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

Percentage Accurate: 86.6% → 99.1%

Time: 12.9s

Alternatives: 18

Speedup: 1.3×

• 23.4% 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: 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: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x / y) + (-2.0 + ((1.0 / t) * (2.0 + (2.0 / 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) + ((1.0d0 / t) * (2.0d0 + (2.0d0 / z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

3. Taylor expanded in t around 0 99.9%

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

   1. sub-neg 99.9%

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

   2. metadata-eval 99.9%

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

   3. associate-*r/ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-*r/ 99.9%

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

   6. metadata-eval 99.9%

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

   7. metadata-eval 99.9%

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

   8. +-commutative 99.9%

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

   9. associate-/l/ 99.9%

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

   10. metadata-eval 99.9%

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

   11. associate-*r/ 99.9%

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

   12. *-rgt-identity 99.9%

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

   13. associate-*r/ 99.9%

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

   14. distribute-rgt-out 99.9%

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

   15. associate-*r/ 99.9%

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

   16. metadata-eval 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 47.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-308}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-16}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.05e+91)
   (/ x y)
   (if (<= (/ x y) 1e-308)
     (/ 2.0 t)
     (if (<= (/ x y) 2e-16)
       -2.0
       (if (<= (/ x y) 5.5e+54) (/ 2.0 t) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.05e+91) {
		tmp = x / y;
	} else if ((x / y) <= 1e-308) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2e-16) {
		tmp = -2.0;
	} else if ((x / y) <= 5.5e+54) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.05d+91)) then
        tmp = x / y
    else if ((x / y) <= 1d-308) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2d-16) then
        tmp = -2.0d0
    else if ((x / y) <= 5.5d+54) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.05e+91) {
		tmp = x / y;
	} else if ((x / y) <= 1e-308) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2e-16) {
		tmp = -2.0;
	} else if ((x / y) <= 5.5e+54) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.05e+91:
		tmp = x / y
	elif (x / y) <= 1e-308:
		tmp = 2.0 / t
	elif (x / y) <= 2e-16:
		tmp = -2.0
	elif (x / y) <= 5.5e+54:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.05e+91)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1e-308)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2e-16)
		tmp = -2.0;
	elseif (Float64(x / y) <= 5.5e+54)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.05e+91)
		tmp = x / y;
	elseif ((x / y) <= 1e-308)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2e-16)
		tmp = -2.0;
	elseif ((x / y) <= 5.5e+54)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.05e+91], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-308], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-16], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 5.5e+54], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.05000000000000004e91 or 5.50000000000000026e54 < (/.f64 x y)

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 77.4%

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

   if -1.05000000000000004e91 < (/.f64 x y) < 9.9999999999999991e-309 or 2e-16 < (/.f64 x y) < 5.50000000000000026e54

   1. Initial program 92.6%

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

   3. Taylor expanded in t around 0 73.4%

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

      1. associate-*r/ 73.4%

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

      2. metadata-eval 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around inf 36.7%

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

   if 9.9999999999999991e-309 < (/.f64 x y) < 2e-16

   1. Initial program 86.3%

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

   3. Taylor expanded in z around inf 53.0%

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

      1. associate-*r/ 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in x around 0 53.0%

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

   7. Taylor expanded in t around inf 35.6%

      \[\leadsto 2 \cdot \color{blue}{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-308}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-16}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+46} \lor \neg \left(t \leq -7.2 \cdot 10^{-65}\right) \land \left(t \leq -6.5 \cdot 10^{-103} \lor \neg \left(t \leq 310\right)\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.9e+46)
         (and (not (<= t -7.2e-65)) (or (<= t -6.5e-103) (not (<= t 310.0)))))
   (+ (/ 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 <= -3.9e+46) || (!(t <= -7.2e-65) && ((t <= -6.5e-103) || !(t <= 310.0)))) {
		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 <= (-3.9d+46)) .or. (.not. (t <= (-7.2d-65))) .and. (t <= (-6.5d-103)) .or. (.not. (t <= 310.0d0))) 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 <= -3.9e+46) || (!(t <= -7.2e-65) && ((t <= -6.5e-103) || !(t <= 310.0)))) {
		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 <= -3.9e+46) or (not (t <= -7.2e-65) and ((t <= -6.5e-103) or not (t <= 310.0))):
		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 <= -3.9e+46) || (!(t <= -7.2e-65) && ((t <= -6.5e-103) || !(t <= 310.0))))
		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 <= -3.9e+46) || (~((t <= -7.2e-65)) && ((t <= -6.5e-103) || ~((t <= 310.0)))))
		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, -3.9e+46], And[N[Not[LessEqual[t, -7.2e-65]], $MachinePrecision], Or[LessEqual[t, -6.5e-103], N[Not[LessEqual[t, 310.0]], $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 < -3.89999999999999995e46 or -7.1999999999999996e-65 < t < -6.49999999999999966e-103 or 310 < t

