y) 5500000000000.0)
       (+ -2.0 (/ 2.0 t))
       (if (<= (/ x y) 1.9e+125)
         (/ 2.0 (* t z))
         (if (<= (/ x y) 4e+168) (/ 2.0 t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if ((x / y) <= -550000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5500000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 1.9e+125) {
		tmp = 2.0 / (t * z);
	} else if ((x / y) <= 4e+168) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	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 ((x / y) <= (-550000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 5500000000000.0d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if ((x / y) <= 1.9d+125) then
        tmp = 2.0d0 / (t * z)
    else if ((x / y) <= 4d+168) then
        tmp = 2.0d0 / t
    else
        tmp = t_1
    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 ((x / y) <= -550000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5500000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 1.9e+125) {
		tmp = 2.0 / (t * z);
	} else if ((x / y) <= 4e+168) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if (x / y) <= -550000.0:
		tmp = t_1
	elif (x / y) <= 5500000000000.0:
		tmp = -2.0 + (2.0 / t)
	elif (x / y) <= 1.9e+125:
		tmp = 2.0 / (t * z)
	elif (x / y) <= 4e+168:
		tmp = 2.0 / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (Float64(x / y) <= -550000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 5500000000000.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (Float64(x / y) <= 1.9e+125)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (Float64(x / y) <= 4e+168)
		tmp = Float64(2.0 / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if ((x / y) <= -550000.0)
		tmp = t_1;
	elseif ((x / y) <= 5500000000000.0)
		tmp = -2.0 + (2.0 / t);
	elseif ((x / y) <= 1.9e+125)
		tmp = 2.0 / (t * z);
	elseif ((x / y) <= 4e+168)
		tmp = 2.0 / t;
	else
		tmp = t_1;
	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[N[(x / y), $MachinePrecision], -550000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5500000000000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.9e+125], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e+168], N[(2.0 / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -5.5e5 or 3.9999999999999997e168 < (/.f64 x y)

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 78.6%

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

   if -5.5e5 < (/.f64 x y) < 5.5e12

   1. Initial program 81.8%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-*r/ 99.9%

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

      11. metadata-eval 99.9%

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

      12. associate-/r* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. metadata-eval 68.2%

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

      3. +-commutative 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in x around 0 66.4%

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

   if 5.5e12 < (/.f64 x y) < 1.90000000000000001e125

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 68.9%

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

      1. associate-*r/ 68.9%

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

      2. metadata-eval 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in z around 0 52.9%

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

   6. Taylor expanded in z around 0 52.9%

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

   if 1.90000000000000001e125 < (/.f64 x y) < 3.9999999999999997e168

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -550000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 5500000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.9 \cdot 10^{+125}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+168}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 3: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+121}:\\ \;\;\;\;-2 + \frac{2}{t} \cdot \left(1 + \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -50000000.0)
   (+ (/ x y) (/ 2.0 (* t z)))
   (if (<= (/ x y) 1e+121)
     (+ -2.0 (* (/ 2.0 t) (+ 1.0 (/ 1.0 z))))
     (+ -2.0 (+ (/ 2.0 t) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -50000000.0) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 1e+121) {
		tmp = -2.0 + ((2.0 / t) * (1.0 + (1.0 / z)));
	} else {
		tmp = -2.0 + ((2.0 / t) + (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) <= (-50000000.0d0)) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else if ((x / y) <= 1d+121) then
        tmp = (-2.0d0) + ((2.0d0 / t) * (1.0d0 + (1.0d0 / z)))
    else
        tmp = (-2.0d0) + ((2.0d0 / t) + (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) <= -50000000.0) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 1e+121) {
		tmp = -2.0 + ((2.0 / t) * (1.0 + (1.0 / z)));
	} else {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -50000000.0:
		tmp = (x / y) + (2.0 / (t * z))
	elif (x / y) <= 1e+121:
		tmp = -2.0 + ((2.0 / t) * (1.0 + (1.0 / z)))
	else:
		tmp = -2.0 + ((2.0 / t) + (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -50000000.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	elseif (Float64(x / y) <= 1e+121)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) * Float64(1.0 + Float64(1.0 / z))));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -50000000.0)
		tmp = (x / y) + (2.0 / (t * z));
	elseif ((x / y) <= 1e+121)
		tmp = -2.0 + ((2.0 / t) * (1.0 + (1.0 / z)));
	else
		tmp = -2.0 + ((2.0 / t) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -50000000.0], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e+121], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] * N[(1.0 + N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e7

