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

Percentage Accurate: 86.7% → 99.1%

Time: 13.6s

Alternatives: 14

Speedup: 1.1×

• 23.9% 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

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.3%

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

3. Taylor expanded in t around 0 98.0%

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

   1. metadata-eval 98.0%

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

   2. associate-*r/ 98.0%

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

   3. +-commutative 98.0%

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

   4. associate-*r/ 98.0%

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

   5. metadata-eval 98.0%

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

   6. associate--l+ 98.0%

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

   7. associate-*r/ 98.0%

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

   8. metadata-eval 98.0%

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

   9. associate-/l/ 98.0%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 78.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1080000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -4.8e-44)
     t_2
     (if (<= t 1.8e-56)
       t_1
       (if (<= t 4.7e-24) (/ x y) (if (<= t 1080000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) * (1.0 / t);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.8e-44) {
		tmp = t_2;
	} else if (t <= 1.8e-56) {
		tmp = t_1;
	} else if (t <= 4.7e-24) {
		tmp = x / y;
	} else if (t <= 1080000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) * (1.0d0 / t)
    t_2 = (x / y) - 2.0d0
    if (t <= (-4.8d-44)) then
        tmp = t_2
    else if (t <= 1.8d-56) then
        tmp = t_1
    else if (t <= 4.7d-24) then
        tmp = x / y
    else if (t <= 1080000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) * (1.0 / t);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.8e-44) {
		tmp = t_2;
	} else if (t <= 1.8e-56) {
		tmp = t_1;
	} else if (t <= 4.7e-24) {
		tmp = x / y;
	} else if (t <= 1080000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) * (1.0 / t)
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -4.8e-44:
		tmp = t_2
	elif t <= 1.8e-56:
		tmp = t_1
	elif t <= 4.7e-24:
		tmp = x / y
	elif t <= 1080000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -4.8e-44)
		tmp = t_2;
	elseif (t <= 1.8e-56)
		tmp = t_1;
	elseif (t <= 4.7e-24)
		tmp = Float64(x / y);
	elseif (t <= 1080000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) * (1.0 / t);
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -4.8e-44)
		tmp = t_2;
	elseif (t <= 1.8e-56)
		tmp = t_1;
	elseif (t <= 4.7e-24)
		tmp = x / y;
	elseif (t <= 1080000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -4.8e-44], t$95$2, If[LessEqual[t, 1.8e-56], t$95$1, If[LessEqual[t, 4.7e-24], N[(x / y), $MachinePrecision], If[LessEqual[t, 1080000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.80000000000000017e-44 or 1.08e12 < 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 88.7%

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

   if -4.80000000000000017e-44 < t < 1.79999999999999989e-56 or 4.69999999999999992e-24 < t < 1.08e12