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 76.9%

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

   if -3.89999999999999995e46 < t < -7.1999999999999996e-65 or -6.49999999999999966e-103 < t < 310

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. metadata-eval 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+46} \lor \neg \left(t \leq -7.2 \cdot 10^{-65}\right) \land \left(t \leq -6.5 \cdot 10^{-103} \lor \neg \left(t \leq 310\right)\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \frac{1 + z}{t \cdot z}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-103} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= t -3.9e+46)
     t_1
     (if (<= t -7.2e-65)
       (* 2.0 (/ (+ 1.0 z) (* t z)))
       (if (or (<= t -6.5e-103) (not (<= t 250.0)))
         t_1
         (/ (+ 2.0 (/ 2.0 z)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -3.9e+46) {
		tmp = t_1;
	} else if (t <= -7.2e-65) {
		tmp = 2.0 * ((1.0 + z) / (t * z));
	} else if ((t <= -6.5e-103) || !(t <= 250.0)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (t <= (-3.9d+46)) then
        tmp = t_1
    else if (t <= (-7.2d-65)) then
        tmp = 2.0d0 * ((1.0d0 + z) / (t * z))
    else if ((t <= (-6.5d-103)) .or. (.not. (t <= 250.0d0))) then
        tmp = t_1
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -3.9e+46) {
		tmp = t_1;
	} else if (t <= -7.2e-65) {
		tmp = 2.0 * ((1.0 + z) / (t * z));
	} else if ((t <= -6.5e-103) || !(t <= 250.0)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -3.9e+46:
		tmp = t_1
	elif t <= -7.2e-65:
		tmp = 2.0 * ((1.0 + z) / (t * z))
	elif (t <= -6.5e-103) or not (t <= 250.0):
		tmp = t_1
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -3.9e+46)
		tmp = t_1;
	elseif (t <= -7.2e-65)
		tmp = Float64(2.0 * Float64(Float64(1.0 + z) / Float64(t * z)));
	elseif ((t <= -6.5e-103) || !(t <= 250.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -3.9e+46)
		tmp = t_1;
	elseif (t <= -7.2e-65)
		tmp = 2.0 * ((1.0 + z) / (t * z));
	elseif ((t <= -6.5e-103) || ~((t <= 250.0)))
		tmp = t_1;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -3.9e+46], t$95$1, If[LessEqual[t, -7.2e-65], N[(2.0 * N[(N[(1.0 + z), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -6.5e-103], N[Not[LessEqual[t, 250.0]], $MachinePrecision]], t$95$1, N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.89999999999999995e46 or -7.1999999999999996e-65 < t < -6.49999999999999966e-103 or 250 < t

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 76.9%

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

   if -3.89999999999999995e46 < t < -7.1999999999999996e-65

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. remove-double-neg 99.6%

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

      3. distribute-frac-neg 99.6%

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

      4. unsub-neg 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-*r* 99.6%

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

      7. distribute-rgt1-in 99.6%

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

      8. associate-*r/ 99.6%

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

      9. /-rgt-identity 99.6%

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

      10. fma-neg 99.6%

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

      11. /-rgt-identity 99.6%

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

      12. *-commutative 99.6%

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

      13. fma-def 99.6%

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

      14. *-commutative 99.6%

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

      15. distribute-frac-neg 99.6%

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

      16. remove-double-neg 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.8%

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

   if -6.49999999999999966e-103 < t < 250

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. metadata-eval 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \frac{1 + z}{t \cdot z}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-103} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 5.5e-13)))
   (+ (/ x y) (+ -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 <= -1.0) || !(z <= 5.5e-13)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-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 <= (-1.0d0)) .or. (.not. (z <= 5.5d-13))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((-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 <= -1.0) || !(z <= 5.5e-13)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 5.5e-13):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 5.5e-13))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / Float64(t * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 5.5e-13)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 5.5e-13]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 5.49999999999999979e-13 < z