   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 z around 0 91.8%

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

   if -5e7 < (/.f64 x y) < 1.00000000000000004e121

   1. Initial program 83.6%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-*r/ 99.9%

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

      11. metadata-eval 99.9%

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

      12. associate-/r* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.8%

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

      1. associate-*r/ 94.8%

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

      2. associate-*l/ 94.8%

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

      3. associate-*r/ 94.8%

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

      4. metadata-eval 94.8%

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

      5. associate-/r* 94.8%

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

      6. *-rgt-identity 94.8%

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

      7. associate-*r/ 94.7%

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

      8. distribute-lft-out 94.7%

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

   7. Simplified 94.7%

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

   if 1.00000000000000004e121 < (/.f64 x y)

   1. Initial program 84.5%

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

   2. Taylor expanded in t around 0 94.9%

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

      1. sub-neg 94.9%

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

      2. metadata-eval 94.9%

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

      3. +-commutative 94.9%

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

      4. associate-+r+ 94.9%

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

      5. metadata-eval 94.9%

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

      6. associate-*r/ 94.9%

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

      7. +-commutative 94.9%

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

      8. associate-*r/ 94.9%

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

      9. metadata-eval 94.9%

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

      10. associate-*r/ 94.9%

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

      11. metadata-eval 94.9%

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

      12. associate-/r* 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in z around inf 97.7%

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

      1. associate-*r/ 97.7%

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

      2. metadata-eval 97.7%

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

      3. +-commutative 97.7%

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

   7. Simplified 97.7%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+121}:\\ \;\;\;\;-2 + \frac{2}{t} \cdot \left(1 + \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-104}:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+82} \lor \neg \left(z \leq 1.8 \cdot 10^{+134}\right) \land z \leq 2.5 \cdot 10^{+244}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -1.55e+209)
     t_2
     (if (<= z -9.5e-37)
       t_1
       (if (<= z 4.8e-104)
         (+ -2.0 (/ 2.0 (* t z)))
         (if (or (<= z 4.5e+82) (and (not (<= z 1.8e+134)) (<= z 2.5e+244)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.55e+209) {
		tmp = t_2;
	} else if (z <= -9.5e-37) {
		tmp = t_1;
	} else if (z <= 4.8e-104) {
		tmp = -2.0 + (2.0 / (t * z));
	} else if ((z <= 4.5e+82) || (!(z <= 1.8e+134) && (z <= 2.5e+244))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-1.55d+209)) then
        tmp = t_2
    else if (z <= (-9.5d-37)) then
        tmp = t_1
    else if (z <= 4.8d-104) then
        tmp = (-2.0d0) + (2.0d0 / (t * z))
    else if ((z <= 4.5d+82) .or. (.not. (z <= 1.8d+134)) .and. (z <= 2.5d+244)) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.55e+209) {
		tmp = t_2;
	} else if (z <= -9.5e-37) {
		tmp = t_1;
	} else if (z <= 4.8e-104) {
		tmp = -2.0 + (2.0 / (t * z));
	} else if ((z <= 4.5e+82) || (!(z <= 1.8e+134) && (z <= 2.5e+244))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -1.55e+209:
		tmp = t_2
	elif z <= -9.5e-37:
		tmp = t_1
	elif z <= 4.8e-104:
		tmp = -2.0 + (2.0 / (t * z))
	elif (z <= 4.5e+82) or (not (z <= 1.8e+134) and (z <= 2.5e+244)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.55e+209)
		tmp = t_2;
	elseif (z <= -9.5e-37)
		tmp = t_1;
	elseif (z <= 4.8e-104)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(t * z)));
	elseif ((z <= 4.5e+82) || (!(z <= 1.8e+134) && (z <= 2.5e+244)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.55e+209)
		tmp = t_2;
	elseif (z <= -9.5e-37)
		tmp = t_1;
	elseif (z <= 4.8e-104)
		tmp = -2.0 + (2.0 / (t * z));
	elseif ((z <= 4.5e+82) || (~((z <= 1.8e+134)) && (z <= 2.5e+244)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+209], t$95$2, If[LessEqual[z, -9.5e-37], t$95$1, If[LessEqual[z, 4.8e-104], N[(-2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.5e+82], And[N[Not[LessEqual[z, 1.8e+134]], $MachinePrecision], LessEqual[z, 2.5e+244]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e209 or 4.4999999999999997e82 < z < 1.79999999999999994e134 or 2.50000000000000011e244 < z

