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

Percentage Accurate: 86.6% → 99.1%

Time: 11.4s

Alternatives: 16

Speedup: 1.3×

• 22.6% 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: 86.6% 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, 1.3× 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 86.9%

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

2. Taylor expanded in t around 0 99.5%

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

   1. sub-neg 99.5%

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

   2. metadata-eval 99.5%

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

   3. +-commutative 99.5%

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

   4. associate-+r+ 99.5%

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

   5. metadata-eval 99.5%

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

   6. associate-*r/ 99.5%

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

   7. +-commutative 99.5%

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

   8. associate-*r/ 99.5%

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

   9. metadata-eval 99.5%

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

   10. associate-/l/ 99.5%

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

   11. associate-*r/ 99.5%

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

   12. associate-*r/ 99.5%

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

   13. metadata-eval 99.5%

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

4. Simplified 99.5%

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

5. Taylor expanded in z around 0 99.5%

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

   1. associate-+r+ 99.5%

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

   2. associate-*r/ 99.5%

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

   3. metadata-eval 99.5%

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

   4. associate-*r/ 99.5%

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

   5. metadata-eval 99.5%

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

   6. *-commutative 99.5%

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

   7. metadata-eval 99.5%

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

   8. associate-*r/ 99.5%

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

   9. associate-/r* 99.5%

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

   10. *-rgt-identity 99.5%

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

   11. associate-*r/ 99.5%

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

   12. distribute-rgt-in 99.5%

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

   13. +-commutative 99.5%

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

   14. associate-*l/ 99.5%

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

   15. *-lft-identity 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 2: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.35 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4.1 \cdot 10^{-36}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ 2.0 (* z t)))))
   (if (<= (/ x y) -7.8e+155)
     (/ x y)
     (if (<= (/ x y) 3.35e-161)
       t_1
       (if (<= (/ x y) 4.1e-36)
         (+ -2.0 (/ 2.0 t))
         (if (<= (/ x y) 9.2e+17) t_1 (- (/ x y) 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -7.8e+155) {
		tmp = x / y;
	} else if ((x / y) <= 3.35e-161) {
		tmp = t_1;
	} else if ((x / y) <= 4.1e-36) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 9.2e+17) {
		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) + (2.0d0 / (z * t))
    if ((x / y) <= (-7.8d+155)) then
        tmp = x / y
    else if ((x / y) <= 3.35d-161) then
        tmp = t_1
    else if ((x / y) <= 4.1d-36) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if ((x / y) <= 9.2d+17) 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 + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -7.8e+155) {
		tmp = x / y;
	} else if ((x / y) <= 3.35e-161) {
		tmp = t_1;
	} else if ((x / y) <= 4.1e-36) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 9.2e+17) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (2.0 / (z * t))
	tmp = 0
	if (x / y) <= -7.8e+155:
		tmp = x / y
	elif (x / y) <= 3.35e-161:
		tmp = t_1
	elif (x / y) <= 4.1e-36:
		tmp = -2.0 + (2.0 / t)
	elif (x / y) <= 9.2e+17:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(2.0 / Float64(z * t)))
	tmp = 0.0
	if (Float64(x / y) <= -7.8e+155)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 3.35e-161)
		tmp = t_1;
	elseif (Float64(x / y) <= 4.1e-36)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (Float64(x / y) <= 9.2e+17)
		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 + (2.0 / (z * t));
	tmp = 0.0;
	if ((x / y) <= -7.8e+155)
		tmp = x / y;
	elseif ((x / y) <= 3.35e-161)
		tmp = t_1;
	elseif ((x / y) <= 4.1e-36)
		tmp = -2.0 + (2.0 / t);
	elseif ((x / y) <= 9.2e+17)
		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[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -7.8e+155], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.35e-161], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4.1e-36], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 9.2e+17], t$95$1, N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -7.7999999999999996e155

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 89.8%

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

   if -7.7999999999999996e155 < (/.f64 x y) < 3.35e-161 or 4.10000000000000013e-36 < (/.f64 x y) < 9.2e17

   1. Initial program 87.9%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. associate-/l/ 99.9%

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

      11. associate-*r/ 99.9%

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

      12. associate-*r/ 99.9%

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

      13. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 71.8%

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

   if 3.35e-161 < (/.f64 x y) < 4.10000000000000013e-36

   1. Initial program 81.6%

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

   2. Taylor expanded in z around inf 82.4%

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

      1. div-sub 82.5%

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

      2. sub-neg 82.5%

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

      3. *-inverses 82.5%

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

      4. metadata-eval 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in x around 0 82.5%