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0 83.1%

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

      1. associate-*r/ 83.1%

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

      2. metadata-eval 83.1%

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

   5. Simplified 83.1%

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

      1. div-inv 83.2%

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

   7. Applied egg-rr 83.2%

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

   if 1.79999999999999989e-56 < t < 4.69999999999999992e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1080000000000:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -6 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-57}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1080000000000:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -6e-44)
     t_1
     (if (<= t 9e-57)
       (+ (/ 2.0 t) (/ (/ 2.0 t) z))
       (if (<= t 2.4e-22)
         (/ x y)
         (if (<= t 1080000000000.0) (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -6e-44) {
		tmp = t_1;
	} else if (t <= 9e-57) {
		tmp = (2.0 / t) + ((2.0 / t) / z);
	} else if (t <= 2.4e-22) {
		tmp = x / y;
	} else if (t <= 1080000000000.0) {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-6d-44)) then
        tmp = t_1
    else if (t <= 9d-57) then
        tmp = (2.0d0 / t) + ((2.0d0 / t) / z)
    else if (t <= 2.4d-22) then
        tmp = x / y
    else if (t <= 1080000000000.0d0) then
        tmp = (2.0d0 + (2.0d0 / z)) * (1.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -6e-44) {
		tmp = t_1;
	} else if (t <= 9e-57) {
		tmp = (2.0 / t) + ((2.0 / t) / z);
	} else if (t <= 2.4e-22) {
		tmp = x / y;
	} else if (t <= 1080000000000.0) {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -6e-44:
		tmp = t_1
	elif t <= 9e-57:
		tmp = (2.0 / t) + ((2.0 / t) / z)
	elif t <= 2.4e-22:
		tmp = x / y
	elif t <= 1080000000000.0:
		tmp = (2.0 + (2.0 / z)) * (1.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -6e-44)
		tmp = t_1;
	elseif (t <= 9e-57)
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(2.0 / t) / z));
	elseif (t <= 2.4e-22)
		tmp = Float64(x / y);
	elseif (t <= 1080000000000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -6e-44)
		tmp = t_1;
	elseif (t <= 9e-57)
		tmp = (2.0 / t) + ((2.0 / t) / z);
	elseif (t <= 2.4e-22)
		tmp = x / y;
	elseif (t <= 1080000000000.0)
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -6e-44], t$95$1, If[LessEqual[t, 9e-57], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-22], N[(x / y), $MachinePrecision], If[LessEqual[t, 1080000000000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.0000000000000005e-44 or 1.08e12 < 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 88.7%

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

   if -6.0000000000000005e-44 < t < 8.99999999999999945e-57

   1. Initial program 95.4%

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

   3. Taylor expanded in t around 0 95.4%

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

   4. Taylor expanded in x around 0 95.6%

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

      1. associate-*r/ 95.6%

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

      2. metadata-eval 95.6%

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

      3. associate-+r+ 95.6%

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

      4. associate-*r/ 95.6%

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

      5. metadata-eval 95.6%

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

      6. associate-/r* 95.6%

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

      7. +-commutative 95.6%

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

      8. associate-+r+ 95.6%

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

      9. +-commutative 95.6%

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

      10. +-commutative 95.6%

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

      11. associate-+l+ 95.6%

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

      12. metadata-eval 95.6%

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

      13. associate-*r/ 95.6%

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

      14. associate-/r* 95.6%

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

      15. metadata-eval 95.6%

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

      16. associate-*r/ 95.6%

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

      17. associate-/r* 95.6%

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

      18. associate-*r/ 95.6%

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

      19. associate-*l/ 95.5%

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

   6. Simplified 95.5%

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

   7. Taylor expanded in x around 0 83.1%

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

      1. associate-*r/ 83.1%

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

      2. metadata-eval 83.1%

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

      3. associate-*r/ 83.1%

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

      4. metadata-eval 83.1%

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

      5. associate-/r* 83.1%

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

   9. Simplified 83.1%

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

   if 8.99999999999999945e-57 < t < 2.40000000000000002e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if 2.40000000000000002e-22 < t < 1.08e12

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 85.6%

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

      1. associate-*r/ 85.6%

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

      2. metadata-eval 85.6%

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

   5. Simplified 85.6%

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

      1. div-inv 85.9%

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

   7. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-57}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1080000000000:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-21}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1080000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -2.5e-45)
     t_2
     (if (<= t 1.82e-56)
       t_1
       (if (<= t 1e-21) (/ x y) (if (<= t 1080000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.5e-45) {
		tmp = t_2;
	} else if (t <= 1.82e-56) {
		tmp = t_1;
	} else if (t <= 1e-21) {
		tmp = x / y;
	} else if (t <= 1080000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) - 2.0d0
    if (t <= (-2.5d-45)) then
        tmp = t_2
    else if (t <= 1.82d-56) then
        tmp = t_1
    else if (t <= 1d-21) then
        tmp = x / y
    else if (t <= 1080000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.5e-45) {
		tmp = t_2;
	} else if (t <= 1.82e-56) {
		tmp = t_1;
	} else if (t <= 1e-21) {
		tmp = x / y;
	} else if (t <= 1080000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -2.5e-45:
		tmp = t_2
	elif t <= 1.82e-56:
		tmp = t_1
	elif t <= 1e-21:
		tmp = x / y
	elif t <= 1080000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -2.5e-45)
		tmp = t_2;
	elseif (t <= 1.82e-56)
		tmp = t_1;
	elseif (t <= 1e-21)
		tmp = Float64(x / y);
	elseif (t <= 1080000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -2.5e-45)
		tmp = t_2;
	elseif (t <= 1.82e-56)
		tmp = t_1;
	elseif (t <= 1e-21)
		tmp = x / y;
	elseif (t <= 1080000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -2.5e-45], t$95$2, If[LessEqual[t, 1.82e-56], t$95$1, If[LessEqual[t, 1e-21], N[(x / y), $MachinePrecision], If[LessEqual[t, 1080000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999988e-45 or 1.08e12 < 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 88.7%

