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

Percentage Accurate: 87.0% → 99.2%

Time: 10.9s

Alternatives: 15

Speedup: 1.1×

• 22.4% 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: 87.0% 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

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

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 86.6%

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

3. Taylor expanded in t around inf 98.7%

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

   1. sub-neg 98.7%

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

   2. metadata-eval 98.7%

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

   3. associate-*r/ 98.7%

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

   4. +-commutative 98.7%

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

   5. metadata-eval 98.7%

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

   6. associate-+l+ 98.7%

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

   7. associate-*r/ 98.7%

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

   8. metadata-eval 98.7%

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

   9. associate-*r/ 98.7%

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

   10. metadata-eval 98.7%

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

5. Simplified 98.7%

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

Alternative 2: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + \frac{2}{t}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.205:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (+ (/ x y) (/ 2.0 t)))
        (t_3 (- (/ x y) 2.0)))
   (if (<= t -5.5e-35)
     t_3
     (if (<= t -2.8e-67)
       t_1
       (if (<= t -5.4e-299)
         t_2
         (if (<= t 2.5e-199) t_1 (if (<= t 0.205) t_2 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + (2.0 / t);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t <= -5.5e-35) {
		tmp = t_3;
	} else if (t <= -2.8e-67) {
		tmp = t_1;
	} else if (t <= -5.4e-299) {
		tmp = t_2;
	} else if (t <= 2.5e-199) {
		tmp = t_1;
	} else if (t <= 0.205) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = (x / y) + (2.0d0 / t)
    t_3 = (x / y) - 2.0d0
    if (t <= (-5.5d-35)) then
        tmp = t_3
    else if (t <= (-2.8d-67)) then
        tmp = t_1
    else if (t <= (-5.4d-299)) then
        tmp = t_2
    else if (t <= 2.5d-199) then
        tmp = t_1
    else if (t <= 0.205d0) then
        tmp = t_2
    else
        tmp = t_3
    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 t_2 = (x / y) + (2.0 / t);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t <= -5.5e-35) {
		tmp = t_3;
	} else if (t <= -2.8e-67) {
		tmp = t_1;
	} else if (t <= -5.4e-299) {
		tmp = t_2;
	} else if (t <= 2.5e-199) {
		tmp = t_1;
	} else if (t <= 0.205) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) + (2.0 / t)
	t_3 = (x / y) - 2.0
	tmp = 0
	if t <= -5.5e-35:
		tmp = t_3
	elif t <= -2.8e-67:
		tmp = t_1
	elif t <= -5.4e-299:
		tmp = t_2
	elif t <= 2.5e-199:
		tmp = t_1
	elif t <= 0.205:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + Float64(2.0 / t))
	t_3 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -5.5e-35)
		tmp = t_3;
	elseif (t <= -2.8e-67)
		tmp = t_1;
	elseif (t <= -5.4e-299)
		tmp = t_2;
	elseif (t <= 2.5e-199)
		tmp = t_1;
	elseif (t <= 0.205)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) + (2.0 / t);
	t_3 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -5.5e-35)
		tmp = t_3;
	elseif (t <= -2.8e-67)
		tmp = t_1;
	elseif (t <= -5.4e-299)
		tmp = t_2;
	elseif (t <= 2.5e-199)
		tmp = t_1;
	elseif (t <= 0.205)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -5.5e-35], t$95$3, If[LessEqual[t, -2.8e-67], t$95$1, If[LessEqual[t, -5.4e-299], t$95$2, If[LessEqual[t, 2.5e-199], t$95$1, If[LessEqual[t, 0.205], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4999999999999997e-35 or 0.204999999999999988 < t

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf 83.5%

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

   if -5.4999999999999997e-35 < t < -2.8000000000000001e-67 or -5.40000000000000004e-299 < t < 2.4999999999999998e-199

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 81.3%

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

   if -2.8000000000000001e-67 < t < -5.40000000000000004e-299 or 2.4999999999999998e-199 < t < 0.204999999999999988

