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

Percentage Accurate: 86.9% → 99.1%

Time: 13.5s

Alternatives: 17

Speedup: 1.3×

• 23.7% 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: 86.9% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((2.0d0 * (1.0d0 / t)) + ((2.0d0 / (t * z)) + (x / y))) - 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

3. Taylor expanded in t around inf 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -2.9 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 3.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))))
   (if (<= (/ x y) -2.9e+106)
     (/ x y)
     (if (<= (/ x y) -1e-14)
       t_1
       (if (<= (/ x y) 3.3e-60)
         (- (/ 2.0 t) 2.0)
         (if (<= (/ x y) 1.85e+21) t_1 (- (/ x y) 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double tmp;
	if ((x / y) <= -2.9e+106) {
		tmp = x / y;
	} else if ((x / y) <= -1e-14) {
		tmp = t_1;
	} else if ((x / y) <= 3.3e-60) {
		tmp = (2.0 / t) - 2.0;
	} else if ((x / y) <= 1.85e+21) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    if ((x / y) <= (-2.9d+106)) then
        tmp = x / y
    else if ((x / y) <= (-1d-14)) then
        tmp = t_1
    else if ((x / y) <= 3.3d-60) then
        tmp = (2.0d0 / t) - 2.0d0
    else if ((x / y) <= 1.85d+21) then
        tmp = t_1
    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 t_1 = 2.0 / (t * z);
	double tmp;
	if ((x / y) <= -2.9e+106) {
		tmp = x / y;
	} else if ((x / y) <= -1e-14) {
		tmp = t_1;
	} else if ((x / y) <= 3.3e-60) {
		tmp = (2.0 / t) - 2.0;
	} else if ((x / y) <= 1.85e+21) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	tmp = 0
	if (x / y) <= -2.9e+106:
		tmp = x / y
	elif (x / y) <= -1e-14:
		tmp = t_1
	elif (x / y) <= 3.3e-60:
		tmp = (2.0 / t) - 2.0
	elif (x / y) <= 1.85e+21:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	tmp = 0.0
	if (Float64(x / y) <= -2.9e+106)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -1e-14)
		tmp = t_1;
	elseif (Float64(x / y) <= 3.3e-60)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (Float64(x / y) <= 1.85e+21)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	tmp = 0.0;
	if ((x / y) <= -2.9e+106)
		tmp = x / y;
	elseif ((x / y) <= -1e-14)
		tmp = t_1;
	elseif ((x / y) <= 3.3e-60)
		tmp = (2.0 / t) - 2.0;
	elseif ((x / y) <= 1.85e+21)
		tmp = t_1;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2.9e+106], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e-14], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 3.3e-60], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.85e+21], t$95$1, N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2.9000000000000002e106

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf 78.2%

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

   if -2.9000000000000002e106 < (/.f64 x y) < -9.99999999999999999e-15 or 3.2999999999999998e-60 < (/.f64 x y) < 1.85e21

   1. Initial program 92.8%

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

   3. Taylor expanded in t around 0 95.3%

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

      1. associate-+r+ 95.3%

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

      2. associate-*r/ 95.3%

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

      3. metadata-eval 95.3%

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

      4. sub-neg 95.3%

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

      5. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in z around 0 60.2%

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

   if -9.99999999999999999e-15 < (/.f64 x y) < 3.2999999999999998e-60

   1. Initial program 83.6%

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

   3. Taylor expanded in t around inf 99.9%

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

   4. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 65.6%

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

   if 1.85e21 < (/.f64 x y)

