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

Percentage Accurate: 87.5% → 99.3%

Time: 10.3s

Alternatives: 13

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: 87.5% 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: 99.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.9%

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

3. Simplified 99.1%

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

Alternative 2: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= z -2.8e+190)
     t_1
     (if (<= z -3.5e+103)
       (+ -2.0 (/ 2.0 t))
       (if (<= z -9e-21) t_1 (if (<= z 3.4e-102) (/ (/ 2.0 t) z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -2.8e+190) {
		tmp = t_1;
	} else if (z <= -3.5e+103) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -9e-21) {
		tmp = t_1;
	} else if (z <= 3.4e-102) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (z <= (-2.8d+190)) then
        tmp = t_1
    else if (z <= (-3.5d+103)) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if (z <= (-9d-21)) then
        tmp = t_1
    else if (z <= 3.4d-102) then
        tmp = (2.0d0 / t) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -2.8e+190) {
		tmp = t_1;
	} else if (z <= -3.5e+103) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -9e-21) {
		tmp = t_1;
	} else if (z <= 3.4e-102) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if z <= -2.8e+190:
		tmp = t_1
	elif z <= -3.5e+103:
		tmp = -2.0 + (2.0 / t)
	elif z <= -9e-21:
		tmp = t_1
	elif z <= 3.4e-102:
		tmp = (2.0 / t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (z <= -2.8e+190)
		tmp = t_1;
	elseif (z <= -3.5e+103)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (z <= -9e-21)
		tmp = t_1;
	elseif (z <= 3.4e-102)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (z <= -2.8e+190)
		tmp = t_1;
	elseif (z <= -3.5e+103)
		tmp = -2.0 + (2.0 / t);
	elseif (z <= -9e-21)
		tmp = t_1;
	elseif (z <= 3.4e-102)
		tmp = (2.0 / t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+190], t$95$1, If[LessEqual[z, -3.5e+103], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-21], t$95$1, If[LessEqual[z, 3.4e-102], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999997e190 or -3.5e103 < z < -8.99999999999999936e-21 or 3.40000000000000013e-102 < z

   1. Initial program 72.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 67.9%

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

   if -2.79999999999999997e190 < z < -3.5e103

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 88.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   8. Simplified 88.0%

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

   if -8.99999999999999936e-21 < z < 3.40000000000000013e-102

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{z}\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot 1}{t}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t}\right), z\right) \]

      7. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, t\right), z\right) \]

   5. Simplified 76.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+190}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-21}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+103}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= z -1.18e+207)
     t_1
     (if (<= z -3.4e+103)
       (+ -2.0 (/ 2.0 t))
       (if (<= z -5.6e-21) t_1 (if (<= z 5.8e-107) (/ 2.0 (* z t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -1.18e+207) {
		tmp = t_1;
	} else if (z <= -3.4e+103) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -5.6e-21) {
		tmp = t_1;
	} else if (z <= 5.8e-107) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (z <= (-1.18d+207)) then
        tmp = t_1
    else if (z <= (-3.4d+103)) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if (z <= (-5.6d-21)) then
        tmp = t_1
    else if (z <= 5.8d-107) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -1.18e+207) {
		tmp = t_1;
	} else if (z <= -3.4e+103) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -5.6e-21) {
		tmp = t_1;
	} else if (z <= 5.8e-107) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if z <= -1.18e+207:
		tmp = t_1
	elif z <= -3.4e+103:
		tmp = -2.0 + (2.0 / t)
	elif z <= -5.6e-21:
		tmp = t_1
	elif z <= 5.8e-107:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (z <= -1.18e+207)
		tmp = t_1;
	elseif (z <= -3.4e+103)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (z <= -5.6e-21)
		tmp = t_1;
	elseif (z <= 5.8e-107)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (z <= -1.18e+207)
		tmp = t_1;
	elseif (z <= -3.4e+103)
		tmp = -2.0 + (2.0 / t);
	elseif (z <= -5.6e-21)
		tmp = t_1;
	elseif (z <= 5.8e-107)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.18e+207], t$95$1, If[LessEqual[z, -3.4e+103], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-21], t$95$1, If[LessEqual[z, 5.8e-107], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.18e207 or -3.3999999999999998e103 < z < -5.60000000000000008e-21 or 5.7999999999999996e-107 < z

   1. Initial program 72.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 67.9%

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

   if -1.18e207 < z < -3.3999999999999998e103

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 88.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   8. Simplified 88.0%

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

   if -5.60000000000000008e-21 < z < 5.7999999999999996e-107

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{z}\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot 1}{t}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t}\right), z\right) \]

      7. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, t\right), z\right) \]