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

   if -2.49999999999999988e-45 < t < 1.82000000000000007e-56 or 9.99999999999999908e-22 < t < 1.08e12

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0 83.1%

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

      1. associate-*r/ 83.1%

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

      2. metadata-eval 83.1%

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

   5. Simplified 83.1%

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

   if 1.82000000000000007e-56 < t < 9.99999999999999908e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-56}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 10^{-21}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1080000000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-245}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-56}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -1.85e-45)
     t_1
     (if (<= t -7.6e-245)
       (/ (/ 2.0 t) z)
       (if (<= t 1.92e-84)
         (+ (/ x y) (/ 2.0 t))
         (if (<= t 1.05e-56) (/ 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 <= -1.85e-45) {
		tmp = t_1;
	} else if (t <= -7.6e-245) {
		tmp = (2.0 / t) / z;
	} else if (t <= 1.92e-84) {
		tmp = (x / y) + (2.0 / t);
	} else if (t <= 1.05e-56) {
		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 <= (-1.85d-45)) then
        tmp = t_1
    else if (t <= (-7.6d-245)) then
        tmp = (2.0d0 / t) / z
    else if (t <= 1.92d-84) then
        tmp = (x / y) + (2.0d0 / t)
    else if (t <= 1.05d-56) 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 <= -1.85e-45) {
		tmp = t_1;
	} else if (t <= -7.6e-245) {
		tmp = (2.0 / t) / z;
	} else if (t <= 1.92e-84) {
		tmp = (x / y) + (2.0 / t);
	} else if (t <= 1.05e-56) {
		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 <= -1.85e-45:
		tmp = t_1
	elif t <= -7.6e-245:
		tmp = (2.0 / t) / z
	elif t <= 1.92e-84:
		tmp = (x / y) + (2.0 / t)
	elif t <= 1.05e-56:
		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 <= -1.85e-45)
		tmp = t_1;
	elseif (t <= -7.6e-245)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 1.92e-84)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (t <= 1.05e-56)
		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 <= -1.85e-45)
		tmp = t_1;
	elseif (t <= -7.6e-245)
		tmp = (2.0 / t) / z;
	elseif (t <= 1.92e-84)
		tmp = (x / y) + (2.0 / t);
	elseif (t <= 1.05e-56)
		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, -1.85e-45], t$95$1, If[LessEqual[t, -7.6e-245], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.92e-84], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-56], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.85e-45 or 1.05000000000000003e-56 < t

   1. Initial program 75.3%

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

   3. Taylor expanded in t around inf 86.0%

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

   if -1.85e-45 < t < -7.6000000000000001e-245

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 97.7%

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

      1. metadata-eval 97.7%

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

      2. associate-*r/ 97.7%

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

      3. +-commutative 97.7%

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

      4. associate-*r/ 97.7%

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

      5. metadata-eval 97.7%

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

      6. associate--l+ 97.7%

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

      7. associate-*r/ 97.7%

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

      8. metadata-eval 97.7%

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

      9. associate-/l/ 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in z around 0 60.6%