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 80.4%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.9 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.9 \cdot 10^{-60}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -7.8e+105)
   (/ x y)
   (if (<= (/ x y) -2.7e-14)
     (/ 2.0 (* t z))
     (if (<= (/ x y) 1.9e-60)
       (- (/ 2.0 t) 2.0)
       (if (<= (/ x y) 2.8e+22) (/ (/ 2.0 z) t) (- (/ x y) 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -7.8e+105) {
		tmp = x / y;
	} else if ((x / y) <= -2.7e-14) {
		tmp = 2.0 / (t * z);
	} else if ((x / y) <= 1.9e-60) {
		tmp = (2.0 / t) - 2.0;
	} else if ((x / y) <= 2.8e+22) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-7.8d+105)) then
        tmp = x / y
    else if ((x / y) <= (-2.7d-14)) then
        tmp = 2.0d0 / (t * z)
    else if ((x / y) <= 1.9d-60) then
        tmp = (2.0d0 / t) - 2.0d0
    else if ((x / y) <= 2.8d+22) then
        tmp = (2.0d0 / z) / t
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -7.8e+105) {
		tmp = x / y;
	} else if ((x / y) <= -2.7e-14) {
		tmp = 2.0 / (t * z);
	} else if ((x / y) <= 1.9e-60) {
		tmp = (2.0 / t) - 2.0;
	} else if ((x / y) <= 2.8e+22) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -7.8e+105:
		tmp = x / y
	elif (x / y) <= -2.7e-14:
		tmp = 2.0 / (t * z)
	elif (x / y) <= 1.9e-60:
		tmp = (2.0 / t) - 2.0
	elif (x / y) <= 2.8e+22:
		tmp = (2.0 / z) / t
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -7.8e+105)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -2.7e-14)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (Float64(x / y) <= 1.9e-60)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (Float64(x / y) <= 2.8e+22)
		tmp = Float64(Float64(2.0 / z) / t);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -7.8e+105)
		tmp = x / y;
	elseif ((x / y) <= -2.7e-14)
		tmp = 2.0 / (t * z);
	elseif ((x / y) <= 1.9e-60)
		tmp = (2.0 / t) - 2.0;
	elseif ((x / y) <= 2.8e+22)
		tmp = (2.0 / z) / t;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -7.8e+105], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2.7e-14], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.9e-60], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.8e+22], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -7.79999999999999957e105

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf 78.2%

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

   if -7.79999999999999957e105 < (/.f64 x y) < -2.6999999999999999e-14

   1. Initial program 88.7%

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

   3. Taylor expanded in t around 0 92.7%

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

      1. associate-+r+ 92.7%

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

      2. associate-*r/ 92.7%

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

      3. metadata-eval 92.7%

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

      4. sub-neg 92.7%

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

      5. metadata-eval 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in z around 0 52.2%

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

   if -2.6999999999999999e-14 < (/.f64 x y) < 1.89999999999999997e-60

   1. Initial program 83.6%

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

   3. Taylor expanded in t around inf 99.9%

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

   4. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 65.6%

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

   if 1.89999999999999997e-60 < (/.f64 x y) < 2.8e22

   1. Initial program 99.4%

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

   3. Taylor expanded in t around 0 99.4%

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

      1. associate-+r+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. metadata-eval 99.4%

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

      4. sub-neg 99.4%

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

      5. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in z around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/r* 72.9%

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

   8. Simplified 72.9%

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

   if 2.8e22 < (/.f64 x y)