   5. Simplified 76.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{\left(t \cdot z\right)}\right) \]

      3. *-lowering-*.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 76.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+207}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+103}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-21}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-290}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 20000000000:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+34)
   (/ x y)
   (if (<= (/ x y) -4e-290)
     (/ 2.0 t)
     (if (<= (/ x y) 20000000000.0) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+34) {
		tmp = x / y;
	} else if ((x / y) <= -4e-290) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 20000000000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+34)) then
        tmp = x / y
    else if ((x / y) <= (-4d-290)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 20000000000.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+34) {
		tmp = x / y;
	} else if ((x / y) <= -4e-290) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 20000000000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+34:
		tmp = x / y
	elif (x / y) <= -4e-290:
		tmp = 2.0 / t
	elif (x / y) <= 20000000000.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+34)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -4e-290)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 20000000000.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+34)
		tmp = x / y;
	elseif ((x / y) <= -4e-290)
		tmp = 2.0 / t;
	elseif ((x / y) <= 20000000000.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+34], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -4e-290], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 20000000000.0], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999998e34 or 2e10 < (/.f64 x y)

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 69.8%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 69.8%

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

   if -4.9999999999999998e34 < (/.f64 x y) < -4.0000000000000003e-290

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 57.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 57.3%

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

   6. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 36.2%

         \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{t}\right) \]

   8. Simplified 36.2%

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

   if -4.0000000000000003e-290 < (/.f64 x y) < 2e10

   1. Initial program 81.9%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 100.0%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 39.6%

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

Alternative 5: 92.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.035:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -1.06e-20)
     t_1
     (if (<= z 0.035) (+ (/ x y) (/ 2.0 (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -1.06e-20) {
		tmp = t_1;
	} else if (z <= 0.035) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-1.06d-20)) then
        tmp = t_1
    else if (z <= 0.035d0) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -1.06e-20) {
		tmp = t_1;
	} else if (z <= 0.035) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -1.06e-20:
		tmp = t_1
	elif z <= 0.035:
		tmp = (x / y) + (2.0 / (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -1.06e-20)
		tmp = t_1;
	elseif (z <= 0.035)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -1.06e-20)
		tmp = t_1;
	elseif (z <= 0.035)
		tmp = (x / y) + (2.0 / (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.06e-20], t$95$1, If[LessEqual[z, 0.035], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.06e-20 or 0.035000000000000003 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 99.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 99.1%

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

   if -1.06e-20 < z < 0.035000000000000003

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\color{blue}{2}, \mathsf{*.f64}\left(t, z\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 90.9%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 0.035:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-102}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -1.8e-17) t_1 (if (<= z 1.5e-102) (+ -2.0 (/ (/ 2.0 z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -1.8e-17) {
		tmp = t_1;
	} else if (z <= 1.5e-102) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-1.8d-17)) then
        tmp = t_1
    else if (z <= 1.5d-102) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -1.8e-17) {
		tmp = t_1;
	} else if (z <= 1.5e-102) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -1.8e-17:
		tmp = t_1
	elif z <= 1.5e-102:
		tmp = -2.0 + ((2.0 / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -1.8e-17)
		tmp = t_1;
	elseif (z <= 1.5e-102)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -1.8e-17)
		tmp = t_1;
	elseif (z <= 1.5e-102)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-17], t$95$1, If[LessEqual[z, 1.5e-102], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999997e-17 or 1.5e-102 < z

   1. Initial program 72.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 95.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 95.2%

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

   if -1.79999999999999997e-17 < z < 1.5e-102

   1. Initial program 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 83.0%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(\frac{2}{z}\right)}, t\right), -2\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 83.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right), -2\right) \]

   10. Simplified 83.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-102}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 20000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+34)
   (/ x y)
   (if (<= (/ x y) 20000000000.0) (+ -2.0 (/ 2.0 t)) (+ -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+34) {
		tmp = x / y;
	} else if ((x / y) <= 20000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = -2.0 + (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+34)) then
        tmp = x / y
    else if ((x / y) <= 20000000000.0d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = (-2.0d0) + (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+34) {
		tmp = x / y;
	} else if ((x / y) <= 20000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = -2.0 + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+34:
		tmp = x / y
	elif (x / y) <= 20000000000.0:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = -2.0 + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+34)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 20000000000.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(-2.0 + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+34)
		tmp = x / y;
	elseif ((x / y) <= 20000000000.0)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = -2.0 + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+34], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 20000000000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999998e34

   1. Initial program 79.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 74.0%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 74.0%

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

   if -4.9999999999999998e34 < (/.f64 x y) < 2e10

   1. Initial program 85.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 60.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 60.0%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 58.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   8. Simplified 58.8%

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

   if 2e10 < (/.f64 x y)

   1. Initial program 77.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 65.9%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 20000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+90}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+34)
   (/ x y)
   (if (<= (/ x y) 1e+90) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+34) {
		tmp = x / y;
	} else if ((x / y) <= 1e+90) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+34)) then
        tmp = x / y
    else if ((x / y) <= 1d+90) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+34) {
		tmp = x / y;
	} else if ((x / y) <= 1e+90) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+34:
		tmp = x / y
	elif (x / y) <= 1e+90:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+34)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1e+90)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+34)
		tmp = x / y;
	elseif ((x / y) <= 1e+90)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+34], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e+90], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999998e34 or 9.99999999999999966e89 < (/.f64 x y)