   1. Initial program 78.5%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 99.1%

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

      1. +-commutative 99.1%

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

      2. associate--l+ 99.1%

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

      3. sub-neg 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. metadata-eval 99.1%

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

   8. Simplified 99.1%

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

   if -1 < z < 5.49999999999999979e-13

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{t}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 5.5e-13)))
   (+ (/ x y) (+ -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 <= -1.0) || !(z <= 5.5e-13)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-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 <= (-1.0d0)) .or. (.not. (z <= 5.5d-13))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((-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 <= -1.0) || !(z <= 5.5e-13)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-2.0 + ((2.0 / t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 5.5e-13):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (-2.0 + ((2.0 / t) / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 5.5e-13))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + 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 <= -1.0) || ~((z <= 5.5e-13)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (-2.0 + ((2.0 / t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 5.5e-13]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 5.49999999999999979e-13 < z

   1. Initial program 78.5%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 99.1%

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

      1. +-commutative 99.1%

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

      2. associate--l+ 99.1%

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

      3. sub-neg 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. metadata-eval 99.1%

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

   8. Simplified 99.1%

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

   if -1 < z < 5.49999999999999979e-13

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in z around 0 99.8%

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

       1. associate-/r* 62.6%

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

   11. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{\frac{2}{t}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -4.8e+110)
     t_2
     (if (<= z -2.6e-57)
       t_1
       (if (<= z 4.8e-154) (/ 2.0 (* t z)) (if (<= z 4.8e+141) 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 <= -4.8e+110) {
		tmp = t_2;
	} else if (z <= -2.6e-57) {
		tmp = t_1;
	} else if (z <= 4.8e-154) {
		tmp = 2.0 / (t * z);
	} else if (z <= 4.8e+141) {
		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 <= (-4.8d+110)) then
        tmp = t_2
    else if (z <= (-2.6d-57)) then
        tmp = t_1
    else if (z <= 4.8d-154) then
        tmp = 2.0d0 / (t * z)
    else if (z <= 4.8d+141) 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 <= -4.8e+110) {
		tmp = t_2;
	} else if (z <= -2.6e-57) {
		tmp = t_1;
	} else if (z <= 4.8e-154) {
		tmp = 2.0 / (t * z);
	} else if (z <= 4.8e+141) {
		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 <= -4.8e+110:
		tmp = t_2
	elif z <= -2.6e-57:
		tmp = t_1
	elif z <= 4.8e-154:
		tmp = 2.0 / (t * z)
	elif z <= 4.8e+141:
		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 <= -4.8e+110)
		tmp = t_2;
	elseif (z <= -2.6e-57)
		tmp = t_1;
	elseif (z <= 4.8e-154)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (z <= 4.8e+141)
		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 <= -4.8e+110)
		tmp = t_2;
	elseif (z <= -2.6e-57)
		tmp = t_1;
	elseif (z <= 4.8e-154)
		tmp = 2.0 / (t * z);
	elseif (z <= 4.8e+141)
		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, -4.8e+110], t$95$2, If[LessEqual[z, -2.6e-57], t$95$1, If[LessEqual[z, 4.8e-154], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+141], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000025e110 or 4.79999999999999995e141 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 73.0%

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

       1. sub-neg 73.0%

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

       2. associate-*r/ 73.0%

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

       3. metadata-eval 73.0%

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

       4. metadata-eval 73.0%

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

   11. Simplified 73.0%

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

   if -4.80000000000000025e110 < z < -2.59999999999999985e-57 or 4.79999999999999974e-154 < z < 4.79999999999999995e141

