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

Percentage Accurate: 86.7% → 99.1%

Time: 10.3s

Alternatives: 14

Speedup: 1.1×

• 23.8% 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: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

2. Taylor expanded in t around 0 98.7%

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

   1. associate--l+ 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

4. Simplified 98.7%

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

5. Final simplification 98.7%

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

Alternative 2: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -11500000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.25 \cdot 10^{-172}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 5.2 \cdot 10^{-46}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -11500000.0)
   (/ x y)
   (if (<= (/ x y) -1.25e-172)
     -2.0
     (if (<= (/ x y) -1e-310)
       (/ 2.0 t)
       (if (<= (/ x y) 5.2e-46) -2.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -11500000.0) {
		tmp = x / y;
	} else if ((x / y) <= -1.25e-172) {
		tmp = -2.0;
	} else if ((x / y) <= -1e-310) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 5.2e-46) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-11500000.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-1.25d-172)) then
        tmp = -2.0d0
    else if ((x / y) <= (-1d-310)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 5.2d-46) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -11500000.0) {
		tmp = x / y;
	} else if ((x / y) <= -1.25e-172) {
		tmp = -2.0;
	} else if ((x / y) <= -1e-310) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 5.2e-46) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -11500000.0:
		tmp = x / y
	elif (x / y) <= -1.25e-172:
		tmp = -2.0
	elif (x / y) <= -1e-310:
		tmp = 2.0 / t
	elif (x / y) <= 5.2e-46:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -11500000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -1.25e-172)
		tmp = -2.0;
	elseif (Float64(x / y) <= -1e-310)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 5.2e-46)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -11500000.0)
		tmp = x / y;
	elseif ((x / y) <= -1.25e-172)
		tmp = -2.0;
	elseif ((x / y) <= -1e-310)
		tmp = 2.0 / t;
	elseif ((x / y) <= 5.2e-46)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -11500000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1.25e-172], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], -1e-310], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5.2e-46], -2.0, N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.15e7 or 5.2000000000000004e-46 < (/.f64 x y)

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf 65.4%

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

   if -1.15e7 < (/.f64 x y) < -1.25e-172 or -9.999999999999969e-311 < (/.f64 x y) < 5.2000000000000004e-46

   1. Initial program 89.3%

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

   2. Taylor expanded in z around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*r/ 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. associate-*l/ 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in t around inf 47.0%

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

   if -1.25e-172 < (/.f64 x y) < -9.999999999999969e-311

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 88.8%

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

      1. associate-*r/ 88.8%

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

      2. metadata-eval 88.8%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in z around inf 42.4%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -11500000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.25 \cdot 10^{-172}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-310}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 5.2 \cdot 10^{-46}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 92.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000000000.0) (not (<= (/ x y) 5e+26)))
   (+ (/ x y) (/ (/ 2.0 z) t))
   (+ (/ (/ 2.0 t) z) (+ (/ 2.0 t) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000000.0) || !((x / y) <= 5e+26)) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else {
		tmp = ((2.0 / t) / z) + ((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) <= (-100000000000.0d0)) .or. (.not. ((x / y) <= 5d+26))) then
        tmp = (x / y) + ((2.0d0 / z) / t)
    else
        tmp = ((2.0d0 / t) / z) + ((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) <= -100000000000.0) || !((x / y) <= 5e+26)) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else {
		tmp = ((2.0 / t) / z) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -100000000000.0) or not ((x / y) <= 5e+26):
		tmp = (x / y) + ((2.0 / z) / t)
	else:
		tmp = ((2.0 / t) / z) + ((2.0 / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -100000000000.0) || !(Float64(x / y) <= 5e+26))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t));
	else
		tmp = Float64(Float64(Float64(2.0 / t) / z) + 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) <= -100000000000.0) || ~(((x / y) <= 5e+26)))
		tmp = (x / y) + ((2.0 / z) / t);
	else
		tmp = ((2.0 / t) / z) + ((2.0 / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -100000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+26]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e11 or 5.0000000000000001e26 < (/.f64 x y)