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 67.4%

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

      1. associate-*r/ 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around 0 66.9%

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

Alternative 3: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-151}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -4.8e-32)
     t_1
     (if (<= t 1.1e-151)
       (/ (+ 2.0 (/ 2.0 z)) t)
       (if (<= t 5e+55) (+ (/ x y) (/ (/ 2.0 t) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.8e-32) {
		tmp = t_1;
	} else if (t <= 1.1e-151) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (t <= 5e+55) {
		tmp = (x / y) + ((2.0 / t) / z);
	} 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 (t <= (-4.8d-32)) then
        tmp = t_1
    else if (t <= 1.1d-151) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if (t <= 5d+55) then
        tmp = (x / y) + ((2.0d0 / t) / z)
    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 (t <= -4.8e-32) {
		tmp = t_1;
	} else if (t <= 1.1e-151) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (t <= 5e+55) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -4.8e-32:
		tmp = t_1
	elif t <= 1.1e-151:
		tmp = (2.0 + (2.0 / z)) / t
	elif t <= 5e+55:
		tmp = (x / y) + ((2.0 / t) / z)
	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 (t <= -4.8e-32)
		tmp = t_1;
	elseif (t <= 1.1e-151)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif (t <= 5e+55)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	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 (t <= -4.8e-32)
		tmp = t_1;
	elseif (t <= 1.1e-151)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif (t <= 5e+55)
		tmp = (x / y) + ((2.0 / t) / z);
	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[t, -4.8e-32], t$95$1, If[LessEqual[t, 1.1e-151], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 5e+55], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000003e-32 or 5.00000000000000046e55 < t

   1. Initial program 75.1%

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

   3. Taylor expanded in t around inf 86.2%

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

   if -4.8000000000000003e-32 < t < 1.1e-151

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. metadata-eval 90.0%

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

   5. Simplified 90.0%

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

   if 1.1e-151 < t < 5.00000000000000046e55

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 80.6%

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

      1. *-commutative 80.6%

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

      2. *-commutative 80.6%

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

      3. *-commutative 80.6%

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

      4. associate-*r* 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in x around 0 80.6%

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

      1. associate--l+ 80.6%

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

      2. associate-*r/ 80.6%

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

      3. metadata-eval 80.6%

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

      4. associate-/r* 80.6%

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

      5. sub-neg 80.6%

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

      6. metadata-eval 80.6%

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

   8. Simplified 80.6%

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

   9. Taylor expanded in x around inf 79.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-151}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+24} \lor \neg \left(t \leq 1\right):\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.4e+24) (not (<= t 1.0)))
   (+ (/ (/ 2.0 t) z) (+ (/ x y) -2.0))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.4e+24) || !(t <= 1.0)) {
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (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 ((t <= (-9.4d+24)) .or. (.not. (t <= 1.0d0))) then
        tmp = ((2.0d0 / t) / z) + ((x / y) + (-2.0d0))
    else
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.4e+24) || !(t <= 1.0)) {
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.4e+24) or not (t <= 1.0):
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0)
	else:
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.4e+24) || !(t <= 1.0))
		tmp = Float64(Float64(Float64(2.0 / t) / z) + Float64(Float64(x / y) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.4e+24) || ~((t <= 1.0)))
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	else
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.4e+24], N[Not[LessEqual[t, 1.0]], $MachinePrecision]], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.3999999999999999e24 or 1 < t

   1. Initial program 74.9%

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

   3. Taylor expanded in t around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. *-commutative 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-*r* 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in x around 0 99.0%