   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 68.0%

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

   if -2.59999999999999985e-57 < z < 4.79999999999999974e-154

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. metadata-eval 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in z around 0 72.7%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+110}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -3.3e+110)
     t_2
     (if (<= z -1.25e-73)
       t_1
       (if (<= z 8e-153) (/ (/ 2.0 t) z) (if (<= z 4.8e+140) 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 <= -3.3e+110) {
		tmp = t_2;
	} else if (z <= -1.25e-73) {
		tmp = t_1;
	} else if (z <= 8e-153) {
		tmp = (2.0 / t) / z;
	} else if (z <= 4.8e+140) {
		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 <= (-3.3d+110)) then
        tmp = t_2
    else if (z <= (-1.25d-73)) then
        tmp = t_1
    else if (z <= 8d-153) then
        tmp = (2.0d0 / t) / z
    else if (z <= 4.8d+140) 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 <= -3.3e+110) {
		tmp = t_2;
	} else if (z <= -1.25e-73) {
		tmp = t_1;
	} else if (z <= 8e-153) {
		tmp = (2.0 / t) / z;
	} else if (z <= 4.8e+140) {
		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 <= -3.3e+110:
		tmp = t_2
	elif z <= -1.25e-73:
		tmp = t_1
	elif z <= 8e-153:
		tmp = (2.0 / t) / z
	elif z <= 4.8e+140:
		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 <= -3.3e+110)
		tmp = t_2;
	elseif (z <= -1.25e-73)
		tmp = t_1;
	elseif (z <= 8e-153)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (z <= 4.8e+140)
		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 <= -3.3e+110)
		tmp = t_2;
	elseif (z <= -1.25e-73)
		tmp = t_1;
	elseif (z <= 8e-153)
		tmp = (2.0 / t) / z;
	elseif (z <= 4.8e+140)
		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, -3.3e+110], t$95$2, If[LessEqual[z, -1.25e-73], t$95$1, If[LessEqual[z, 8e-153], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.8e+140], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999971e110 or 4.7999999999999999e140 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 73.0%

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

       1. sub-neg 73.0%

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

       2. associate-*r/ 73.0%

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

       3. metadata-eval 73.0%

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

       4. metadata-eval 73.0%

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

   11. Simplified 73.0%

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

   if -3.29999999999999971e110 < z < -1.25e-73 or 8.00000000000000031e-153 < z < 4.7999999999999999e140

   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 68.0%

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

   if -1.25e-73 < z < 8.00000000000000031e-153

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. metadata-eval 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in z around 0 72.7%

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

      1. associate-/r* 72.8%

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

   8. Simplified 72.8%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+110}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-39}:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -4.3e+110)
     t_2
     (if (<= z -4e-52)
       t_1
       (if (<= z 5.2e-39)
         (+ -2.0 (/ 2.0 (* t z)))
         (if (<= z 3.6e+141) 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 <= -4.3e+110) {
		tmp = t_2;
	} else if (z <= -4e-52) {
		tmp = t_1;
	} else if (z <= 5.2e-39) {
		tmp = -2.0 + (2.0 / (t * z));
	} else if (z <= 3.6e+141) {
		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 <= (-4.3d+110)) then
        tmp = t_2
    else if (z <= (-4d-52)) then
        tmp = t_1
    else if (z <= 5.2d-39) then
        tmp = (-2.0d0) + (2.0d0 / (t * z))
    else if (z <= 3.6d+141) 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 <= -4.3e+110) {
		tmp = t_2;
	} else if (z <= -4e-52) {
		tmp = t_1;
	} else if (z <= 5.2e-39) {
		tmp = -2.0 + (2.0 / (t * z));
	} else if (z <= 3.6e+141) {
		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 <= -4.3e+110:
		tmp = t_2
	elif z <= -4e-52:
		tmp = t_1
	elif z <= 5.2e-39:
		tmp = -2.0 + (2.0 / (t * z))
	elif z <= 3.6e+141:
		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 <= -4.3e+110)
		tmp = t_2;
	elseif (z <= -4e-52)
		tmp = t_1;
	elseif (z <= 5.2e-39)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(t * z)));
	elseif (z <= 3.6e+141)
		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 <= -4.3e+110)
		tmp = t_2;
	elseif (z <= -4e-52)
		tmp = t_1;
	elseif (z <= 5.2e-39)
		tmp = -2.0 + (2.0 / (t * z));
	elseif (z <= 3.6e+141)
		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, -4.3e+110], t$95$2, If[LessEqual[z, -4e-52], t$95$1, If[LessEqual[z, 5.2e-39], N[(-2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+141], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.30000000000000007e110 or 3.6000000000000001e141 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 73.0%