   1. Initial program 90.6%

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

   2. Taylor expanded in z around 0 90.5%

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

   3. Taylor expanded in x around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*r/ 90.5%

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

      3. metadata-eval 90.5%

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

      4. *-commutative 90.5%

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

      5. associate-/r* 90.6%

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

   5. Simplified 90.6%

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

   if -1e11 < (/.f64 x y) < 5.0000000000000001e26

   1. Initial program 91.1%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 98.9%

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

      1. associate-*r/ 98.9%

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

      2. metadata-eval 98.9%

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

      3. +-commutative 98.9%

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

      4. associate--l+ 98.9%

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

      5. associate-/r* 98.9%

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

      6. sub-neg 98.9%

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

      7. associate-*r/ 98.9%

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

      8. metadata-eval 98.9%

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

      9. metadata-eval 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]

Alternative 4: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{if}\;z \leq -680:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 (* t z)))) (t_2 (+ (/ x y) (+ (/ 2.0 t) -2.0))))
   (if (<= z -680.0)
     t_2
     (if (<= z -1.25e-130)
       t_1
       (if (<= z -1.5e-157) (- (/ x y) 2.0) (if (<= z 4.4e-67) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (t * z));
	double t_2 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (z <= -680.0) {
		tmp = t_2;
	} else if (z <= -1.25e-130) {
		tmp = t_1;
	} else if (z <= -1.5e-157) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4.4e-67) {
		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 * z))
    t_2 = (x / y) + ((2.0d0 / t) + (-2.0d0))
    if (z <= (-680.0d0)) then
        tmp = t_2
    else if (z <= (-1.25d-130)) then
        tmp = t_1
    else if (z <= (-1.5d-157)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 4.4d-67) 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 / (t * z));
	double t_2 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (z <= -680.0) {
		tmp = t_2;
	} else if (z <= -1.25e-130) {
		tmp = t_1;
	} else if (z <= -1.5e-157) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4.4e-67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / (t * z))
	t_2 = (x / y) + ((2.0 / t) + -2.0)
	tmp = 0
	if z <= -680.0:
		tmp = t_2
	elif z <= -1.25e-130:
		tmp = t_1
	elif z <= -1.5e-157:
		tmp = (x / y) - 2.0
	elif z <= 4.4e-67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)))
	t_2 = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0))
	tmp = 0.0
	if (z <= -680.0)
		tmp = t_2;
	elseif (z <= -1.25e-130)
		tmp = t_1;
	elseif (z <= -1.5e-157)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 4.4e-67)
		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 * z));
	t_2 = (x / y) + ((2.0 / t) + -2.0);
	tmp = 0.0;
	if (z <= -680.0)
		tmp = t_2;
	elseif (z <= -1.25e-130)
		tmp = t_1;
	elseif (z <= -1.5e-157)
		tmp = (x / y) - 2.0;
	elseif (z <= 4.4e-67)
		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] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -680.0], t$95$2, If[LessEqual[z, -1.25e-130], t$95$1, If[LessEqual[z, -1.5e-157], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 4.4e-67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -680 or 4.4000000000000002e-67 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 95.0%

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

      1. associate--l+ 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*r/ 95.0%

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

      4. metadata-eval 95.0%

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

      5. metadata-eval 95.0%

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

   7. Simplified 95.0%

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

   if -680 < z < -1.2499999999999999e-130 or -1.5e-157 < z < 4.4000000000000002e-67

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 85.7%

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

   if -1.2499999999999999e-130 < z < -1.5e-157

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -680:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]

