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

Percentage Accurate: 86.7% → 99.0%

Time: 10.5s

Alternatives: 12

Speedup: 1.1×

• 24.3% 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: 86.7% 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: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

3. Taylor expanded in t around inf 98.7%

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

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

   4. metadata-eval 98.7%

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

   5. associate-*r/ 98.7%

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

   6. sub-neg 98.7%

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

   7. associate-*r/ 98.7%

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

   8. metadata-eval 98.7%

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

   9. metadata-eval 98.7%

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

5. Simplified 98.7%

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

Alternative 2: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ 2.0 z) t)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -5.8e-7)
     t_2
     (if (<= t -1.2e-273)
       t_1
       (if (<= t 4.3e-306) (/ 2.0 t) (if (<= t 5.5e+19) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -5.8e-7) {
		tmp = t_2;
	} else if (t <= -1.2e-273) {
		tmp = t_1;
	} else if (t <= 4.3e-306) {
		tmp = 2.0 / t;
	} else if (t <= 5.5e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 / z) / t
    t_2 = (x / y) - 2.0d0
    if (t <= (-5.8d-7)) then
        tmp = t_2
    else if (t <= (-1.2d-273)) then
        tmp = t_1
    else if (t <= 4.3d-306) then
        tmp = 2.0d0 / t
    else if (t <= 5.5d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -5.8e-7) {
		tmp = t_2;
	} else if (t <= -1.2e-273) {
		tmp = t_1;
	} else if (t <= 4.3e-306) {
		tmp = 2.0 / t;
	} else if (t <= 5.5e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) / t
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -5.8e-7:
		tmp = t_2
	elif t <= -1.2e-273:
		tmp = t_1
	elif t <= 4.3e-306:
		tmp = 2.0 / t
	elif t <= 5.5e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -5.8e-7)
		tmp = t_2;
	elseif (t <= -1.2e-273)
		tmp = t_1;
	elseif (t <= 4.3e-306)
		tmp = Float64(2.0 / t);
	elseif (t <= 5.5e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) / t;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -5.8e-7)
		tmp = t_2;
	elseif (t <= -1.2e-273)
		tmp = t_1;
	elseif (t <= 4.3e-306)
		tmp = 2.0 / t;
	elseif (t <= 5.5e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -5.8e-7], t$95$2, If[LessEqual[t, -1.2e-273], t$95$1, If[LessEqual[t, 4.3e-306], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 5.5e+19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999995e-7 or 5.5e19 < t

   1. Initial program 73.4%

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

   3. Taylor expanded in t around inf 90.3%

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

   if -5.7999999999999995e-7 < t < -1.19999999999999991e-273 or 4.2999999999999999e-306 < t < 5.5e19

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in t around 0 98.9%

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

   5. Taylor expanded in z around 0 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-/r* 59.4%

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

   7. Simplified 59.4%

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

   if -1.19999999999999991e-273 < t < 4.2999999999999999e-306

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 78.8%

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

Alternative 3: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-271}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -6.2e-7)
     t_1
     (if (<= t -8e-271)
       (/ (/ 2.0 t) z)
       (if (<= t 2.7e-306)
         (/ 2.0 t)
         (if (<= t 1.6e+17) (/ 2.0 (* t z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -6.2e-7) {
		tmp = t_1;
	} else if (t <= -8e-271) {
		tmp = (2.0 / t) / z;
	} else if (t <= 2.7e-306) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-6.2d-7)) then
        tmp = t_1
    else if (t <= (-8d-271)) then
        tmp = (2.0d0 / t) / z
    else if (t <= 2.7d-306) then
        tmp = 2.0d0 / t
    else if (t <= 1.6d+17) then
        tmp = 2.0d0 / (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -6.2e-7) {
		tmp = t_1;
	} else if (t <= -8e-271) {
		tmp = (2.0 / t) / z;
	} else if (t <= 2.7e-306) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -6.2e-7:
		tmp = t_1
	elif t <= -8e-271:
		tmp = (2.0 / t) / z
	elif t <= 2.7e-306:
		tmp = 2.0 / t
	elif t <= 1.6e+17:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -6.2e-7)
		tmp = t_1;
	elseif (t <= -8e-271)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 2.7e-306)
		tmp = Float64(2.0 / t);
	elseif (t <= 1.6e+17)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -6.2e-7)
		tmp = t_1;
	elseif (t <= -8e-271)
		tmp = (2.0 / t) / z;
	elseif (t <= 2.7e-306)
		tmp = 2.0 / t;
	elseif (t <= 1.6e+17)
		tmp = 2.0 / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -6.2e-7], t$95$1, If[LessEqual[t, -8e-271], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 2.7e-306], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 1.6e+17], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.1999999999999999e-7 or 1.6e17 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf 89.8%