   1. Initial program 73.8%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate-*r/ 100.0%

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

      11. metadata-eval 100.0%

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

      12. associate-/r* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 85.6%

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

   if -1.55e209 < z < -9.49999999999999927e-37 or 4.8000000000000001e-104 < z < 4.4999999999999997e82 or 1.79999999999999994e134 < z < 2.50000000000000011e244

   1. Initial program 78.2%

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

   2. Taylor expanded in t around inf 72.9%

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

   if -9.49999999999999927e-37 < z < 4.8000000000000001e-104

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 97.8%

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

      1. sub-neg 97.8%

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

      2. metadata-eval 97.8%

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

      3. +-commutative 97.8%

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

      4. associate-+r+ 97.8%

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

      5. metadata-eval 97.8%

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

      6. associate-*r/ 97.8%

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

      7. +-commutative 97.8%

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

      8. associate-*r/ 97.8%

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

      9. metadata-eval 97.8%

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

      10. associate-*r/ 97.8%

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

      11. metadata-eval 97.8%

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

      12. associate-/r* 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in z around 0 74.9%

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

      1. *-commutative 74.9%

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

   7. Simplified 74.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+209}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-104}:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+82} \lor \neg \left(z \leq 1.8 \cdot 10^{+134}\right) \land z \leq 2.5 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 5: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+82} \lor \neg \left(z \leq 2.1 \cdot 10^{+134}\right) \land z \leq 3.4 \cdot 10^{+246}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -1.55e+209)
     t_2
     (if (<= z -3.5e-35)
       t_1
       (if (<= z 2.6e-103)
         (+ -2.0 (/ (/ 2.0 t) z))
         (if (or (<= z 4.8e+82) (and (not (<= z 2.1e+134)) (<= z 3.4e+246)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.55e+209) {
		tmp = t_2;
	} else if (z <= -3.5e-35) {
		tmp = t_1;
	} else if (z <= 2.6e-103) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if ((z <= 4.8e+82) || (!(z <= 2.1e+134) && (z <= 3.4e+246))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    t_2 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-1.55d+209)) then
        tmp = t_2
    else if (z <= (-3.5d-35)) then
        tmp = t_1
    else if (z <= 2.6d-103) then
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    else if ((z <= 4.8d+82) .or. (.not. (z <= 2.1d+134)) .and. (z <= 3.4d+246)) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.55e+209) {
		tmp = t_2;
	} else if (z <= -3.5e-35) {
		tmp = t_1;
	} else if (z <= 2.6e-103) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if ((z <= 4.8e+82) || (!(z <= 2.1e+134) && (z <= 3.4e+246))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -1.55e+209:
		tmp = t_2
	elif z <= -3.5e-35:
		tmp = t_1
	elif z <= 2.6e-103:
		tmp = -2.0 + ((2.0 / t) / z)
	elif (z <= 4.8e+82) or (not (z <= 2.1e+134) and (z <= 3.4e+246)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.55e+209)
		tmp = t_2;
	elseif (z <= -3.5e-35)
		tmp = t_1;
	elseif (z <= 2.6e-103)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	elseif ((z <= 4.8e+82) || (!(z <= 2.1e+134) && (z <= 3.4e+246)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.55e+209)
		tmp = t_2;
	elseif (z <= -3.5e-35)
		tmp = t_1;
	elseif (z <= 2.6e-103)
		tmp = -2.0 + ((2.0 / t) / z);
	elseif ((z <= 4.8e+82) || (~((z <= 2.1e+134)) && (z <= 3.4e+246)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+209], t$95$2, If[LessEqual[z, -3.5e-35], t$95$1, If[LessEqual[z, 2.6e-103], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.8e+82], And[N[Not[LessEqual[z, 2.1e+134]], $MachinePrecision], LessEqual[z, 3.4e+246]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e209 or 4.79999999999999996e82 < z < 2.1000000000000001e134 or 3.39999999999999988e246 < z