Alternative 5: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{if}\;z \leq -680:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ (/ 2.0 t) -2.0))))
   (if (<= z -680.0)
     t_1
     (if (<= z -1.25e-130)
       (+ (/ x y) (/ (/ 2.0 z) t))
       (if (<= z -1.5e-157)
         (- (/ x y) 2.0)
         (if (<= z 4e-67) (+ (/ x y) (/ 2.0 (* t z))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (z <= -680.0) {
		tmp = t_1;
	} else if (z <= -1.25e-130) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else if (z <= -1.5e-157) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4e-67) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((2.0d0 / t) + (-2.0d0))
    if (z <= (-680.0d0)) then
        tmp = t_1
    else if (z <= (-1.25d-130)) then
        tmp = (x / y) + ((2.0d0 / z) / t)
    else if (z <= (-1.5d-157)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 4d-67) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (z <= -680.0) {
		tmp = t_1;
	} else if (z <= -1.25e-130) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else if (z <= -1.5e-157) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4e-67) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 / t) + -2.0)
	tmp = 0
	if z <= -680.0:
		tmp = t_1
	elif z <= -1.25e-130:
		tmp = (x / y) + ((2.0 / z) / t)
	elif z <= -1.5e-157:
		tmp = (x / y) - 2.0
	elif z <= 4e-67:
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0))
	tmp = 0.0
	if (z <= -680.0)
		tmp = t_1;
	elseif (z <= -1.25e-130)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t));
	elseif (z <= -1.5e-157)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 4e-67)
		tmp = Float64(Float64(x / y) + 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 / t) + -2.0);
	tmp = 0.0;
	if (z <= -680.0)
		tmp = t_1;
	elseif (z <= -1.25e-130)
		tmp = (x / y) + ((2.0 / z) / t);
	elseif (z <= -1.5e-157)
		tmp = (x / y) - 2.0;
	elseif (z <= 4e-67)
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -680.0], t$95$1, If[LessEqual[z, -1.25e-130], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-157], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 4e-67], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -680 or 3.99999999999999977e-67 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 95.0%

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

      1. associate--l+ 95.0%

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

      2. sub-neg 95.0%

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

      3. associate-*r/ 95.0%

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

      4. metadata-eval 95.0%

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

      5. metadata-eval 95.0%

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

   7. Simplified 95.0%

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

   if -680 < z < -1.2499999999999999e-130

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 82.9%

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

   3. Taylor expanded in x around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. associate-*r/ 82.9%

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

      3. metadata-eval 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-/r* 82.9%

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

   5. Simplified 82.9%

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

   if -1.2499999999999999e-130 < z < -1.5e-157

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.0%

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

   if -1.5e-157 < z < 3.99999999999999977e-67

   1. Initial program 95.9%

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

   2. Taylor expanded in z around 0 86.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -680:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]

Alternative 6: 62.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-140}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -1.4e-29)
     t_2
     (if (<= t -8e-295)
       t_1
       (if (<= t 5e-140) (/ 2.0 t) (if (<= t 1.1e-53) 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 <= -1.4e-29) {
		tmp = t_2;
	} else if (t <= -8e-295) {
		tmp = t_1;
	} else if (t <= 5e-140) {
		tmp = 2.0 / t;
	} else if (t <= 1.1e-53) {
		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 <= (-1.4d-29)) then
        tmp = t_2
    else if (t <= (-8d-295)) then
        tmp = t_1
    else if (t <= 5d-140) then
        tmp = 2.0d0 / t
    else if (t <= 1.1d-53) 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 <= -1.4e-29) {
		tmp = t_2;
	} else if (t <= -8e-295) {
		tmp = t_1;
	} else if (t <= 5e-140) {
		tmp = 2.0 / t;
	} else if (t <= 1.1e-53) {
		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 <= -1.4e-29:
		tmp = t_2
	elif t <= -8e-295:
		tmp = t_1
	elif t <= 5e-140:
		tmp = 2.0 / t
	elif t <= 1.1e-53:
		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 <= -1.4e-29)
		tmp = t_2;
	elseif (t <= -8e-295)
		tmp = t_1;
	elseif (t <= 5e-140)
		tmp = Float64(2.0 / t);
	elseif (t <= 1.1e-53)
		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 <= -1.4e-29)
		tmp = t_2;
	elseif (t <= -8e-295)
		tmp = t_1;
	elseif (t <= 5e-140)
		tmp = 2.0 / t;
	elseif (t <= 1.1e-53)
		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, -1.4e-29], t$95$2, If[LessEqual[t, -8e-295], t$95$1, If[LessEqual[t, 5e-140], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 1.1e-53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4000000000000001e-29 or 1.10000000000000009e-53 < t