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

   if -6.1999999999999999e-7 < t < -7.9999999999999997e-271

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate-*r/ 99.8%

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

      6. sub-neg 99.8%

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

      7. associate-*r/ 99.8%

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

      8. metadata-eval 99.8%

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

      9. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 63.4%

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

      1. associate-/r* 63.5%

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

   8. Applied egg-rr 63.5%

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

   if -7.9999999999999997e-271 < t < 2.70000000000000009e-306

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 78.8%

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

   if 2.70000000000000009e-306 < t < 1.6e17

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 94.5%

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

      1. associate--l+ 94.5%

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

      2. associate-*r/ 94.5%

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

      3. metadata-eval 94.5%

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

      4. metadata-eval 94.5%

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

      5. associate-*r/ 94.5%

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

      6. sub-neg 94.5%

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

      7. associate-*r/ 94.5%

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

      8. metadata-eval 94.5%

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

      9. metadata-eval 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in z around 0 56.3%

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

Alternative 4: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-306}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -2.05e-7)
     t_2
     (if (<= t -6.5e-269)
       t_1
       (if (<= t 5e-306) (/ 2.0 t) (if (<= t 1.6e+17) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.05e-7) {
		tmp = t_2;
	} else if (t <= -6.5e-269) {
		tmp = t_1;
	} else if (t <= 5e-306) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = (x / y) - 2.0d0
    if (t <= (-2.05d-7)) then
        tmp = t_2
    else if (t <= (-6.5d-269)) then
        tmp = t_1
    else if (t <= 5d-306) then
        tmp = 2.0d0 / t
    else if (t <= 1.6d+17) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.05e-7) {
		tmp = t_2;
	} else if (t <= -6.5e-269) {
		tmp = t_1;
	} else if (t <= 5e-306) {
		tmp = 2.0 / t;
	} else if (t <= 1.6e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -2.05e-7:
		tmp = t_2
	elif t <= -6.5e-269:
		tmp = t_1
	elif t <= 5e-306:
		tmp = 2.0 / t
	elif t <= 1.6e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -2.05e-7)
		tmp = t_2;
	elseif (t <= -6.5e-269)
		tmp = t_1;
	elseif (t <= 5e-306)
		tmp = Float64(2.0 / t);
	elseif (t <= 1.6e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -2.05e-7)
		tmp = t_2;
	elseif (t <= -6.5e-269)
		tmp = t_1;
	elseif (t <= 5e-306)
		tmp = 2.0 / t;
	elseif (t <= 1.6e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -2.05e-7], t$95$2, If[LessEqual[t, -6.5e-269], t$95$1, If[LessEqual[t, 5e-306], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 1.6e+17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e-7 or 1.6e17 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf 89.8%

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

   if -2.05e-7 < t < -6.50000000000000006e-269 or 4.99999999999999998e-306 < t < 1.6e17

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf 96.9%

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

      1. associate--l+ 96.9%

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

      2. associate-*r/ 96.9%

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

      3. metadata-eval 96.9%

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

      4. metadata-eval 96.9%

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

      5. associate-*r/ 96.9%

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

      6. sub-neg 96.9%

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

      7. associate-*r/ 96.9%

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

      8. metadata-eval 96.9%

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

      9. metadata-eval 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around 0 59.5%

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

   if -6.50000000000000006e-269 < t < 4.99999999999999998e-306

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 78.8%

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

Alternative 5: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1300000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.00055:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 5.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1300000000000.0)
   (/ x y)
   (if (<= (/ x y) 0.00055) -2.0 (if (<= (/ x y) 5.3e+41) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1300000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 0.00055) {
		tmp = -2.0;
	} else if ((x / y) <= 5.3e+41) {
		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) <= (-1300000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 0.00055d0) then
        tmp = -2.0d0
    else if ((x / y) <= 5.3d+41) 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) <= -1300000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 0.00055) {
		tmp = -2.0;
	} else if ((x / y) <= 5.3e+41) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1300000000000.0:
		tmp = x / y
	elif (x / y) <= 0.00055:
		tmp = -2.0
	elif (x / y) <= 5.3e+41:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1300000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 0.00055)
		tmp = -2.0;
	elseif (Float64(x / y) <= 5.3e+41)
		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) <= -1300000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 0.00055)
		tmp = -2.0;
	elseif ((x / y) <= 5.3e+41)
		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], -1300000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.00055], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 5.3e+41], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.3e12 or 5.2999999999999997e41 < (/.f64 x y)