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

      1. associate-/r* 60.6%

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

   8. Simplified 60.6%

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

   if -7.6000000000000001e-245 < t < 1.92e-84

   1. Initial program 93.5%

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

   3. Taylor expanded in t around 0 93.5%

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

   4. Taylor expanded in z around inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. metadata-eval 68.1%

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

      3. +-commutative 68.1%

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

   6. Simplified 68.1%

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

   if 1.92e-84 < t < 1.05000000000000003e-56

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-*r/ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate--l+ 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. associate-/l/ 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in z around 0 84.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-245}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-56}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -32000 \lor \neg \left(\frac{x}{y} \leq 3.8 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \left(\frac{\frac{2}{z}}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -32000.0) (not (<= (/ x y) 3.8e-11)))
   (+ (/ x y) (/ (+ 2.0 (/ 2.0 z)) t))
   (+ (/ 2.0 t) (+ (/ (/ 2.0 z) t) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -32000.0) || !((x / y) <= 3.8e-11)) {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (2.0 / t) + (((2.0 / z) / 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) <= (-32000.0d0)) .or. (.not. ((x / y) <= 3.8d-11))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (2.0d0 / t) + (((2.0d0 / z) / 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) <= -32000.0) || !((x / y) <= 3.8e-11)) {
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (2.0 / t) + (((2.0 / z) / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -32000.0) or not ((x / y) <= 3.8e-11):
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (2.0 / t) + (((2.0 / z) / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -32000.0) || !(Float64(x / y) <= 3.8e-11))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(Float64(2.0 / z) / t) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -32000.0) || ~(((x / y) <= 3.8e-11)))
		tmp = (x / y) + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (2.0 / t) + (((2.0 / z) / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -32000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.8e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -32000 or 3.7999999999999998e-11 < (/.f64 x y)

   1. Initial program 84.9%

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

   3. Taylor expanded in t around 0 96.4%

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

   4. Taylor expanded in x around 0 96.5%

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

      1. associate-*r/ 96.5%

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

      2. metadata-eval 96.5%

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

      3. associate-+r+ 96.5%

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

      4. associate-*r/ 96.5%

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

      5. metadata-eval 96.5%

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

      6. associate-/r* 96.5%

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

      7. +-commutative 96.5%

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

      8. associate-+r+ 96.5%

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

      9. +-commutative 96.5%

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

      10. +-commutative 96.5%

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

      11. associate-+l+ 96.5%

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

      12. metadata-eval 96.5%

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

      13. associate-*r/ 96.5%

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

      14. associate-/r* 96.5%

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

      15. metadata-eval 96.5%

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

      16. associate-*r/ 96.5%

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

      17. associate-/r* 96.5%

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

      18. associate-*r/ 96.5%

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

      19. associate-*l/ 96.5%

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

   6. Simplified 96.4%

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

   if -32000 < (/.f64 x y) < 3.7999999999999998e-11

   1. Initial program 83.5%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-*r/ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate--l+ 99.9%

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

      7. associate-*r/ 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. metadata-eval 99.7%