   1. Initial program 73.8%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate-*r/ 100.0%

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

      11. metadata-eval 100.0%

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

      12. associate-/r* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 85.6%

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

   if -1.55e209 < z < -3.49999999999999996e-35 or 2.59999999999999996e-103 < z < 4.79999999999999996e82 or 2.1000000000000001e134 < z < 3.39999999999999988e246

   1. Initial program 78.2%

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

   2. Taylor expanded in t around inf 72.9%

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

   if -3.49999999999999996e-35 < z < 2.59999999999999996e-103

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 97.8%

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

      1. sub-neg 97.8%

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

      2. metadata-eval 97.8%

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

      3. +-commutative 97.8%

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

      4. associate-+r+ 97.8%

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

      5. metadata-eval 97.8%

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

      6. associate-*r/ 97.8%

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

      7. +-commutative 97.8%

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

      8. associate-*r/ 97.8%

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

      9. metadata-eval 97.8%

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

      10. associate-*r/ 97.8%

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

      11. metadata-eval 97.8%

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

      12. associate-/r* 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in x around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. associate-*l/ 74.9%

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

      3. associate-*r/ 74.9%

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

      4. metadata-eval 74.9%

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

      5. associate-/r* 74.9%

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

      6. *-rgt-identity 74.9%

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

      7. associate-*r/ 74.8%

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

      8. distribute-lft-out 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in z around 0 74.9%

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

      1. associate-/r* 74.9%

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

   10. Simplified 74.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+209}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-103}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+82} \lor \neg \left(z \leq 2.1 \cdot 10^{+134}\right) \land z \leq 3.4 \cdot 10^{+246}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 6: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -4.6e-46)
     t_2
     (if (<= t -4.2e-160)
       t_1
       (if (<= t -2.4e-202) (/ x y) (if (<= t 1.42e+19) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.6e-46) {
		tmp = t_2;
	} else if (t <= -4.2e-160) {
		tmp = t_1;
	} else if (t <= -2.4e-202) {
		tmp = x / y;
	} else if (t <= 1.42e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) - 2.0d0
    if (t <= (-4.6d-46)) then
        tmp = t_2
    else if (t <= (-4.2d-160)) then
        tmp = t_1
    else if (t <= (-2.4d-202)) then
        tmp = x / y
    else if (t <= 1.42d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.6e-46) {
		tmp = t_2;
	} else if (t <= -4.2e-160) {
		tmp = t_1;
	} else if (t <= -2.4e-202) {
		tmp = x / y;
	} else if (t <= 1.42e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -4.6e-46:
		tmp = t_2
	elif t <= -4.2e-160:
		tmp = t_1
	elif t <= -2.4e-202:
		tmp = x / y
	elif t <= 1.42e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -4.6e-46)
		tmp = t_2;
	elseif (t <= -4.2e-160)
		tmp = t_1;
	elseif (t <= -2.4e-202)
		tmp = Float64(x / y);
	elseif (t <= 1.42e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -4.6e-46)
		tmp = t_2;
	elseif (t <= -4.2e-160)
		tmp = t_1;
	elseif (t <= -2.4e-202)
		tmp = x / y;
	elseif (t <= 1.42e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -4.6e-46], t$95$2, If[LessEqual[t, -4.2e-160], t$95$1, If[LessEqual[t, -2.4e-202], N[(x / y), $MachinePrecision], If[LessEqual[t, 1.42e+19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5999999999999998e-46 or 1.42e19 < t