   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 x around inf 77.4%

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

   if -1.3e12 < (/.f64 x y) < 5.50000000000000033e-4

   1. Initial program 86.1%

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

   3. Taylor expanded in z around 0 91.8%

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

   4. Taylor expanded in x around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. metadata-eval 77.5%

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

      3. +-commutative 77.5%

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

      4. associate-/l* 90.3%

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

      5. associate-*r* 90.3%

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

      6. *-commutative 90.3%

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

      7. div-sub 90.3%

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

      8. sub-neg 90.3%

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

      9. *-inverses 90.3%

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

      10. metadata-eval 90.3%

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

      11. associate-*r* 90.3%

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

      12. distribute-lft-in 90.3%

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

      13. associate-*r/ 90.3%

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

      14. metadata-eval 90.3%

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

      15. metadata-eval 90.3%

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

   6. Simplified 90.3%

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

   7. Taylor expanded in t around inf 42.7%

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

   if 5.50000000000000033e-4 < (/.f64 x y) < 5.2999999999999997e41

   1. Initial program 72.9%

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

   3. Taylor expanded in t around 0 74.2%

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

      1. associate-*r/ 74.2%

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

      2. metadata-eval 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in z around inf 55.0%

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

Alternative 6: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+17) (not (<= (/ x y) 1e+42)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+17) || !((x / y) <= 1e+42)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = -2.0 + ((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 (((x / y) <= (-1d+17)) .or. (.not. ((x / y) <= 1d+42))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = (-2.0d0) + ((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 (((x / y) <= -1e+17) || !((x / y) <= 1e+42)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+17) or not ((x / y) <= 1e+42):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+17) || !(Float64(x / y) <= 1e+42))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(-2.0 + 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 (((x / y) <= -1e+17) || ~(((x / y) <= 1e+42)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+17], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+42]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e17 or 1.00000000000000004e42 < (/.f64 x y)

   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 z around 0 93.9%

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

   if -1e17 < (/.f64 x y) < 1.00000000000000004e42

   1. Initial program 84.6%

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

   3. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate-*r/ 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-*r/ 99.9%

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

      8. metadata-eval 99.9%

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

      9. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 95.7%

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

      1. sub-neg 95.7%

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

      2. associate-*r/ 95.7%

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

      3. metadata-eval 95.7%

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

      4. associate-*r/ 95.7%

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

      5. metadata-eval 95.7%

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

      6. associate-/r* 95.8%

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

      7. metadata-eval 95.8%

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

      8. associate-+r+ 95.8%

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

      9. +-commutative 95.8%

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

      10. +-commutative 95.8%

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

      11. associate-+l+ 95.8%

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

      12. metadata-eval 95.8%

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

      13. associate-*l/ 95.8%

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

      14. associate-*r/ 95.7%

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

      15. metadata-eval 95.7%

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

      16. associate-*l/ 95.7%

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

      17. distribute-lft-in 95.7%

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

      18. +-commutative 95.7%

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

      19. associate-*l/ 95.7%

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

      20. *-lft-identity 95.7%

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

   8. Simplified 95.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+15} \lor \neg \left(t \leq 1.7 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.15e+15) (not (<= t 1.7e+21)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.15e+15) || !(t <= 1.7e+21)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + ((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 <= (-1.15d+15)) .or. (.not. (t <= 1.7d+21))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + ((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 <= -1.15e+15) || !(t <= 1.7e+21)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.15e+15) or not (t <= 1.7e+21):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.15e+15) || !(t <= 1.7e+21))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + 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 <= -1.15e+15) || ~((t <= 1.7e+21)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.15e+15], N[Not[LessEqual[t, 1.7e+21]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e15 or 1.7e21 < t