   1. Initial program 85.8%

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

   2. Taylor expanded in t around inf 82.9%

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

   if -1.4000000000000001e-29 < t < -8.00000000000000048e-295 or 5.00000000000000015e-140 < t < 1.10000000000000009e-53

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.8%

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

   if -8.00000000000000048e-295 < t < 5.00000000000000015e-140

   1. Initial program 93.6%

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

   2. Taylor expanded in t around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. metadata-eval 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in z around inf 50.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-295}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-140}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 7: 62.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-295}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-141}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -1.05e-26)
     t_1
     (if (<= t -2.1e-295)
       (/ (/ 2.0 t) z)
       (if (<= t 3.9e-141)
         (/ 2.0 t)
         (if (<= t 1.4e-53) (/ 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 <= -1.05e-26) {
		tmp = t_1;
	} else if (t <= -2.1e-295) {
		tmp = (2.0 / t) / z;
	} else if (t <= 3.9e-141) {
		tmp = 2.0 / t;
	} else if (t <= 1.4e-53) {
		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 <= (-1.05d-26)) then
        tmp = t_1
    else if (t <= (-2.1d-295)) then
        tmp = (2.0d0 / t) / z
    else if (t <= 3.9d-141) then
        tmp = 2.0d0 / t
    else if (t <= 1.4d-53) 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 <= -1.05e-26) {
		tmp = t_1;
	} else if (t <= -2.1e-295) {
		tmp = (2.0 / t) / z;
	} else if (t <= 3.9e-141) {
		tmp = 2.0 / t;
	} else if (t <= 1.4e-53) {
		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 <= -1.05e-26:
		tmp = t_1
	elif t <= -2.1e-295:
		tmp = (2.0 / t) / z
	elif t <= 3.9e-141:
		tmp = 2.0 / t
	elif t <= 1.4e-53:
		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 <= -1.05e-26)
		tmp = t_1;
	elseif (t <= -2.1e-295)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 3.9e-141)
		tmp = Float64(2.0 / t);
	elseif (t <= 1.4e-53)
		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 <= -1.05e-26)
		tmp = t_1;
	elseif (t <= -2.1e-295)
		tmp = (2.0 / t) / z;
	elseif (t <= 3.9e-141)
		tmp = 2.0 / t;
	elseif (t <= 1.4e-53)
		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, -1.05e-26], t$95$1, If[LessEqual[t, -2.1e-295], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 3.9e-141], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 1.4e-53], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05000000000000004e-26 or 1.39999999999999993e-53 < t

   1. Initial program 85.8%

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

   2. Taylor expanded in t around inf 82.9%

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

   if -1.05000000000000004e-26 < t < -2.09999999999999993e-295

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.3%

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

      1. associate-/r* 57.3%

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

   7. Simplified 57.3%

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

   if -2.09999999999999993e-295 < t < 3.8999999999999997e-141

   1. Initial program 93.6%

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

   2. Taylor expanded in t around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. metadata-eval 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in z around inf 50.7%

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

   if 3.8999999999999997e-141 < t < 1.39999999999999993e-53

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 59.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-295}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-141}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 8: 65.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.00014 \lor \neg \left(\frac{x}{y} \leq 5.5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.00014) (not (<= (/ x y) 5.5e+26)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.00014) || !((x / y) <= 5.5e+26)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-0.00014d0)) .or. (.not. ((x / y) <= 5.5d+26))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.00014) || !((x / y) <= 5.5e+26)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.00014) or not ((x / y) <= 5.5e+26):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -0.00014) || !(Float64(x / y) <= 5.5e+26))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -0.00014) || ~(((x / y) <= 5.5e+26)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -0.00014], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5.5e+26]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.3999999999999999e-4 or 5.4999999999999997e26 < (/.f64 x y)