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

      1. associate--l+ 99.0%

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

      2. associate-*r/ 99.0%

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

      3. metadata-eval 99.0%

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

      4. associate-/r* 99.0%

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

      5. sub-neg 99.0%

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

      6. metadata-eval 99.0%

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

   8. Simplified 99.0%

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

   if -9.3999999999999999e24 < t < 1

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 97.2%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+24} \lor \neg \left(t \leq 1\right):\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -102 \lor \neg \left(z \leq 2.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -102.0) (not (<= z 2.5e-7)))
   (+ (/ x y) (/ (* 2.0 (- 1.0 t)) t))
   (+ (/ (/ 2.0 t) z) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -102.0) || !(z <= 2.5e-7)) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} else {
		tmp = ((2.0 / t) / z) + ((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 ((z <= (-102.0d0)) .or. (.not. (z <= 2.5d-7))) then
        tmp = (x / y) + ((2.0d0 * (1.0d0 - t)) / t)
    else
        tmp = ((2.0d0 / t) / z) + ((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 ((z <= -102.0) || !(z <= 2.5e-7)) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} else {
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -102.0) or not (z <= 2.5e-7):
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t)
	else:
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -102.0) || !(z <= 2.5e-7))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 * Float64(1.0 - t)) / t));
	else
		tmp = Float64(Float64(Float64(2.0 / t) / z) + Float64(Float64(x / y) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -102.0) || ~((z <= 2.5e-7)))
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	else
		tmp = ((2.0 / t) / z) + ((x / y) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -102.0], N[Not[LessEqual[z, 2.5e-7]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -102 or 2.49999999999999989e-7 < z

   1. Initial program 76.2%

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

   3. Taylor expanded in z around inf 99.5%

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

      1. associate-*r/ 99.5%

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

   5. Simplified 99.5%

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

   if -102 < z < 2.49999999999999989e-7

   1. Initial program 97.4%

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

   3. Taylor expanded in t around inf 96.6%

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

      1. *-commutative 96.6%

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

      2. *-commutative 96.6%

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

      3. *-commutative 96.6%

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

      4. associate-*r* 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in x around 0 96.6%

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

      1. associate--l+ 96.6%

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

      2. associate-*r/ 96.6%

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

      3. metadata-eval 96.6%

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

      4. associate-/r* 96.6%

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

      5. sub-neg 96.6%

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

      6. metadata-eval 96.6%

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

   8. Simplified 96.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -102 \lor \neg \left(z \leq 2.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{x}{y} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-21} \lor \neg \left(z \leq 1.36 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e-21) (not (<= z 1.36e-13)))
   (+ (/ x y) (/ (* 2.0 (- 1.0 t)) t))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e-21) || !(z <= 1.36e-13)) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} 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 <= (-2.9d-21)) .or. (.not. (z <= 1.36d-13))) then
        tmp = (x / y) + ((2.0d0 * (1.0d0 - t)) / t)
    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 <= -2.9e-21) || !(z <= 1.36e-13)) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e-21) or not (z <= 1.36e-13):
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e-21) || !(z <= 1.36e-13))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 * Float64(1.0 - t)) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e-21) || ~((z <= 1.36e-13)))
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e-21], N[Not[LessEqual[z, 1.36e-13]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e-21 or 1.36000000000000001e-13 < 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. Add Preprocessing

   3. Taylor expanded in z around inf 98.0%

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

      1. associate-*r/ 98.0%

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

   5. Simplified 98.0%

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

   if -2.9e-21 < z < 1.36000000000000001e-13

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf 97.3%

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

      1. *-commutative 97.3%

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

      2. *-commutative 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in x around 0 97.3%