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

      3. sub-neg 99.7%

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

      4. associate-*r/ 99.7%

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

      5. metadata-eval 99.7%

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

      6. associate-/r* 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-+r+ 99.8%

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

      9. +-commutative 99.8%

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

      10. *-rgt-identity 99.8%

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

      11. associate-*r/ 99.7%

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

      12. associate-*l/ 99.7%

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

      13. associate-*r/ 99.7%

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

      14. metadata-eval 99.7%

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

   8. Simplified 99.7%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -32000 \lor \neg \left(\frac{x}{y} \leq 3.8 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \left(\frac{\frac{2}{z}}{t} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-294}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 10^{-145}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -1.9e-45)
     t_1
     (if (<= t -7.5e-294) (/ 2.0 (* t z)) (if (<= t 1e-145) (/ 2.0 t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.9e-45) {
		tmp = t_1;
	} else if (t <= -7.5e-294) {
		tmp = 2.0 / (t * z);
	} else if (t <= 1e-145) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-1.9d-45)) then
        tmp = t_1
    else if (t <= (-7.5d-294)) then
        tmp = 2.0d0 / (t * z)
    else if (t <= 1d-145) then
        tmp = 2.0d0 / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.9e-45) {
		tmp = t_1;
	} else if (t <= -7.5e-294) {
		tmp = 2.0 / (t * z);
	} else if (t <= 1e-145) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -1.9e-45:
		tmp = t_1
	elif t <= -7.5e-294:
		tmp = 2.0 / (t * z)
	elif t <= 1e-145:
		tmp = 2.0 / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.9e-45)
		tmp = t_1;
	elseif (t <= -7.5e-294)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t <= 1e-145)
		tmp = Float64(2.0 / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.9e-45)
		tmp = t_1;
	elseif (t <= -7.5e-294)
		tmp = 2.0 / (t * z);
	elseif (t <= 1e-145)
		tmp = 2.0 / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.9e-45], t$95$1, If[LessEqual[t, -7.5e-294], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-145], N[(2.0 / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.89999999999999999e-45 or 9.99999999999999915e-146 < t

   1. Initial program 78.8%

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

   3. Taylor expanded in t around inf 79.2%

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

   if -1.89999999999999999e-45 < t < -7.5000000000000004e-294

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 96.6%

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

      1. metadata-eval 96.6%

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

      2. associate-*r/ 96.6%

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

      3. +-commutative 96.6%

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

      4. associate-*r/ 96.6%

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

      5. metadata-eval 96.6%

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

      6. associate--l+ 96.6%

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

      7. associate-*r/ 96.6%

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

      8. metadata-eval 96.6%

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

      9. associate-/l/ 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in z around 0 57.9%

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

   if -7.5000000000000004e-294 < t < 9.99999999999999915e-146

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. metadata-eval 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 60.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-294}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 10^{-145}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-294}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-150}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -4.4e-45)
     t_1
     (if (<= t -9e-294) (/ (/ 2.0 t) z) (if (<= t 2.9e-150) (/ 2.0 t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.4e-45) {
		tmp = t_1;
	} else if (t <= -9e-294) {
		tmp = (2.0 / t) / z;
	} else if (t <= 2.9e-150) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-4.4d-45)) then
        tmp = t_1
    else if (t <= (-9d-294)) then
        tmp = (2.0d0 / t) / z
    else if (t <= 2.9d-150) then
        tmp = 2.0d0 / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.4e-45) {
		tmp = t_1;
	} else if (t <= -9e-294) {
		tmp = (2.0 / t) / z;
	} else if (t <= 2.9e-150) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -4.4e-45:
		tmp = t_1
	elif t <= -9e-294:
		tmp = (2.0 / t) / z
	elif t <= 2.9e-150:
		tmp = 2.0 / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -4.4e-45)
		tmp = t_1;
	elseif (t <= -9e-294)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t <= 2.9e-150)
		tmp = Float64(2.0 / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -4.4e-45)
		tmp = t_1;
	elseif (t <= -9e-294)
		tmp = (2.0 / t) / z;
	elseif (t <= 2.9e-150)
		tmp = 2.0 / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -4.4e-45], t$95$1, If[LessEqual[t, -9e-294], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 2.9e-150], N[(2.0 / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.39999999999999987e-45 or 2.8999999999999998e-150 < t

   1. Initial program 78.8%

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

   3. Taylor expanded in t around inf 79.2%

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

   if -4.39999999999999987e-45 < t < -8.99999999999999963e-294

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 96.6%

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

      1. metadata-eval 96.6%

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

      2. associate-*r/ 96.6%

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

      3. +-commutative 96.6%

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

      4. associate-*r/ 96.6%

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

      5. metadata-eval 96.6%

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

      6. associate--l+ 96.6%

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

      7. associate-*r/ 96.6%

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

      8. metadata-eval 96.6%

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

      9. associate-/l/ 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in z around 0 57.9%