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 80.4%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.9 \cdot 10^{-60}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{t}}{z}\\ \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.16 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ 2.0 t) z)))
   (if (<= (/ x y) -7.8e+105)
     (/ x y)
     (if (<= (/ x y) -2.5e-10)
       t_1
       (if (<= (/ x y) 3.7e-62)
         (- (/ 2.0 t) 2.0)
         (if (<= (/ x y) 1.16e+23) t_1 (- (/ x y) 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) / z;
	double tmp;
	if ((x / y) <= -7.8e+105) {
		tmp = x / y;
	} else if ((x / y) <= -2.5e-10) {
		tmp = t_1;
	} else if ((x / y) <= 3.7e-62) {
		tmp = (2.0 / t) - 2.0;
	} else if ((x / y) <= 1.16e+23) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / t) / z
    if ((x / y) <= (-7.8d+105)) then
        tmp = x / y
    else if ((x / y) <= (-2.5d-10)) then
        tmp = t_1
    else if ((x / y) <= 3.7d-62) then
        tmp = (2.0d0 / t) - 2.0d0
    else if ((x / y) <= 1.16d+23) then
        tmp = t_1
    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 t_1 = (2.0 / t) / z;
	double tmp;
	if ((x / y) <= -7.8e+105) {
		tmp = x / y;
	} else if ((x / y) <= -2.5e-10) {
		tmp = t_1;
	} else if ((x / y) <= 3.7e-62) {
		tmp = (2.0 / t) - 2.0;
	} else if ((x / y) <= 1.16e+23) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) / z
	tmp = 0
	if (x / y) <= -7.8e+105:
		tmp = x / y
	elif (x / y) <= -2.5e-10:
		tmp = t_1
	elif (x / y) <= 3.7e-62:
		tmp = (2.0 / t) - 2.0
	elif (x / y) <= 1.16e+23:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) / z)
	tmp = 0.0
	if (Float64(x / y) <= -7.8e+105)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -2.5e-10)
		tmp = t_1;
	elseif (Float64(x / y) <= 3.7e-62)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (Float64(x / y) <= 1.16e+23)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) / z;
	tmp = 0.0;
	if ((x / y) <= -7.8e+105)
		tmp = x / y;
	elseif ((x / y) <= -2.5e-10)
		tmp = t_1;
	elseif ((x / y) <= 3.7e-62)
		tmp = (2.0 / t) - 2.0;
	elseif ((x / y) <= 1.16e+23)
		tmp = t_1;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -7.8e+105], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2.5e-10], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 3.7e-62], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.16e+23], t$95$1, N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -7.79999999999999957e105

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf 78.2%

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

   if -7.79999999999999957e105 < (/.f64 x y) < -2.50000000000000016e-10 or 3.6999999999999998e-62 < (/.f64 x y) < 1.16e23

   1. Initial program 92.8%

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

   3. Taylor expanded in t around 0 95.3%

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

      1. associate-+r+ 95.3%

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

      2. associate-*r/ 95.3%

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

      3. metadata-eval 95.3%

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

      4. sub-neg 95.3%

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

      5. metadata-eval 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in z around 0 60.2%

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

      1. *-un-lft-identity 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-/r* 60.3%

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

   8. Applied egg-rr 60.3%

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

   if -2.50000000000000016e-10 < (/.f64 x y) < 3.6999999999999998e-62

   1. Initial program 83.6%

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

   3. Taylor expanded in t around inf 99.9%

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

   4. Taylor expanded in t around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. metadata-eval 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 65.6%

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

   if 1.16e23 < (/.f64 x y)

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 80.4%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.16 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+25} \lor \neg \left(t \leq 7 \cdot 10^{-19}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -7.8e+97)
     t_1
     (if (<= t -1.25e+35)
       (/ (/ 2.0 t) z)
       (if (or (<= t -1.8e+25) (not (<= t 7e-19)))
         t_1
         (+ (/ 2.0 (* t z)) (/ 2.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -7.8e+97) {
		tmp = t_1;
	} else if (t <= -1.25e+35) {
		tmp = (2.0 / t) / z;
	} else if ((t <= -1.8e+25) || !(t <= 7e-19)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / (t * z)) + (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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-7.8d+97)) then
        tmp = t_1
    else if (t <= (-1.25d+35)) then
        tmp = (2.0d0 / t) / z
    else if ((t <= (-1.8d+25)) .or. (.not. (t <= 7d-19))) then
        tmp = t_1
    else
        tmp = (2.0d0 / (t * z)) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -7.8e+97) {
		tmp = t_1;
	} else if (t <= -1.25e+35) {
		tmp = (2.0 / t) / z;
	} else if ((t <= -1.8e+25) || !(t <= 7e-19)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / (t * z)) + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -7.8e+97:
		tmp = t_1
	elif t <= -1.25e+35:
		tmp = (2.0 / t) / z
	elif (t <= -1.8e+25) or not (t <= 7e-19):
		tmp = t_1
	else:
		tmp = (2.0 / (t * z)) + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -7.8e+97)
		tmp = t_1;
	elseif (t <= -1.25e+35)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif ((t <= -1.8e+25) || !(t <= 7e-19))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -7.8e+97)
		tmp = t_1;
	elseif (t <= -1.25e+35)
		tmp = (2.0 / t) / z;
	elseif ((t <= -1.8e+25) || ~((t <= 7e-19)))
		tmp = t_1;
	else
		tmp = (2.0 / (t * z)) + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -7.8e+97], t$95$1, If[LessEqual[t, -1.25e+35], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t, -1.8e+25], N[Not[LessEqual[t, 7e-19]], $MachinePrecision]], t$95$1, N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.7999999999999999e97 or -1.25000000000000005e35 < t < -1.80000000000000008e25 or 7.00000000000000031e-19 < t