   1. Initial program 73.2%

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

   3. Taylor expanded in t around inf 90.9%

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

   if -1.15e15 < t < 1.7e21

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 97.2%

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

      1. associate--l+ 97.2%

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

      2. associate-*r/ 97.2%

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

      3. metadata-eval 97.2%

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

      4. metadata-eval 97.2%

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

      5. associate-*r/ 97.2%

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

      6. sub-neg 97.2%

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

      7. associate-*r/ 97.2%

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

      8. metadata-eval 97.2%

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

      9. metadata-eval 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in x around 0 86.3%

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

      1. sub-neg 86.3%

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

      2. associate-*r/ 86.3%

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

      3. metadata-eval 86.3%

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

      4. associate-*r/ 86.3%

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

      5. metadata-eval 86.3%

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

      6. associate-/r* 86.3%

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

      7. metadata-eval 86.3%

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

      8. associate-+r+ 86.3%

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

      9. +-commutative 86.3%

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

      10. +-commutative 86.3%

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

      11. associate-+l+ 86.3%

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

      12. metadata-eval 86.3%

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

      13. associate-*l/ 86.3%

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

      14. associate-*r/ 86.3%

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

      15. metadata-eval 86.3%

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

      16. associate-*l/ 86.3%

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

      17. distribute-lft-in 86.3%

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

      18. +-commutative 86.3%

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

      19. associate-*l/ 86.3%

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

      20. *-lft-identity 86.3%

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

   8. Simplified 86.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+15} \lor \neg \left(t \leq 1.7 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1300000000000 \lor \neg \left(\frac{x}{y} \leq 5.3 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1300000000000.0) (not (<= (/ x y) 5.3e+41)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1300000000000.0) || !((x / y) <= 5.3e+41)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1300000000000.0d0)) .or. (.not. ((x / y) <= 5.3d+41))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1300000000000.0) || !((x / y) <= 5.3e+41)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1300000000000.0) or not ((x / y) <= 5.3e+41):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1300000000000.0) || !(Float64(x / y) <= 5.3e+41))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1300000000000.0) || ~(((x / y) <= 5.3e+41)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1300000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5.3e+41]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.3e12 or 5.2999999999999997e41 < (/.f64 x y)

   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 x around inf 77.4%

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

   if -1.3e12 < (/.f64 x y) < 5.2999999999999997e41

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 89.2%

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

   4. Taylor expanded in x around 0 73.7%

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

      1. associate-*r/ 73.7%

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

      2. metadata-eval 73.7%

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

      3. +-commutative 73.7%

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

      4. associate-/l* 85.1%

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

      5. associate-*r* 85.1%

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

      6. *-commutative 85.1%

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

      7. div-sub 85.1%

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

      8. sub-neg 85.1%

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

      9. *-inverses 85.1%

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

      10. metadata-eval 85.1%

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

      11. associate-*r* 85.1%

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

      12. distribute-lft-in 85.1%

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

      13. associate-*r/ 85.1%

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

      14. metadata-eval 85.1%

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

      15. metadata-eval 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in z around inf 59.8%

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

      1. sub-neg 59.8%

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

      2. associate-*r/ 59.8%

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

      3. metadata-eval 59.8%

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

      4. metadata-eval 59.8%

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

      5. +-commutative 59.8%

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

   9. Simplified 59.8%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1300000000000 \lor \neg \left(\frac{x}{y} \leq 5.3 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1300000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3600000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1300000000000.0)
   (/ x y)
   (if (<= (/ x y) 3600000.0) (+ (/ 2.0 t) -2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1300000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 3600000.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1300000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 3600000.0d0) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1300000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 3600000.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1300000000000.0:
		tmp = x / y
	elif (x / y) <= 3600000.0:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1300000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 3600000.0)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1300000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 3600000.0)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1300000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3600000.0], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.3e12