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

      1. associate-/r* 57.9%

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

   8. Simplified 57.9%

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

   if -8.99999999999999963e-294 < t < 2.8999999999999998e-150

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. metadata-eval 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 60.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-294}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-150}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3500000000 \lor \neg \left(\frac{x}{y} \leq 9500000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3500000000.0) (not (<= (/ x y) 9500000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3500000000.0) || !((x / y) <= 9500000.0)) {
		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) <= (-3500000000.0d0)) .or. (.not. ((x / y) <= 9500000.0d0))) 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) <= -3500000000.0) || !((x / y) <= 9500000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3500000000.0) or not ((x / y) <= 9500000.0):
		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) <= -3500000000.0) || !(Float64(x / y) <= 9500000.0))
		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) <= -3500000000.0) || ~(((x / y) <= 9500000.0)))
		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], -3500000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 9500000.0]], $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) < -3.5e9 or 9.5e6 < (/.f64 x y)

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf 71.4%

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

   if -3.5e9 < (/.f64 x y) < 9.5e6

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-*r/ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate--l+ 99.9%

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

      7. associate-*r/ 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. associate-*r/ 63.4%

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

      3. metadata-eval 63.4%

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

      4. +-commutative 63.4%

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

      5. metadata-eval 63.4%

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

      6. associate-+l+ 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in x around 0 63.2%

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

       1. sub-neg 63.2%

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

       2. associate-*r/ 63.2%

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

       3. metadata-eval 63.2%

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

       4. metadata-eval 63.2%

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

   11. Simplified 63.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3500000000 \lor \neg \left(\frac{x}{y} \leq 9500000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-45} \lor \neg \left(t \leq 4.85 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.5e-45) (not (<= t 4.85e-57)))
   (+ (/ 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 <= -4.5e-45) || !(t <= 4.85e-57)) {
		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 <= (-4.5d-45)) .or. (.not. (t <= 4.85d-57))) 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 <= -4.5e-45) || !(t <= 4.85e-57)) {
		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 <= -4.5e-45) or not (t <= 4.85e-57):
		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 <= -4.5e-45) || !(t <= 4.85e-57))
		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 <= -4.5e-45) || ~((t <= 4.85e-57)))
		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, -4.5e-45], N[Not[LessEqual[t, 4.85e-57]], $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 < -4.4999999999999999e-45 or 4.85e-57 < t

   1. Initial program 75.3%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-*r/ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate--l+ 99.9%