   1. Initial program 90.8%

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

   2. Taylor expanded in t around inf 70.4%

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

   if -1.3999999999999999e-4 < (/.f64 x y) < 5.4999999999999997e26

   1. Initial program 90.9%

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

   2. Taylor expanded in z around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. associate-*r/ 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in x around 0 65.9%

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

      1. associate-*r/ 65.9%

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

      2. associate-*l/ 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in t around 0 65.9%

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

      1. sub-neg 65.9%

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

      2. associate-*r/ 65.9%

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

      3. metadata-eval 65.9%

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

      4. metadata-eval 65.9%

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

   10. Simplified 65.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.00014 \lor \neg \left(\frac{x}{y} \leq 5.5 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 9: 80.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -260000000 \lor \neg \left(t \leq 7.5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -260000000.0) (not (<= t 7.5e-30)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -260000000.0) || !(t <= 7.5e-30)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + ((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 ((t <= (-260000000.0d0)) .or. (.not. (t <= 7.5d-30))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / t) + ((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 ((t <= -260000000.0) || !(t <= 7.5e-30)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -260000000.0) or not (t <= 7.5e-30):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -260000000.0) || !(t <= 7.5e-30))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -260000000.0) || ~((t <= 7.5e-30)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -260000000.0], N[Not[LessEqual[t, 7.5e-30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e8 or 7.5000000000000006e-30 < t

   1. Initial program 84.9%

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

   2. Taylor expanded in t around inf 85.4%

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

   if -2.6e8 < t < 7.5000000000000006e-30

   1. Initial program 97.3%

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

   2. Taylor expanded in t around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. metadata-eval 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. associate-*r/ 81.1%

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

      2. metadata-eval 81.1%

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

      3. +-commutative 81.1%

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

      4. associate-*r/ 81.1%

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

      5. metadata-eval 81.1%

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

      6. associate-/r* 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -260000000 \lor \neg \left(t \leq 7.5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 10: 81.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-28} \lor \neg \left(t \leq 5.6 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-28) (not (<= t 5.6e-30)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ 2.0 t) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-28) || !(t <= 5.6e-30)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (2.0 / t) + ((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 ((t <= (-3.2d-28)) .or. (.not. (t <= 5.6d-30))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (2.0d0 / t) + ((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 ((t <= -3.2e-28) || !(t <= 5.6e-30)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (2.0 / t) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e-28) or not (t <= 5.6e-30):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (2.0 / t) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-28) || !(t <= 5.6e-30))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.2e-28) || ~((t <= 5.6e-30)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (2.0 / t) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-28], N[Not[LessEqual[t, 5.6e-30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999982e-28 or 5.59999999999999977e-30 < t

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. associate--l+ 87.4%

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

      2. sub-neg 87.4%

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

      3. associate-*r/ 87.4%

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

      4. metadata-eval 87.4%

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

      5. metadata-eval 87.4%

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

   7. Simplified 87.4%

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

   if -3.19999999999999982e-28 < t < 5.59999999999999977e-30

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. metadata-eval 82.0%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. metadata-eval 82.0%

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

      3. +-commutative 82.0%

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

      4. associate-*r/ 82.0%

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

      5. metadata-eval 82.0%

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

      6. associate-/r* 82.0%

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

   7. Simplified 82.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-28} \lor \neg \left(t \leq 5.6 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 11: 65.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -106000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -106000000.0)
   (/ x y)
   (if (<= (/ x y) 3.1e+26) (+ (/ 2.0 t) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -106000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 3.1e+26) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-106000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 3.1d+26) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -106000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 3.1e+26) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -106000000.0:
		tmp = x / y
	elif (x / y) <= 3.1e+26:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -106000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 3.1e+26)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -106000000.0)
		tmp = x / y;
	elseif ((x / y) <= 3.1e+26)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -106000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.1e+26], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.06e8 or 3.1e26 < (/.f64 x y)