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 72.5%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 72.5%

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

   if -4.9999999999999998e34 < (/.f64 x y) < 9.99999999999999966e89

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 62.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 62.3%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 57.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   8. Simplified 57.9%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+90}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= t -1.7e+48) t_1 (if (<= t 2.3e+14) (/ (+ 2.0 (/ 2.0 z)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -1.7e+48) {
		tmp = t_1;
	} else if (t <= 2.3e+14) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (t <= (-1.7d+48)) then
        tmp = t_1
    else if (t <= 2.3d+14) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -1.7e+48) {
		tmp = t_1;
	} else if (t <= 2.3e+14) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if t <= -1.7e+48:
		tmp = t_1
	elif t <= 2.3e+14:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t <= -1.7e+48)
		tmp = t_1;
	elseif (t <= 2.3e+14)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (t <= -1.7e+48)
		tmp = t_1;
	elseif (t <= 2.3e+14)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+48], t$95$1, If[LessEqual[t, 2.3e+14], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7000000000000002e48 or 2.3e14 < t

   1. Initial program 61.7%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 86.8%

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

   if -1.7000000000000002e48 < t < 2.3e14

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(2 + 2 \cdot \frac{1}{z}\right), \color{blue}{t}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(2 \cdot \frac{1}{z}\right)\right), t\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(\frac{2 \cdot 1}{z}\right)\right), t\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(\frac{2}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right) \]

   5. Simplified 82.4%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+48}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-61}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= z -3.8e-18) t_1 (if (<= z 7.6e-61) (+ -2.0 (/ (/ 2.0 z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -3.8e-18) {
		tmp = t_1;
	} else if (z <= 7.6e-61) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / t)
    if (z <= (-3.8d-18)) then
        tmp = t_1
    else if (z <= 7.6d-61) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -3.8e-18) {
		tmp = t_1;
	} else if (z <= 7.6e-61) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if z <= -3.8e-18:
		tmp = t_1
	elif z <= 7.6e-61:
		tmp = -2.0 + ((2.0 / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -3.8e-18)
		tmp = t_1;
	elseif (z <= 7.6e-61)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if (z <= -3.8e-18)
		tmp = t_1;
	elseif (z <= 7.6e-61)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-18], t$95$1, If[LessEqual[z, 7.6e-61], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999998e-18 or 7.59999999999999961e-61 < z

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 97.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 97.4%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 75.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{t}\right)\right) \]

   8. Simplified 75.8%

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

   if -3.7999999999999998e-18 < z < 7.59999999999999961e-61

   1. Initial program 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 80.7%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(\frac{2}{z}\right)}, t\right), -2\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 80.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right), -2\right) \]

   10. Simplified 80.7%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-61}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-104}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= z -4.3e-18) t_1 (if (<= z 2.1e-104) (/ (/ 2.0 t) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -4.3e-18) {
		tmp = t_1;
	} else if (z <= 2.1e-104) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / t)
    if (z <= (-4.3d-18)) then
        tmp = t_1
    else if (z <= 2.1d-104) then
        tmp = (2.0d0 / t) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if (z <= -4.3e-18) {
		tmp = t_1;
	} else if (z <= 2.1e-104) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if z <= -4.3e-18:
		tmp = t_1
	elif z <= 2.1e-104:
		tmp = (2.0 / t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -4.3e-18)
		tmp = t_1;
	elseif (z <= 2.1e-104)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if (z <= -4.3e-18)
		tmp = t_1;
	elseif (z <= 2.1e-104)
		tmp = (2.0 / t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e-18], t$95$1, If[LessEqual[z, 2.1e-104], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000002e-18 or 2.09999999999999999e-104 < z

   1. Initial program 72.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 95.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 95.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 74.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{t}\right)\right) \]

   8. Simplified 74.2%

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

   if -4.3000000000000002e-18 < z < 2.09999999999999999e-104

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{z}\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot 1}{t}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t}\right), z\right) \]

      7. /-lowering-/.f64 75.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, t\right), z\right) \]

   5. Simplified 75.5%

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

Alternative 12: 37.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 1.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 1.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 1.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1 < t

   1. Initial program 63.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 48.7%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 33.3%

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

   if -1 < t < 1

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 54.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 54.9%

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

   6. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 38.7%

         \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{t}\right) \]

   8. Simplified 38.7%

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

Alternative 13: 20.4% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 81.9%

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

3. Simplified 99.1%

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

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
6. Step-by-step derivation

7. Simplified 67.6%

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

8. Taylor expanded in t around inf

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

10. Simplified 17.1%

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

Developer Target 1: 99.3% 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 2024160 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

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