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

       1. sub-neg 73.0%

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

       2. associate-*r/ 73.0%

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

       3. metadata-eval 73.0%

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

       4. metadata-eval 73.0%

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

   11. Simplified 73.0%

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

   if -4.30000000000000007e110 < z < -4e-52 or 5.2e-39 < z < 3.6000000000000001e141

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 71.6%

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

   if -4e-52 < z < 5.2e-39

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 79.3%

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

       1. sub-neg 79.3%

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

       2. associate-*r/ 79.3%

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

       3. metadata-eval 79.3%

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

       4. *-commutative 79.3%

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

       5. metadata-eval 79.3%

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

       6. +-commutative 79.3%

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

       7. *-commutative 79.3%

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

   11. Simplified 79.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+110}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-39}:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-38}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -2.7e+110)
     t_2
     (if (<= z -3.45e-63)
       t_1
       (if (<= z 5.4e-38)
         (+ -2.0 (/ (/ 2.0 t) z))
         (if (<= z 1.5e+142) 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 <= -2.7e+110) {
		tmp = t_2;
	} else if (z <= -3.45e-63) {
		tmp = t_1;
	} else if (z <= 5.4e-38) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if (z <= 1.5e+142) {
		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 <= (-2.7d+110)) then
        tmp = t_2
    else if (z <= (-3.45d-63)) then
        tmp = t_1
    else if (z <= 5.4d-38) then
        tmp = (-2.0d0) + ((2.0d0 / t) / z)
    else if (z <= 1.5d+142) 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 <= -2.7e+110) {
		tmp = t_2;
	} else if (z <= -3.45e-63) {
		tmp = t_1;
	} else if (z <= 5.4e-38) {
		tmp = -2.0 + ((2.0 / t) / z);
	} else if (z <= 1.5e+142) {
		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 <= -2.7e+110:
		tmp = t_2
	elif z <= -3.45e-63:
		tmp = t_1
	elif z <= 5.4e-38:
		tmp = -2.0 + ((2.0 / t) / z)
	elif z <= 1.5e+142:
		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 <= -2.7e+110)
		tmp = t_2;
	elseif (z <= -3.45e-63)
		tmp = t_1;
	elseif (z <= 5.4e-38)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) / z));
	elseif (z <= 1.5e+142)
		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 <= -2.7e+110)
		tmp = t_2;
	elseif (z <= -3.45e-63)
		tmp = t_1;
	elseif (z <= 5.4e-38)
		tmp = -2.0 + ((2.0 / t) / z);
	elseif (z <= 1.5e+142)
		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, -2.7e+110], t$95$2, If[LessEqual[z, -3.45e-63], t$95$1, If[LessEqual[z, 5.4e-38], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+142], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000001e110 or 1.49999999999999987e142 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 73.0%

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

       1. sub-neg 73.0%

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

       2. associate-*r/ 73.0%

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

       3. metadata-eval 73.0%

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

       4. metadata-eval 73.0%

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

   11. Simplified 73.0%

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

   if -2.7000000000000001e110 < z < -3.45e-63 or 5.40000000000000011e-38 < z < 1.49999999999999987e142

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 71.6%

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

   if -3.45e-63 < z < 5.40000000000000011e-38

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 79.3%

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

       1. sub-neg 79.3%

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

       2. associate-*r/ 79.3%

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

       3. metadata-eval 79.3%

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

       4. *-commutative 79.3%

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

       5. metadata-eval 79.3%

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

       6. +-commutative 79.3%

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

       7. associate-/l/ 79.4%

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

   11. Simplified 79.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-38}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{+91} \lor \neg \left(\frac{x}{y} \leq 2.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.05e+91) (not (<= (/ x y) 2.2e+54)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.05e+91) || !((x / y) <= 2.2e+54)) {
		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) <= (-1.05d+91)) .or. (.not. ((x / y) <= 2.2d+54))) 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) <= -1.05e+91) || !((x / y) <= 2.2e+54)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.05e+91) or not ((x / y) <= 2.2e+54):
		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) <= -1.05e+91) || !(Float64(x / y) <= 2.2e+54))
		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) <= -1.05e+91) || ~(((x / y) <= 2.2e+54)))
		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], -1.05e+91], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.2e+54]], $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) < -1.05000000000000004e91 or 2.1999999999999999e54 < (/.f64 x y)

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 77.4%

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

   if -1.05000000000000004e91 < (/.f64 x y) < 2.1999999999999999e54

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.9%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate--l+ 59.1%

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

      3. sub-neg 59.1%

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

      4. associate-*r/ 59.1%

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

      5. metadata-eval 59.1%

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

      6. metadata-eval 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in x around 0 53.7%