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

      7. associate-*r/ 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 87.7%

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

      1. sub-neg 87.7%

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

      2. associate-*r/ 87.7%

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

      3. metadata-eval 87.7%

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

      4. +-commutative 87.7%

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

      5. metadata-eval 87.7%

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

      6. associate-+l+ 87.7%

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

   8. Simplified 87.7%

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

   if -4.4999999999999999e-45 < t < 4.85e-57

   1. Initial program 95.4%

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

   3. Taylor expanded in t around 0 95.4%

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

   4. Taylor expanded in x around 0 95.6%

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

      1. associate-*r/ 95.6%

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

      2. metadata-eval 95.6%

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

      3. associate-+r+ 95.6%

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

      4. associate-*r/ 95.6%

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

      5. metadata-eval 95.6%

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

      6. associate-/r* 95.6%

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

      7. +-commutative 95.6%

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

      8. associate-+r+ 95.6%

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

      9. +-commutative 95.6%

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

      10. +-commutative 95.6%

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

      11. associate-+l+ 95.6%

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

      12. metadata-eval 95.6%

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

      13. associate-*r/ 95.6%

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

      14. associate-/r* 95.6%

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

      15. metadata-eval 95.6%

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

      16. associate-*r/ 95.6%

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

      17. associate-/r* 95.6%

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

      18. associate-*r/ 95.6%

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

      19. associate-*l/ 95.5%

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

   6. Simplified 95.5%

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

   7. Taylor expanded in x around 0 83.1%

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

      1. associate-*r/ 83.1%

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

      2. metadata-eval 83.1%

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

      3. associate-*r/ 83.1%

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

      4. metadata-eval 83.1%

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

      5. associate-/r* 83.1%

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

   9. Simplified 83.1%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-45} \lor \neg \left(t \leq 4.85 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-7} \lor \neg \left(z \leq 3.6 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-7) (not (<= z 3.6e-10)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-7) || !(z <= 3.6e-10)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.7d-7)) .or. (.not. (z <= 3.6d-10))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-7) || !(z <= 3.6e-10)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-7) or not (z <= 3.6e-10):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-7) || !(z <= 3.6e-10))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-7) || ~((z <= 3.6e-10)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-7], N[Not[LessEqual[z, 3.6e-10]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999987e-7 or 3.6e-10 < z

   1. Initial program 73.8%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-*r/ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate--l+ 100.0%

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

      7. associate-*r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 98.8%

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

      1. sub-neg 98.8%

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

      2. associate-*r/ 98.8%

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

      3. metadata-eval 98.8%

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

      4. +-commutative 98.8%

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

      5. metadata-eval 98.8%

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

      6. associate-+l+ 98.8%

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

   8. Simplified 98.8%

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

   if -1.69999999999999987e-7 < z < 3.6e-10

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 87.0%

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

      1. associate-/r* 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-7} \lor \neg \left(z \leq 3.6 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5800000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8500000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5800000000000.0)
   (/ x y)
   (if (<= (/ x y) 8500000.0) (+ (/ 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) <= -5800000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 8500000.0) {
		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) <= (-5800000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 8500000.0d0) 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) <= -5800000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 8500000.0) {
		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) <= -5800000000000.0:
		tmp = x / y
	elif (x / y) <= 8500000.0:
		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) <= -5800000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 8500000.0)
		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) <= -5800000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 8500000.0)
		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], -5800000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 8500000.0], 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) < -5.8e12

   1. Initial program 84.0%

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

   3. Taylor expanded in x around inf 70.4%

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

   if -5.8e12 < (/.f64 x y) < 8.5e6

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. metadata-eval 99.9%

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

      2. associate-*r/ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate--l+ 99.9%

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

      7. associate-*r/ 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. associate-*r/ 63.4%

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

      3. metadata-eval 63.4%

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

      4. +-commutative 63.4%

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

      5. metadata-eval 63.4%

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

      6. associate-+l+ 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in x around 0 63.2%

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

       1. sub-neg 63.2%

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

       2. associate-*r/ 63.2%

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

       3. metadata-eval 63.2%

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

       4. metadata-eval 63.2%

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

   11. Simplified 63.2%

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

   if 8.5e6 < (/.f64 x y)

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf 72.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5800000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 8500000:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3900000000000 \lor \neg \left(\frac{x}{y} \leq 370000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3900000000000.0) (not (<= (/ x y) 370000.0)))
   (/ x y)
   (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3900000000000.0) || !((x / y) <= 370000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-3900000000000.0d0)) .or. (.not. ((x / y) <= 370000.0d0))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3900000000000.0) || !((x / y) <= 370000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3900000000000.0) or not ((x / y) <= 370000.0):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3900000000000.0) || !(Float64(x / y) <= 370000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3900000000000.0) || ~(((x / y) <= 370000.0)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3900000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 370000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.9e12 or 3.7e5 < (/.f64 x y)

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf 71.4%

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

   if -3.9e12 < (/.f64 x y) < 3.7e5

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. metadata-eval 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in z around inf 26.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3900000000000 \lor \neg \left(\frac{x}{y} \leq 370000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 18.5% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.3%

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

3. Taylor expanded in t around 0 45.6%

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

   1. associate-*r/ 45.6%

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

   2. metadata-eval 45.6%

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

5. Simplified 45.6%

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

6. Taylor expanded in z around inf 18.3%

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

7. Final simplification 18.3%

   \[\leadsto \frac{2}{t} \]
8. Add Preprocessing

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024021 
(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))))