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf 84.4%

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

   if -7.7999999999999999e97 < t < -1.25000000000000005e35

   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 90.8%

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

      1. associate-+r+ 90.8%

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

      2. associate-*r/ 90.8%

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

      3. metadata-eval 90.8%

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

      4. sub-neg 90.8%

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

      5. metadata-eval 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in z around 0 74.3%

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

      1. *-un-lft-identity 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-/r* 74.5%

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

   8. Applied egg-rr 74.5%

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

   if -1.80000000000000008e25 < t < 7.00000000000000031e-19

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0 76.0%

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

      1. associate-*r/ 76.0%

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

      2. metadata-eval 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in z around 0 62.3%

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

   7. Taylor expanded in z around inf 76.0%

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

      1. associate-*r/ 76.0%

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

      2. metadata-eval 76.0%

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

      3. associate-*r/ 76.0%

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

      4. metadata-eval 76.0%

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

   9. Simplified 76.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+25} \lor \neg \left(t \leq 7 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+26} \lor \neg \left(t \leq 1.4 \cdot 10^{-19}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -2.3e+100)
     t_1
     (if (<= t -2.2e+35)
       (/ (/ 2.0 t) z)
       (if (or (<= t -1.5e+26) (not (<= t 1.4e-19)))
         t_1
         (/ (+ 2.0 (/ 2.0 z)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.3e+100) {
		tmp = t_1;
	} else if (t <= -2.2e+35) {
		tmp = (2.0 / t) / z;
	} else if ((t <= -1.5e+26) || !(t <= 1.4e-19)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-2.3d+100)) then
        tmp = t_1
    else if (t <= (-2.2d+35)) then
        tmp = (2.0d0 / t) / z
    else if ((t <= (-1.5d+26)) .or. (.not. (t <= 1.4d-19))) then
        tmp = t_1
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.3e+100) {
		tmp = t_1;
	} else if (t <= -2.2e+35) {
		tmp = (2.0 / t) / z;
	} else if ((t <= -1.5e+26) || !(t <= 1.4e-19)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -2.3e+100:
		tmp = t_1
	elif t <= -2.2e+35:
		tmp = (2.0 / t) / z
	elif (t <= -1.5e+26) or not (t <= 1.4e-19):
		tmp = t_1
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -2.3e+100)
		tmp = t_1;
	elseif (t <= -2.2e+35)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif ((t <= -1.5e+26) || !(t <= 1.4e-19))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -2.3e+100)
		tmp = t_1;
	elseif (t <= -2.2e+35)
		tmp = (2.0 / t) / z;
	elseif ((t <= -1.5e+26) || ~((t <= 1.4e-19)))
		tmp = t_1;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -2.3e+100], t$95$1, If[LessEqual[t, -2.2e+35], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t, -1.5e+26], N[Not[LessEqual[t, 1.4e-19]], $MachinePrecision]], t$95$1, N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2999999999999999e100 or -2.1999999999999999e35 < t < -1.49999999999999999e26 or 1.40000000000000001e-19 < t