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

      1. associate--l+ 97.3%

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

      2. associate-*r/ 97.3%

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

      3. metadata-eval 97.3%

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

      4. associate-/r* 97.4%

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

      5. sub-neg 97.4%

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

      6. metadata-eval 97.4%

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

   8. Simplified 97.4%

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

   9. Taylor expanded in x around inf 86.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-21} \lor \neg \left(z \leq 1.36 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.018 \lor \neg \left(\frac{x}{y} \leq 1.1 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.018) (not (<= (/ x y) 1.1e+30)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.018) || !((x / y) <= 1.1e+30)) {
		tmp = (x / y) + (2.0 / t);
	} 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 (((x / y) <= (-0.018d0)) .or. (.not. ((x / y) <= 1.1d+30))) then
        tmp = (x / y) + (2.0d0 / t)
    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 (((x / y) <= -0.018) || !((x / y) <= 1.1e+30)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.018) or not ((x / y) <= 1.1e+30):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -0.018) || !(Float64(x / y) <= 1.1e+30))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	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 (((x / y) <= -0.018) || ~(((x / y) <= 1.1e+30)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = -2.0 + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -0.018], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.1e+30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.0179999999999999986 or 1.1e30 < (/.f64 x y)

   1. Initial program 85.4%

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

   3. Taylor expanded in z around inf 83.6%

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

      1. associate-*r/ 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around 0 82.4%

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

   if -0.0179999999999999986 < (/.f64 x y) < 1.1e30

   1. Initial program 87.7%

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

   3. Taylor expanded in t around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*r* 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in x around 0 74.2%

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

      1. sub-neg 74.2%

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

      2. associate-*r/ 74.2%

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

      3. metadata-eval 74.2%

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

      4. associate-/r* 74.3%

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

      5. metadata-eval 74.3%

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

   8. Simplified 74.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.018 \lor \neg \left(\frac{x}{y} \leq 1.1 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-159}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -9.5e-36)
     t_1
     (if (<= t 7.5e-198) (/ (/ 2.0 t) z) (if (<= t 3e-159) (/ 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 (t <= -9.5e-36) {
		tmp = t_1;
	} else if (t <= 7.5e-198) {
		tmp = (2.0 / t) / z;
	} else if (t <= 3e-159) {
		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 (t <= (-9.5d-36)) then
        tmp = t_1
    else if (t <= 7.5d-198) then
        tmp = (2.0d0 / t) / z
    else if (t <= 3d-159) 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 (t <= -9.5e-36) {
		tmp = t_1;
	} else if (t <= 7.5e-198) {
		tmp = (2.0 / t) / z;
	} else if (t <= 3e-159) {
		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 t <= -9.5e-36:
		tmp = t_1
	elif t <= 7.5e-198:
		tmp = (2.0 / t) / z
	elif t <= 3e-159:
		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 (t <= -9.5e-36)
		tmp = t_1;
	elseif (t <= 7.5e-198)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 3e-159)
		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 (t <= -9.5e-36)
		tmp = t_1;
	elseif (t <= 7.5e-198)
		tmp = (2.0 / t) / z;
	elseif (t <= 3e-159)
		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[t, -9.5e-36], t$95$1, If[LessEqual[t, 7.5e-198], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 3e-159], N[(2.0 / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5000000000000003e-36 or 3.00000000000000009e-159 < t

   1. Initial program 81.1%

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

   3. Taylor expanded in t around inf 75.5%

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

   if -9.5000000000000003e-36 < t < 7.50000000000000064e-198

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf 97.2%

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

      1. sub-neg 97.2%

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

      2. metadata-eval 97.2%

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

      3. associate-*r/ 97.2%

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

      4. +-commutative 97.2%

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

      5. metadata-eval 97.2%

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

      6. associate-+l+ 97.2%

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

      7. associate-*r/ 97.2%

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

      8. metadata-eval 97.2%

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

      9. associate-*r/ 97.2%

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

      10. metadata-eval 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in z around 0 53.9%

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

      1. associate-/r* 53.9%

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

   8. Simplified 53.9%

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

   if 7.50000000000000064e-198 < t < 3.00000000000000009e-159

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 92.1%

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

      1. associate-*r/ 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in t around 0 83.8%