   1. Initial program 72.3%

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

   2. Taylor expanded in t around inf 83.4%

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

   if -4.5999999999999998e-46 < t < -4.2000000000000001e-160 or -2.4000000000000001e-202 < t < 1.42e19

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. metadata-eval 87.0%

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

   4. Simplified 87.0%

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

   if -4.2000000000000001e-160 < t < -2.4000000000000001e-202

   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 x around inf 86.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-202}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+19}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 7: 62.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -245000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -245000.0) (not (<= (/ x y) 4e+168)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -245000.0) || !((x / y) <= 4e+168)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / 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 (((x / y) <= (-245000.0d0)) .or. (.not. ((x / y) <= 4d+168))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -245000.0) || !((x / y) <= 4e+168)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -245000.0) or not ((x / y) <= 4e+168):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -245000.0) || !(Float64(x / y) <= 4e+168))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -245000.0) || ~(((x / y) <= 4e+168)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -245000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+168]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -245000 or 3.9999999999999997e168 < (/.f64 x y)

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 77.3%

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

   if -245000 < (/.f64 x y) < 3.9999999999999997e168

   1. Initial program 83.9%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-*r/ 99.9%

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

      11. metadata-eval 99.9%

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

      12. associate-/r* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. metadata-eval 67.2%

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

      3. +-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in x around 0 62.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -245000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 8: 62.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1050000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1050000.0) (not (<= (/ x y) 4e+168)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1050000.0) || !((x / y) <= 4e+168)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / 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 (((x / y) <= (-1050000.0d0)) .or. (.not. ((x / y) <= 4d+168))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1050000.0) || !((x / y) <= 4e+168)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1050000.0) or not ((x / y) <= 4e+168):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1050000.0) || !(Float64(x / y) <= 4e+168))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1050000.0) || ~(((x / y) <= 4e+168)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1050000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+168]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.05e6 or 3.9999999999999997e168 < (/.f64 x y)

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 78.6%

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

   if -1.05e6 < (/.f64 x y) < 3.9999999999999997e168

   1. Initial program 83.9%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-*r/ 99.9%

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

      11. metadata-eval 99.9%

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

      12. associate-/r* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. metadata-eval 67.2%

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

      3. +-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in x around 0 62.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1050000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 9: 85.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-34} \lor \neg \left(z \leq 1.7 \cdot 10^{-105}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e-34) (not (<= z 1.7e-105)))
   (+ -2.0 (+ (/ 2.0 t) (/ x y)))
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e-34) || !(z <= 1.7e-105)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} else {
		tmp = -2.0 + ((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 <= (-1.4d-34)) .or. (.not. (z <= 1.7d-105))) then
        tmp = (-2.0d0) + ((2.0d0 / t) + (x / y))
    else
        tmp = (-2.0d0) + ((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 <= -1.4e-34) || !(z <= 1.7e-105)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e-34) or not (z <= 1.7e-105):
		tmp = -2.0 + ((2.0 / t) + (x / y))
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e-34) || !(z <= 1.7e-105))
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(x / y)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e-34) || ~((z <= 1.7e-105)))
		tmp = -2.0 + ((2.0 / t) + (x / y));
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e-34], N[Not[LessEqual[z, 1.7e-105]], $MachinePrecision]], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999998e-34 or 1.69999999999999996e-105 < z

   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 t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate-*r/ 100.0%