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

       1. sub-neg 53.7%

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

       2. associate-*r/ 53.7%

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

       3. metadata-eval 53.7%

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

       4. metadata-eval 53.7%

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

   11. Simplified 53.7%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{+91} \lor \neg \left(\frac{x}{y} \leq 2.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-44} \lor \neg \left(z \leq 1.15 \cdot 10^{-152}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e-44) (not (<= z 1.15e-152)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ -2.0 (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-44) || !(z <= 1.15e-152)) {
		tmp = (x / y) + (-2.0 + (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 ((z <= (-3.6d-44)) .or. (.not. (z <= 1.15d-152))) then
        tmp = (x / y) + ((-2.0d0) + (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 ((z <= -3.6e-44) || !(z <= 1.15e-152)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.6e-44) or not (z <= 1.15e-152):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = -2.0 + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e-44) || !(z <= 1.15e-152))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + 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 ((z <= -3.6e-44) || ~((z <= 1.15e-152)))
		tmp = (x / y) + (-2.0 + (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[z, -3.6e-44], N[Not[LessEqual[z, 1.15e-152]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $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 < -3.5999999999999999e-44 or 1.1500000000000001e-152 < z

   1. Initial program 82.8%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 92.8%

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

      1. +-commutative 92.8%

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

      2. associate--l+ 92.8%

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

      3. sub-neg 92.8%

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

      4. associate-*r/ 92.8%

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

      5. metadata-eval 92.8%

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

      6. metadata-eval 92.8%

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

   8. Simplified 92.8%

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

   if -3.5999999999999999e-44 < z < 1.1500000000000001e-152

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. sub-neg 99.7%

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

      2. metadata-eval 99.7%

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

      3. associate-*r/ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-*r/ 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-/l/ 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*r/ 99.7%

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

      12. *-rgt-identity 99.7%

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

      13. associate-*r/ 99.8%

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

      14. distribute-rgt-out 99.8%

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

      15. associate-*r/ 99.8%

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

      16. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 83.5%

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

       1. sub-neg 83.5%

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

       2. associate-*r/ 83.5%

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

       3. metadata-eval 83.5%

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

       4. *-commutative 83.5%

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

       5. metadata-eval 83.5%

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

       6. +-commutative 83.5%

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

       7. associate-/l/ 83.6%

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

   11. Simplified 83.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-44} \lor \neg \left(z \leq 1.15 \cdot 10^{-152}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 91.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-5} \lor \neg \left(z \leq 4.4 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e-5) (not (<= z 4.4e-40)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-5) || !(z <= 4.4e-40)) {
		tmp = (x / y) + (-2.0 + (2.0 / 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 <= (-7.5d-5)) .or. (.not. (z <= 4.4d-40))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / 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 <= -7.5e-5) || !(z <= 4.4e-40)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e-5) or not (z <= 4.4e-40):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e-5) || !(z <= 4.4e-40))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	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 <= -7.5e-5) || ~((z <= 4.4e-40)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e-5], N[Not[LessEqual[z, 4.4e-40]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $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 < -7.49999999999999934e-5 or 4.40000000000000018e-40 < z

   1. Initial program 79.3%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 98.4%

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

      1. +-commutative 98.4%

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

      2. associate--l+ 98.4%

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

      3. sub-neg 98.4%

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

      4. associate-*r/ 98.4%

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

      5. metadata-eval 98.4%

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

      6. metadata-eval 98.4%

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

   8. Simplified 98.4%

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

   if -7.49999999999999934e-5 < z < 4.40000000000000018e-40

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 87.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-5} \lor \neg \left(z \leq 4.4 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 91.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-6} \lor \neg \left(z \leq 5.4 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e-6) (not (<= z 5.4e-38)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-6) || !(z <= 5.4e-38)) {
		tmp = (x / y) + (-2.0 + (2.0 / 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 <= (-8d-6)) .or. (.not. (z <= 5.4d-38))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / 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 <= -8e-6) || !(z <= 5.4e-38)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e-6) or not (z <= 5.4e-38):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e-6) || !(z <= 5.4e-38))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / 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 <= -8e-6) || ~((z <= 5.4e-38)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e-6], N[Not[LessEqual[z, 5.4e-38]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $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 < -7.99999999999999964e-6 or 5.40000000000000011e-38 < z