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

Alternative 9: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-196}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-160}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -2.1e-32)
     t_1
     (if (<= t 6.4e-196) (/ 2.0 (* t z)) (if (<= t 5.3e-160) (/ 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 (t <= -2.1e-32) {
		tmp = t_1;
	} else if (t <= 6.4e-196) {
		tmp = 2.0 / (t * z);
	} else if (t <= 5.3e-160) {
		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 (t <= (-2.1d-32)) then
        tmp = t_1
    else if (t <= 6.4d-196) then
        tmp = 2.0d0 / (t * z)
    else if (t <= 5.3d-160) 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 (t <= -2.1e-32) {
		tmp = t_1;
	} else if (t <= 6.4e-196) {
		tmp = 2.0 / (t * z);
	} else if (t <= 5.3e-160) {
		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 t <= -2.1e-32:
		tmp = t_1
	elif t <= 6.4e-196:
		tmp = 2.0 / (t * z)
	elif t <= 5.3e-160:
		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 (t <= -2.1e-32)
		tmp = t_1;
	elseif (t <= 6.4e-196)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t <= 5.3e-160)
		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 (t <= -2.1e-32)
		tmp = t_1;
	elseif (t <= 6.4e-196)
		tmp = 2.0 / (t * z);
	elseif (t <= 5.3e-160)
		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[t, -2.1e-32], t$95$1, If[LessEqual[t, 6.4e-196], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e-160], N[(2.0 / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e-32 or 5.3000000000000001e-160 < t

   1. Initial program 81.1%

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

   3. Taylor expanded in t around inf 75.5%

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

   if -2.0999999999999999e-32 < t < 6.3999999999999999e-196

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 53.9%

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

   if 6.3999999999999999e-196 < t < 5.3000000000000001e-160

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 92.1%

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

      1. associate-*r/ 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in t around 0 83.8%

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

Alternative 10: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.5 \lor \neg \left(\frac{x}{y} \leq 9.8 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -9.5) (not (<= (/ x y) 9.8e+39)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -9.5) || !((x / y) <= 9.8e+39)) {
		tmp = (x / y) - 2.0;
	} 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) <= (-9.5d0)) .or. (.not. ((x / y) <= 9.8d+39))) then
        tmp = (x / y) - 2.0d0
    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) <= -9.5) || !((x / y) <= 9.8e+39)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -9.5) or not ((x / y) <= 9.8e+39):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -9.5) || !(Float64(x / y) <= 9.8e+39))
		tmp = Float64(Float64(x / y) - 2.0);
	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) <= -9.5) || ~(((x / y) <= 9.8e+39)))
		tmp = (x / y) - 2.0;
	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], -9.5], N[Not[LessEqual[N[(x / y), $MachinePrecision], 9.8e+39]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.5 or 9.79999999999999974e39 < (/.f64 x y)

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf 74.8%

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

   if -9.5 < (/.f64 x y) < 9.79999999999999974e39

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf 61.8%

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

      1. associate-*r/ 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in x around 0 59.8%

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

   7. Taylor expanded in t around inf 59.8%

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

      1. sub-neg 59.8%

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

      2. associate-*r/ 59.8%

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

      3. metadata-eval 59.8%

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

      4. metadata-eval 59.8%

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

   9. Simplified 59.8%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.5 \lor \neg \left(\frac{x}{y} \leq 9.8 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000 \lor \neg \left(\frac{x}{y} \leq 9.8 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000.0) (not (<= (/ x y) 9.8e+39)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000.0) || !((x / y) <= 9.8e+39)) {
		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) <= (-100000.0d0)) .or. (.not. ((x / y) <= 9.8d+39))) 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) <= -100000.0) || !((x / y) <= 9.8e+39)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -100000.0) or not ((x / y) <= 9.8e+39):
		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) <= -100000.0) || !(Float64(x / y) <= 9.8e+39))
		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) <= -100000.0) || ~(((x / y) <= 9.8e+39)))
		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], -100000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 9.8e+39]], $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) < -1e5 or 9.79999999999999974e39 < (/.f64 x y)

   1. Initial program 85.0%

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

   3. Taylor expanded in x around inf 73.6%

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

   if -1e5 < (/.f64 x y) < 9.79999999999999974e39

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf 61.8%

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

      1. associate-*r/ 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in x around 0 59.8%