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf 84.4%

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

   if -2.2999999999999999e100 < t < -2.1999999999999999e35

   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 90.8%

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

      1. associate-+r+ 90.8%

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

      2. associate-*r/ 90.8%

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

      3. metadata-eval 90.8%

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

      4. sub-neg 90.8%

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

      5. metadata-eval 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in z around 0 74.3%

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

      1. *-un-lft-identity 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-/r* 74.5%

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

   8. Applied egg-rr 74.5%

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

   if -1.49999999999999999e26 < t < 1.40000000000000001e-19

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0 76.0%

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

      1. associate-*r/ 76.0%

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

      2. metadata-eval 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+26} \lor \neg \left(t \leq 1.4 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+19)
   (+ (/ 2.0 (* t z)) (/ x y))
   (if (<= (/ x y) 2e-5)
     (- (/ (+ 2.0 (/ 2.0 z)) t) 2.0)
     (+ (/ x y) (/ (/ 2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+19) {
		tmp = (2.0 / (t * z)) + (x / y);
	} else if ((x / y) <= 2e-5) {
		tmp = ((2.0 + (2.0 / z)) / 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 ((x / y) <= (-2d+19)) then
        tmp = (2.0d0 / (t * z)) + (x / y)
    else if ((x / y) <= 2d-5) then
        tmp = ((2.0d0 + (2.0d0 / z)) / 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 ((x / y) <= -2e+19) {
		tmp = (2.0 / (t * z)) + (x / y);
	} else if ((x / y) <= 2e-5) {
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0;
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+19:
		tmp = (2.0 / (t * z)) + (x / y)
	elif (x / y) <= 2e-5:
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+19)
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	elseif (Float64(x / y) <= 2e-5)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / 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 ((x / y) <= -2e+19)
		tmp = (2.0 / (t * z)) + (x / y);
	elseif ((x / y) <= 2e-5)
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0;
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+19], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-5], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e19

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 84.3%

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

   if -2e19 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 83.8%

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

   3. Taylor expanded in t around inf 99.8%

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

   4. Taylor expanded in t around 0 97.6%

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

      1. associate-*r/ 97.6%

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

      2. metadata-eval 97.6%

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

   6. Simplified 97.6%

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

   if 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 77.7%

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

   3. Taylor expanded in z around 0 93.8%

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

      1. associate-/r* 93.9%

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

   5. Simplified 93.9%

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

4. Final simplification 93.2%

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

Alternative 8: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + \frac{2}{t \cdot \left(z \cdot x\right)}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+113)
   (* x (+ (/ 1.0 y) (/ 2.0 (* t (* z x)))))
   (if (<= (/ x y) 2e-5)
     (- (/ (+ 2.0 (/ 2.0 z)) t) 2.0)
     (+ (/ x y) (/ (/ 2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+113) {
		tmp = x * ((1.0 / y) + (2.0 / (t * (z * x))));
	} else if ((x / y) <= 2e-5) {
		tmp = ((2.0 + (2.0 / z)) / 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 ((x / y) <= (-2d+113)) then
        tmp = x * ((1.0d0 / y) + (2.0d0 / (t * (z * x))))
    else if ((x / y) <= 2d-5) then
        tmp = ((2.0d0 + (2.0d0 / z)) / 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 ((x / y) <= -2e+113) {
		tmp = x * ((1.0 / y) + (2.0 / (t * (z * x))));
	} else if ((x / y) <= 2e-5) {
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0;
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+113:
		tmp = x * ((1.0 / y) + (2.0 / (t * (z * x))))
	elif (x / y) <= 2e-5:
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+113)
		tmp = Float64(x * Float64(Float64(1.0 / y) + Float64(2.0 / Float64(t * Float64(z * x)))));
	elseif (Float64(x / y) <= 2e-5)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / 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 ((x / y) <= -2e+113)
		tmp = x * ((1.0 / y) + (2.0 / (t * (z * x))));
	elseif ((x / y) <= 2e-5)
		tmp = ((2.0 + (2.0 / z)) / t) - 2.0;
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+113], N[(x * N[(N[(1.0 / y), $MachinePrecision] + N[(2.0 / N[(t * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-5], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e113