   1. Initial program 79.3%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 98.4%

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

      1. +-commutative 98.4%

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

      2. associate--l+ 98.4%

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

      3. sub-neg 98.4%

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

      4. associate-*r/ 98.4%

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

      5. metadata-eval 98.4%

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

      6. metadata-eval 98.4%

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

   8. Simplified 98.4%

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

   if -7.99999999999999964e-6 < z < 5.40000000000000011e-38

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 87.7%

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

      1. associate-/r* 87.8%

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

   5. Simplified 87.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-6} \lor \neg \left(z \leq 5.4 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.4 \cdot 10^{+55}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.05e+91)
   (/ x y)
   (if (<= (/ x y) 9.4e+55) (+ -2.0 (/ 2.0 t)) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.05e+91) {
		tmp = x / y;
	} else if ((x / y) <= 9.4e+55) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.05d+91)) then
        tmp = x / y
    else if ((x / y) <= 9.4d+55) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.05e+91) {
		tmp = x / y;
	} else if ((x / y) <= 9.4e+55) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.05e+91:
		tmp = x / y
	elif (x / y) <= 9.4e+55:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.05e+91)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 9.4e+55)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.05e+91)
		tmp = x / y;
	elseif ((x / y) <= 9.4e+55)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.05e+91], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 9.4e+55], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.05000000000000004e91

   1. Initial program 83.3%

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

   3. Taylor expanded in x around inf 89.4%

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

   if -1.05000000000000004e91 < (/.f64 x y) < 9.4000000000000001e55

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-/l/ 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*r/ 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. associate-*r/ 99.9%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate--l+ 59.1%

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

      3. sub-neg 59.1%

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

      4. associate-*r/ 59.1%

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

      5. metadata-eval 59.1%

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

      6. metadata-eval 59.1%

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

   8. Simplified 59.1%

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

   9. Taylor expanded in x around 0 53.7%

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

       1. sub-neg 53.7%

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

       2. associate-*r/ 53.7%

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

       3. metadata-eval 53.7%

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

       4. metadata-eval 53.7%

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

   11. Simplified 53.7%

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

   if 9.4000000000000001e55 < (/.f64 x y)

   1. Initial program 88.9%

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

   3. Taylor expanded in t around inf 69.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.4 \cdot 10^{+55}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

3. Taylor expanded in t around 0 99.9%

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

   1. sub-neg 99.9%

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

   2. metadata-eval 99.9%

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

   3. associate-*r/ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-*r/ 99.9%

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

   6. metadata-eval 99.9%

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

   7. metadata-eval 99.9%

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

   8. +-commutative 99.9%

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

   9. associate-/l/ 99.9%

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

   10. metadata-eval 99.9%

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

   11. associate-*r/ 99.9%

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

   12. *-rgt-identity 99.9%

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

   13. associate-*r/ 99.9%

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

   14. distribute-rgt-out 99.9%

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

   15. associate-*r/ 99.9%

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

   16. metadata-eval 99.9%

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

5. Simplified 99.9%

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

6. Taylor expanded in t around 0 99.9%

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

   1. associate-*r/ 99.9%

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

   2. metadata-eval 99.9%

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

8. Simplified 99.9%

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

9. Final simplification 99.9%

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

Alternative 17: 37.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-22}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 470:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e-22) -2.0 (if (<= t 470.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e-22) {
		tmp = -2.0;
	} else if (t <= 470.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5d-22)) then
        tmp = -2.0d0
    else if (t <= 470.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e-22) {
		tmp = -2.0;
	} else if (t <= 470.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5e-22:
		tmp = -2.0
	elif t <= 470.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e-22)
		tmp = -2.0;
	elseif (t <= 470.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5e-22)
		tmp = -2.0;
	elseif (t <= 470.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e-22], -2.0, If[LessEqual[t, 470.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999954e-22 or 470 < t

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 74.2%

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

      1. associate-*r/ 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in x around 0 34.4%

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

   7. Taylor expanded in t around inf 33.7%

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

   if -4.99999999999999954e-22 < t < 470

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. metadata-eval 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around inf 40.7%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-22}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 470:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.2% 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 89.2%

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

3. Taylor expanded in z around inf 68.3%

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

   1. associate-*r/ 68.3%

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

5. Simplified 68.3%

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

6. Taylor expanded in x around 0 38.0%

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

7. Taylor expanded in t around inf 16.8%

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

8. Final simplification 16.8%

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

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024011 
(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))))