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

   7. Taylor expanded in t around inf 59.8%

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

      1. sub-neg 59.8%

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

      2. associate-*r/ 59.8%

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

      3. metadata-eval 59.8%

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

      4. metadata-eval 59.8%

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

   9. Simplified 59.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000 \lor \neg \left(\frac{x}{y} \leq 9.8 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-32} \lor \neg \left(t \leq 2.9 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.4e-32) (not (<= t 2.9e-78)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e-32) || !(t <= 2.9e-78)) {
		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 ((t <= (-4.4d-32)) .or. (.not. (t <= 2.9d-78))) 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 ((t <= -4.4e-32) || !(t <= 2.9e-78)) {
		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 (t <= -4.4e-32) or not (t <= 2.9e-78):
		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 ((t <= -4.4e-32) || !(t <= 2.9e-78))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.4e-32) || ~((t <= 2.9e-78)))
		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[Or[LessEqual[t, -4.4e-32], N[Not[LessEqual[t, 2.9e-78]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e-32 or 2.9000000000000001e-78 < t

   1. Initial program 78.9%

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

   3. Taylor expanded in t around inf 81.1%

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

   if -4.4e-32 < t < 2.9000000000000001e-78

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 85.5%

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

      1. associate-*r/ 85.5%

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

      2. metadata-eval 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-32} \lor \neg \left(t \leq 2.9 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.085 \lor \neg \left(\frac{x}{y} \leq 0.000135\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.085) (not (<= (/ x y) 0.000135))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.085) || !((x / y) <= 0.000135)) {
		tmp = x / y;
	} 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 (((x / y) <= (-0.085d0)) .or. (.not. ((x / y) <= 0.000135d0))) then
        tmp = x / y
    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 (((x / y) <= -0.085) || !((x / y) <= 0.000135)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.085) or not ((x / y) <= 0.000135):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -0.085) || !(Float64(x / y) <= 0.000135))
		tmp = Float64(x / y);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -0.085) || ~(((x / y) <= 0.000135)))
		tmp = x / y;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -0.085], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.000135]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.0850000000000000061 or 1.35000000000000002e-4 < (/.f64 x y)

   1. Initial program 86.1%

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

   3. Taylor expanded in x around inf 68.9%

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

   if -0.0850000000000000061 < (/.f64 x y) < 1.35000000000000002e-4

   1. Initial program 87.0%

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

   3. Taylor expanded in t around inf 39.5%

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

   4. Taylor expanded in x around 0 38.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.085 \lor \neg \left(\frac{x}{y} \leq 0.000135\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.45 \cdot 10^{-9}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.205:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.45e-9) -2.0 (if (<= t 0.205) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.45e-9) {
		tmp = -2.0;
	} else if (t <= 0.205) {
		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 <= (-3.45d-9)) then
        tmp = -2.0d0
    else if (t <= 0.205d0) 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 <= -3.45e-9) {
		tmp = -2.0;
	} else if (t <= 0.205) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.45e-9:
		tmp = -2.0
	elif t <= 0.205:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.45e-9)
		tmp = -2.0;
	elseif (t <= 0.205)
		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 <= -3.45e-9)
		tmp = -2.0;
	elseif (t <= 0.205)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.45e-9], -2.0, If[LessEqual[t, 0.205], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -3.44999999999999987e-9 or 0.204999999999999988 < t

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 83.8%

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

   4. Taylor expanded in x around 0 36.8%

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

   if -3.44999999999999987e-9 < t < 0.204999999999999988

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 58.5%

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

      1. associate-*r/ 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in t around 0 35.5%

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

Alternative 15: 20.5% 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 86.6%

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

3. Taylor expanded in t around inf 55.1%

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

4. Taylor expanded in x around 0 20.0%

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

Developer Target 1: 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 2024185 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

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