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 86.1%

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

      1. associate-/r* 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in x around inf 92.3%

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

      1. associate-*r/ 92.3%

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

      2. metadata-eval 92.3%

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

      3. *-commutative 92.3%

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

   8. Simplified 92.3%

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

   if -2e113 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf 99.8%

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

   4. Taylor expanded in t around 0 95.1%

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

      1. associate-*r/ 95.1%

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

      2. metadata-eval 95.1%

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

   6. Simplified 95.1%

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

   if 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 77.7%

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

   3. Taylor expanded in z around 0 93.8%

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

      1. associate-/r* 93.9%

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

   5. Simplified 93.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(\frac{1}{y} + \frac{2}{t \cdot \left(z \cdot x\right)}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -124000 \lor \neg \left(\frac{x}{y} \leq 8.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -124000.0) (not (<= (/ x y) 8.8e+20)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -124000.0) || !((x / y) <= 8.8e+20)) {
		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) <= (-124000.0d0)) .or. (.not. ((x / y) <= 8.8d+20))) 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) <= -124000.0) || !((x / y) <= 8.8e+20)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -124000.0) or not ((x / y) <= 8.8e+20):
		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) <= -124000.0) || !(Float64(x / y) <= 8.8e+20))
		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) <= -124000.0) || ~(((x / y) <= 8.8e+20)))
		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], -124000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 8.8e+20]], $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) < -124000 or 8.8e20 < (/.f64 x y)

   1. Initial program 82.1%

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

   3. Taylor expanded in x around inf 70.2%

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

   if -124000 < (/.f64 x y) < 8.8e20

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 99.8%

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

   4. Taylor expanded in t around 0 98.8%

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

      1. associate-*r/ 98.8%

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

      2. metadata-eval 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in z around inf 58.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -124000 \lor \neg \left(\frac{x}{y} \leq 8.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.115 \lor \neg \left(\frac{x}{y} \leq 9.2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.115) (not (<= (/ x y) 9.2e+20)))
   (- (/ x y) 2.0)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.115) || !((x / y) <= 9.2e+20)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-0.115d0)) .or. (.not. ((x / y) <= 9.2d+20))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.115) || !((x / y) <= 9.2e+20)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.115) or not ((x / y) <= 9.2e+20):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -0.115) || !(Float64(x / y) <= 9.2e+20))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -0.115) || ~(((x / y) <= 9.2e+20)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -0.115], N[Not[LessEqual[N[(x / y), $MachinePrecision], 9.2e+20]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.115000000000000005 or 9.2e20 < (/.f64 x y)

   1. Initial program 81.6%

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

   3. Taylor expanded in t around inf 70.5%

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

   if -0.115000000000000005 < (/.f64 x y) < 9.2e20

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 99.8%

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

   4. Taylor expanded in t around 0 99.4%

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

      1. associate-*r/ 99.4%

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

      2. metadata-eval 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in z around inf 58.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.115 \lor \neg \left(\frac{x}{y} \leq 9.2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-189} \lor \neg \left(z \leq 7 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-189) (not (<= z 7e-38)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (/ (/ 2.0 t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-189) || !(z <= 7e-38)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (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-189)) .or. (.not. (z <= 7d-38))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (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-189) || !(z <= 7e-38)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-189) or not (z <= 7e-38):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (2.0 / t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-189) || !(z <= 7e-38))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = 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-189) || ~((z <= 7e-38)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (2.0 / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-189], N[Not[LessEqual[z, 7e-38]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7000000000000001e-189 or 7.0000000000000003e-38 < z