   1. Initial program 90.6%

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

   2. Taylor expanded in x around inf 70.1%

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

   if -1.06e8 < (/.f64 x y) < 3.1e26

   1. Initial program 91.1%

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

   2. Taylor expanded in z around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. associate-*r/ 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in x around 0 65.6%

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

      1. associate-*r/ 65.6%

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

      2. associate-*l/ 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in t around 0 65.6%

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

      1. sub-neg 65.6%

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

      2. associate-*r/ 65.6%

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

      3. metadata-eval 65.6%

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

      4. metadata-eval 65.6%

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

   10. Simplified 65.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -106000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 12: 80.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -132000000 \lor \neg \left(t \leq 5.8 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -132000000.0) (not (<= t 5.8e-54)))
   (- (/ 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 <= -132000000.0) || !(t <= 5.8e-54)) {
		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 <= (-132000000.0d0)) .or. (.not. (t <= 5.8d-54))) 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 <= -132000000.0) || !(t <= 5.8e-54)) {
		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 <= -132000000.0) or not (t <= 5.8e-54):
		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 <= -132000000.0) || !(t <= 5.8e-54))
		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 <= -132000000.0) || ~((t <= 5.8e-54)))
		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, -132000000.0], N[Not[LessEqual[t, 5.8e-54]], $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 < -1.32e8 or 5.80000000000000029e-54 < t

   1. Initial program 85.1%

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

   2. Taylor expanded in t around inf 84.9%

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

   if -1.32e8 < t < 5.80000000000000029e-54

   1. Initial program 97.3%

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

   2. Taylor expanded in t around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. metadata-eval 81.6%

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

   4. Simplified 81.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -132000000 \lor \neg \left(t \leq 5.8 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 13: 36.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.023:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.5e-7) -2.0 (if (<= t 0.023) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.5e-7) {
		tmp = -2.0;
	} else if (t <= 0.023) {
		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 <= (-9.5d-7)) then
        tmp = -2.0d0
    else if (t <= 0.023d0) 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 <= -9.5e-7) {
		tmp = -2.0;
	} else if (t <= 0.023) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.5e-7:
		tmp = -2.0
	elif t <= 0.023:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.5e-7)
		tmp = -2.0;
	elseif (t <= 0.023)
		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 <= -9.5e-7)
		tmp = -2.0;
	elseif (t <= 0.023)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.5e-7], -2.0, If[LessEqual[t, 0.023], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5000000000000001e-7 or 0.023 < t

   1. Initial program 84.6%

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

   2. Taylor expanded in z around inf 86.5%

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

      1. +-commutative 86.5%

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

      2. associate-*r/ 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in x around 0 43.7%

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

      1. associate-*r/ 43.7%

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

      2. associate-*l/ 43.6%

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

   7. Simplified 43.6%

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

   8. Taylor expanded in t around inf 42.7%

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

   if -9.5000000000000001e-7 < t < 0.023

   1. Initial program 97.4%

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

   2. Taylor expanded in t around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. metadata-eval 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in z around inf 34.0%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.023:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 14: 19.8% 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 90.9%

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

2. Taylor expanded in z around inf 71.3%

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

   1. +-commutative 71.3%

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

   2. associate-*r/ 71.3%

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

4. Simplified 71.3%

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

5. Taylor expanded in x around 0 39.4%

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

   1. associate-*r/ 39.4%

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

   2. associate-*l/ 39.3%

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

7. Simplified 39.3%

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

8. Taylor expanded in t around inf 22.8%

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

9. Final simplification 22.8%

   \[\leadsto -2 \]

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023268 
(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))))