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

      11. metadata-eval 100.0%

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

      12. associate-/r* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 94.3%

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

      1. associate-*r/ 94.3%

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

      2. metadata-eval 94.3%

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

      3. +-commutative 94.3%

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

   7. Simplified 94.3%

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

   if -1.39999999999999998e-34 < z < 1.69999999999999996e-105

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 97.8%

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

      1. sub-neg 97.8%

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

      2. metadata-eval 97.8%

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

      3. +-commutative 97.8%

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

      4. associate-+r+ 97.8%

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

      5. metadata-eval 97.8%

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

      6. associate-*r/ 97.8%

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

      7. +-commutative 97.8%

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

      8. associate-*r/ 97.8%

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

      9. metadata-eval 97.8%

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

      10. associate-*r/ 97.8%

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

      11. metadata-eval 97.8%

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

      12. associate-/r* 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in x around 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. associate-*l/ 75.4%

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

      3. associate-*r/ 75.4%

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

      4. metadata-eval 75.4%

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

      5. associate-/r* 75.5%

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

      6. *-rgt-identity 75.5%

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

      7. associate-*r/ 75.4%

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

      8. distribute-lft-out 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in z around 0 75.4%

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

      1. associate-/r* 75.5%

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

   10. Simplified 75.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-34} \lor \neg \left(z \leq 1.7 \cdot 10^{-105}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 10: 92.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-6} \lor \neg \left(z \leq 2.5 \cdot 10^{-19}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e-6) (not (<= z 2.5e-19)))
   (+ -2.0 (+ (/ 2.0 t) (/ x y)))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e-6) || !(z <= 2.5e-19)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} else {
		tmp = (x / y) + (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 <= (-4.1d-6)) .or. (.not. (z <= 2.5d-19))) then
        tmp = (-2.0d0) + ((2.0d0 / t) + (x / y))
    else
        tmp = (x / y) + (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 <= -4.1e-6) || !(z <= 2.5e-19)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e-6) or not (z <= 2.5e-19):
		tmp = -2.0 + ((2.0 / t) + (x / y))
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e-6) || !(z <= 2.5e-19))
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(x / y)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.1e-6) || ~((z <= 2.5e-19)))
		tmp = -2.0 + ((2.0 / t) + (x / y));
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.1e-6], N[Not[LessEqual[z, 2.5e-19]], $MachinePrecision]], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0999999999999997e-6 or 2.5000000000000002e-19 < z

   1. Initial program 73.4%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate-*r/ 100.0%

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

      11. metadata-eval 100.0%

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

      12. associate-/r* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

      2. metadata-eval 99.5%

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

      3. +-commutative 99.5%

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

   7. Simplified 99.5%

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

   if -4.0999999999999997e-6 < z < 2.5000000000000002e-19

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 86.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-6} \lor \neg \left(z \leq 2.5 \cdot 10^{-19}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]

Alternative 11: 43.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -32000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -32000.0) (not (<= (/ x y) 4e+168))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -32000.0) || !((x / y) <= 4e+168)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / 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 (((x / y) <= (-32000.0d0)) .or. (.not. ((x / y) <= 4d+168))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -32000.0) || !((x / y) <= 4e+168)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -32000.0) or not ((x / y) <= 4e+168):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -32000.0) || !(Float64(x / y) <= 4e+168))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -32000.0) || ~(((x / y) <= 4e+168)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -32000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+168]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -32000 or 3.9999999999999997e168 < (/.f64 x y)

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 77.3%

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

   if -32000 < (/.f64 x y) < 3.9999999999999997e168

   1. Initial program 83.9%

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

   2. Taylor expanded in t around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. metadata-eval 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in z around inf 31.7%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -32000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 12: 19.2% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{2}{t} \end{array} \]

FPCore

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

C

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

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 / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(2.0 / t), $MachinePrecision]

Derivation

1. Initial program 84.6%

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

2. Taylor expanded in t around 0 48.8%

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

   1. associate-*r/ 48.8%

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

   2. metadata-eval 48.8%

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

4. Simplified 48.8%

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

5. Taylor expanded in z around inf 22.3%

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

6. Final simplification 22.3%

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

Developer target: 99.2% 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 2023333 
(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))))