   1. Initial program 76.1%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. div-sub 89.6%

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

      2. sub-neg 89.6%

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

      3. *-inverses 89.6%

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

      4. metadata-eval 89.6%

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

      5. distribute-lft-in 89.6%

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

      6. associate-*r/ 89.6%

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

      7. metadata-eval 89.6%

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

      8. metadata-eval 89.6%

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

   5. Simplified 89.6%

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

   if -1.7000000000000001e-189 < z < 7.0000000000000003e-38

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 89.9%

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

      1. associate-+r+ 89.9%

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

      2. associate-*r/ 89.9%

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

      3. metadata-eval 89.9%

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

      4. sub-neg 89.9%

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

      5. metadata-eval 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in z around 0 69.6%

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

      1. *-un-lft-identity 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/r* 69.7%

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

   8. Applied egg-rr 69.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-189} \lor \neg \left(z \leq 7 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-32} \lor \neg \left(z \leq 4.9 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-32) (not (<= z 4.9e-8)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ 2.0 (* t z)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-32) || !(z <= 4.9e-8)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (2.0 / (t * z)) + (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-32)) .or. (.not. (z <= 4.9d-8))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (2.0d0 / (t * z)) + (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-32) || !(z <= 4.9e-8)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (2.0 / (t * z)) + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-32) or not (z <= 4.9e-8):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (2.0 / (t * z)) + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-32) || !(z <= 4.9e-8))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-32) || ~((z <= 4.9e-8)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (2.0 / (t * z)) + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-32], N[Not[LessEqual[z, 4.9e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e-32 or 4.9000000000000002e-8 < z

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf 97.4%

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

      1. div-sub 97.4%

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

      2. sub-neg 97.4%

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

      3. *-inverses 97.4%

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

      4. metadata-eval 97.4%

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

      5. distribute-lft-in 97.4%

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

      6. associate-*r/ 97.4%

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

      7. metadata-eval 97.4%

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

      8. metadata-eval 97.4%

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

   5. Simplified 97.4%

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

   if -1.6000000000000001e-32 < z < 4.9000000000000002e-8

   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 z around 0 87.3%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-32} \lor \neg \left(z \leq 4.9 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 92.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-33} \lor \neg \left(z \leq 8.5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e-33) (not (<= z 8.5e-9)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-33) || !(z <= 8.5e-9)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.8d-33)) .or. (.not. (z <= 8.5d-9))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-33) || !(z <= 8.5e-9)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-33) or not (z <= 8.5e-9):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-33) || !(z <= 8.5e-9))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.8e-33) || ~((z <= 8.5e-9)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e-33], N[Not[LessEqual[z, 8.5e-9]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000022e-33 or 8.5e-9 < z

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf 97.4%

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

      1. div-sub 97.4%

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

      2. sub-neg 97.4%

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

      3. *-inverses 97.4%

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

      4. metadata-eval 97.4%

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

      5. distribute-lft-in 97.4%

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

      6. associate-*r/ 97.4%

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

      7. metadata-eval 97.4%

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

      8. metadata-eval 97.4%

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

   5. Simplified 97.4%

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

   if -8.80000000000000022e-33 < z < 8.5e-9

   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 z around 0 87.3%

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

      1. associate-/r* 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-33} \lor \neg \left(z \leq 8.5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} + \frac{2}{t}\right) - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e-31)
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (if (<= z 7.2e-8)
     (+ (/ x y) (/ (/ 2.0 t) z))
     (- (+ (/ x y) (/ 2.0 t)) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-31) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else if (z <= 7.2e-8) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = ((x / y) + (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 (z <= (-4.2d-31)) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else if (z <= 7.2d-8) then
        tmp = (x / y) + ((2.0d0 / t) / z)
    else
        tmp = ((x / y) + (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 (z <= -4.2e-31) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else if (z <= 7.2e-8) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = ((x / y) + (2.0 / t)) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e-31:
		tmp = (x / y) + (-2.0 + (2.0 / t))
	elif z <= 7.2e-8:
		tmp = (x / y) + ((2.0 / t) / z)
	else:
		tmp = ((x / y) + (2.0 / t)) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e-31)
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	elseif (z <= 7.2e-8)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	else
		tmp = Float64(Float64(Float64(x / y) + Float64(2.0 / t)) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e-31)
		tmp = (x / y) + (-2.0 + (2.0 / t));
	elseif (z <= 7.2e-8)
		tmp = (x / y) + ((2.0 / t) / z);
	else
		tmp = ((x / y) + (2.0 / t)) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e-31], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-8], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999982e-31