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

      1. sub-neg 82.5%

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

      2. metadata-eval 82.5%

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

      3. distribute-lft-in 82.5%

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

      4. associate-*r/ 82.5%

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

      5. metadata-eval 82.5%

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

      6. metadata-eval 82.5%

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

   7. Simplified 82.5%

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

   if 9.2e17 < (/.f64 x y)

   1. Initial program 85.8%

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

   2. Taylor expanded in t around inf 70.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.35 \cdot 10^{-161}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.1 \cdot 10^{-36}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 3: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.8 \cdot 10^{-161}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{+16}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6e+154)
   (/ x y)
   (if (<= (/ x y) 3.8e-161)
     (+ -2.0 (/ (/ 2.0 z) t))
     (if (<= (/ x y) 2.15e-36)
       (+ -2.0 (/ 2.0 t))
       (if (<= (/ x y) 6e+16) (+ -2.0 (/ 2.0 (* z t))) (- (/ x y) 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6e+154) {
		tmp = x / y;
	} else if ((x / y) <= 3.8e-161) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else if ((x / y) <= 2.15e-36) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 6e+16) {
		tmp = -2.0 + (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) <= (-6d+154)) then
        tmp = x / y
    else if ((x / y) <= 3.8d-161) then
        tmp = (-2.0d0) + ((2.0d0 / z) / t)
    else if ((x / y) <= 2.15d-36) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if ((x / y) <= 6d+16) then
        tmp = (-2.0d0) + (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) <= -6e+154) {
		tmp = x / y;
	} else if ((x / y) <= 3.8e-161) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else if ((x / y) <= 2.15e-36) {
		tmp = -2.0 + (2.0 / t);
	} else if ((x / y) <= 6e+16) {
		tmp = -2.0 + (2.0 / (z * t));
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6e+154:
		tmp = x / y
	elif (x / y) <= 3.8e-161:
		tmp = -2.0 + ((2.0 / z) / t)
	elif (x / y) <= 2.15e-36:
		tmp = -2.0 + (2.0 / t)
	elif (x / y) <= 6e+16:
		tmp = -2.0 + (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) <= -6e+154)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 3.8e-161)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	elseif (Float64(x / y) <= 2.15e-36)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (Float64(x / y) <= 6e+16)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(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) <= -6e+154)
		tmp = x / y;
	elseif ((x / y) <= 3.8e-161)
		tmp = -2.0 + ((2.0 / z) / t);
	elseif ((x / y) <= 2.15e-36)
		tmp = -2.0 + (2.0 / t);
	elseif ((x / y) <= 6e+16)
		tmp = -2.0 + (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], -6e+154], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.8e-161], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.15e-36], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6e+16], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -6.00000000000000052e154

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 89.8%

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

   if -6.00000000000000052e154 < (/.f64 x y) < 3.8000000000000001e-161

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. associate-/l/ 99.9%

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

      11. associate-*r/ 99.9%

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

      12. associate-*r/ 99.9%

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

      13. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-*r/ 99.8%

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

      5. metadata-eval 99.8%

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

      6. *-commutative 99.8%

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

      7. metadata-eval 99.8%

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

      8. associate-*r/ 99.8%

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

      9. associate-/r* 99.9%

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

      10. *-rgt-identity 99.9%

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

      11. associate-*r/ 99.8%

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

      12. distribute-rgt-in 99.8%

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

      13. +-commutative 99.8%

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

      14. associate-*l/ 99.9%

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

      15. *-lft-identity 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 81.9%

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

   9. Taylor expanded in x around 0 71.6%

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

       1. associate-/l/ 71.6%

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

   11. Simplified 71.6%

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

   if 3.8000000000000001e-161 < (/.f64 x y) < 2.1500000000000001e-36

   1. Initial program 81.6%

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

   2. Taylor expanded in z around inf 82.4%

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

      1. div-sub 82.5%

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

      2. sub-neg 82.5%

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

      3. *-inverses 82.5%

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

      4. metadata-eval 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in x around 0 82.5%