   1. Initial program 83.8%

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

   3. Taylor expanded in x around inf 80.8%

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

   if -1.3e12 < (/.f64 x y) < 3.6e6

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 91.3%

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

   4. Taylor expanded in x around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. metadata-eval 77.7%

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

      3. +-commutative 77.7%

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

      4. associate-/l* 89.9%

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

      5. associate-*r* 89.9%

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

      6. *-commutative 89.9%

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

      7. div-sub 89.9%

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

      8. sub-neg 89.9%

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

      9. *-inverses 89.9%

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

      10. metadata-eval 89.9%

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

      11. associate-*r* 89.9%

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

      12. distribute-lft-in 89.9%

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

      13. associate-*r/ 89.9%

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

      14. metadata-eval 89.9%

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

      15. metadata-eval 89.9%

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

   6. Simplified 89.9%

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

   7. Taylor expanded in z around inf 61.2%

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

      1. sub-neg 61.2%

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

      2. associate-*r/ 61.2%

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

      3. metadata-eval 61.2%

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

      4. metadata-eval 61.2%

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

      5. +-commutative 61.2%

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

   9. Simplified 61.2%

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

   if 3.6e6 < (/.f64 x y)

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 68.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1300000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3600000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2020000000 \lor \neg \left(t \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2020000000.0) (not (<= t 5e+19)))
   (- (/ 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 <= -2020000000.0) || !(t <= 5e+19)) {
		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 <= (-2020000000.0d0)) .or. (.not. (t <= 5d+19))) 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 <= -2020000000.0) || !(t <= 5e+19)) {
		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 <= -2020000000.0) or not (t <= 5e+19):
		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 <= -2020000000.0) || !(t <= 5e+19))
		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 <= -2020000000.0) || ~((t <= 5e+19)))
		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, -2020000000.0], N[Not[LessEqual[t, 5e+19]], $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 < -2.02e9 or 5e19 < t

   1. Initial program 73.2%

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

   3. Taylor expanded in t around inf 90.9%

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

   if -2.02e9 < t < 5e19

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 85.5%

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

      1. associate-*r/ 85.5%

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

      2. metadata-eval 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2020000000 \lor \neg \left(t \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+20}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.7e+20) -2.0 (if (<= t 1.6e+17) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.7e+20) {
		tmp = -2.0;
	} else if (t <= 1.6e+17) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.7d+20)) then
        tmp = -2.0d0
    else if (t <= 1.6d+17) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.7e+20) {
		tmp = -2.0;
	} else if (t <= 1.6e+17) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.7e+20:
		tmp = -2.0
	elif t <= 1.6e+17:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.7e+20)
		tmp = -2.0;
	elseif (t <= 1.6e+17)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.7e+20)
		tmp = -2.0;
	elseif (t <= 1.6e+17)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.7e+20], -2.0, If[LessEqual[t, 1.6e+17], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7e20 or 1.6e17 < t

   1. Initial program 73.4%

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

   3. Taylor expanded in z around 0 94.0%

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

   4. Taylor expanded in x around 0 37.4%

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

      1. associate-*r/ 37.4%

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

      2. metadata-eval 37.4%

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

      3. +-commutative 37.4%

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

      4. associate-/l* 47.2%

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

      5. associate-*r* 47.2%

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

      6. *-commutative 47.2%

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

      7. div-sub 47.2%

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

      8. sub-neg 47.2%

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

      9. *-inverses 47.2%

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

      10. metadata-eval 47.2%

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

      11. associate-*r* 47.2%

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

      12. distribute-lft-in 47.2%

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

      13. associate-*r/ 47.2%

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

      14. metadata-eval 47.2%

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

      15. metadata-eval 47.2%

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

   6. Simplified 47.2%

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

   7. Taylor expanded in t around inf 37.5%

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

   if -5.7e20 < t < 1.6e17

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 85.4%

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

      1. associate-*r/ 85.4%

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

      2. metadata-eval 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 32.0%

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

Alternative 12: 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 83.8%

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

3. Taylor expanded in z around 0 88.2%

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

4. Taylor expanded in x around 0 52.8%

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

   1. associate-*r/ 52.8%

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

   2. metadata-eval 52.8%

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

   3. +-commutative 52.8%

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

   4. associate-/l* 58.3%

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

   5. associate-*r* 58.3%

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

   6. *-commutative 58.3%

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

   7. div-sub 58.3%

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

   8. sub-neg 58.3%

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

   9. *-inverses 58.3%

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

   10. metadata-eval 58.3%

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

   11. associate-*r* 58.3%

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

   12. distribute-lft-in 58.3%

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

   13. associate-*r/ 58.3%

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

   14. metadata-eval 58.3%

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

   15. metadata-eval 58.3%

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

6. Simplified 58.3%

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

7. Taylor expanded in t around inf 22.1%

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

Developer target: 99.0% 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 2024096 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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