   1. Initial program 66.4%

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

   3. Taylor expanded in z around inf 95.5%

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

      1. div-sub 95.5%

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

      2. sub-neg 95.5%

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

      3. *-inverses 95.5%

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

      4. metadata-eval 95.5%

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

      5. distribute-lft-in 95.5%

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

      6. associate-*r/ 95.5%

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

      7. metadata-eval 95.5%

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

      8. metadata-eval 95.5%

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

   5. Simplified 95.5%

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

   if -4.19999999999999982e-31 < z < 7.19999999999999962e-8

   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 z around 0 87.3%

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

      1. associate-/r* 87.4%

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

   5. Simplified 87.4%

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

   if 7.19999999999999962e-8 < z

   1. Initial program 73.0%

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

   3. Taylor expanded in t around inf 100.0%

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

   4. Taylor expanded in z around inf 99.1%

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

      1. associate-*r/ 99.1%

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

      2. metadata-eval 99.1%

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

      3. +-commutative 99.1%

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

   6. Simplified 99.1%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} + \frac{2}{t}\right) - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.106 \lor \neg \left(\frac{x}{y} \leq 1.26 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.106) (not (<= (/ x y) 1.26e+21))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.106) || !((x / y) <= 1.26e+21)) {
		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) <= (-0.106d0)) .or. (.not. ((x / y) <= 1.26d+21))) 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) <= -0.106) || !((x / y) <= 1.26e+21)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.106) or not ((x / y) <= 1.26e+21):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -0.106) || !(Float64(x / y) <= 1.26e+21))
		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) <= -0.106) || ~(((x / y) <= 1.26e+21)))
		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], -0.106], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.26e+21]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.105999999999999997 or 1.26e21 < (/.f64 x y)

   1. Initial program 81.6%

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

   3. Taylor expanded in x around inf 69.2%

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

   if -0.105999999999999997 < (/.f64 x y) < 1.26e21

   1. Initial program 86.1%

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

   3. Taylor expanded in t around 0 66.4%

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

      1. associate-*r/ 66.4%

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

      2. metadata-eval 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around inf 26.7%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.106 \lor \neg \left(\frac{x}{y} \leq 1.26 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. +-commutative 83.8%

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

   2. remove-double-neg 83.8%

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

   3. distribute-frac-neg 83.8%

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

   4. unsub-neg 83.8%

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

   5. *-commutative 83.8%

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

   6. associate-*r* 83.8%

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

   7. distribute-rgt1-in 83.8%

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

   8. associate-/l* 83.7%

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

   9. fma-neg 83.7%

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

   10. *-commutative 83.7%

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

   11. fma-define 83.7%

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

   12. *-commutative 83.7%

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

   13. distribute-frac-neg 83.7%

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

   14. remove-double-neg 83.7%

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

3. Simplified 83.7%

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

5. Taylor expanded in t around inf 98.3%

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

   1. sub-neg 98.3%

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

   2. metadata-eval 98.3%

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

   3. +-commutative 98.3%

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

   4. +-commutative 98.3%

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

   5. associate-*r/ 98.3%

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

   6. distribute-lft-in 98.3%

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

   7. metadata-eval 98.3%

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

   8. associate-*r/ 98.3%

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

   9. metadata-eval 98.3%

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

7. Simplified 98.3%

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

8. Final simplification 98.3%

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

Alternative 17: 19.7% 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 83.8%

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

3. Taylor expanded in t around 0 48.8%

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

   1. associate-*r/ 48.8%

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

   2. metadata-eval 48.8%

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

5. Simplified 48.8%

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

6. Taylor expanded in z around inf 18.0%

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

7. Final simplification 18.0%

   \[\leadsto \frac{2}{t} \]
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 2024053 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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