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

      1. sub-neg 82.5%

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

      2. metadata-eval 82.5%

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

      3. distribute-lft-in 82.5%

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

      4. associate-*r/ 82.5%

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

      5. metadata-eval 82.5%

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

      6. metadata-eval 82.5%

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

   7. Simplified 82.5%

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

   if 2.1500000000000001e-36 < (/.f64 x y) < 6e16

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. associate-/l/ 99.8%

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

      11. associate-*r/ 99.8%

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

      12. associate-*r/ 99.8%

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

      13. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 75.0%

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

   if 6e16 < (/.f64 x y)

   1. Initial program 85.8%

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

   2. Taylor expanded in t around inf 70.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.8 \cdot 10^{-161}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{+16}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 4: 92.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -200000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 8.8 \cdot 10^{+20}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 (* z t)))))
   (if (<= (/ x y) -200000000000.0)
     t_1
     (if (<= (/ x y) 8.8e+20)
       (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
       (if (<= (/ x y) 2.9e+118) (+ (/ x y) (+ -2.0 (/ 2.0 t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -200000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 8.8e+20) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 2.9e+118) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / (z * t))
    if ((x / y) <= (-200000000000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 8.8d+20) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else if ((x / y) <= 2.9d+118) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -200000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 8.8e+20) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 2.9e+118) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / (z * t))
	tmp = 0
	if (x / y) <= -200000000000.0:
		tmp = t_1
	elif (x / y) <= 8.8e+20:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	elif (x / y) <= 2.9e+118:
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)))
	tmp = 0.0
	if (Float64(x / y) <= -200000000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 8.8e+20)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	elseif (Float64(x / y) <= 2.9e+118)
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / (z * t));
	tmp = 0.0;
	if ((x / y) <= -200000000000.0)
		tmp = t_1;
	elseif ((x / y) <= 8.8e+20)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	elseif ((x / y) <= 2.9e+118)
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -200000000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 8.8e+20], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.9e+118], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e11 or 2.90000000000000016e118 < (/.f64 x y)

   1. Initial program 87.2%

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

   2. Taylor expanded in z around 0 95.1%

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

   if -2e11 < (/.f64 x y) < 8.8e20

   1. Initial program 86.3%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-/l/ 99.9%

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

      11. associate-*r/ 99.9%

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

      12. associate-*r/ 99.9%

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

      13. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in t around 0 98.5%

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

      1. associate-*r/ 98.5%

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

      2. metadata-eval 98.5%

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

   7. Simplified 98.5%

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

   if 8.8e20 < (/.f64 x y) < 2.90000000000000016e118

   1. Initial program 89.9%

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

   2. Taylor expanded in z around inf 85.7%

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

      1. div-sub 85.7%

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

      2. sub-neg 85.7%

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

      3. *-inverses 85.7%

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

      4. metadata-eval 85.7%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in x around 0 85.7%

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

      1. +-commutative 85.7%

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

      2. sub-neg 85.7%

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

      3. metadata-eval 85.7%

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

      4. distribute-lft-in 85.7%

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

      5. associate-*r/ 85.7%

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

      6. metadata-eval 85.7%

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

      7. metadata-eval 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 8.8 \cdot 10^{+20}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 5: 92.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000000000:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -200000000000.0)
   (+ (/ x y) (/ (/ 2.0 z) t))
   (if (<= (/ x y) 5e+15)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (if (<= (/ x y) 4e+118)
       (+ (/ x y) (+ -2.0 (/ 2.0 t)))
       (+ (/ x y) (/ 2.0 (* z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -200000000000.0) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else if ((x / y) <= 5e+15) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 4e+118) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-200000000000.0d0)) then
        tmp = (x / y) + ((2.0d0 / z) / t)
    else if ((x / y) <= 5d+15) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else if ((x / y) <= 4d+118) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + (2.0d0 / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -200000000000.0) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else if ((x / y) <= 5e+15) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else if ((x / y) <= 4e+118) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -200000000000.0:
		tmp = (x / y) + ((2.0 / z) / t)
	elif (x / y) <= 5e+15:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	elif (x / y) <= 4e+118:
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -200000000000.0)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t));
	elseif (Float64(x / y) <= 5e+15)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	elseif (Float64(x / y) <= 4e+118)
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -200000000000.0)
		tmp = (x / y) + ((2.0 / z) / t);
	elseif ((x / y) <= 5e+15)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	elseif ((x / y) <= 4e+118)
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -200000000000.0], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+15], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e+118], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2e11

   1. Initial program 89.7%

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

   2. Taylor expanded in z around 0 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-/r* 92.7%

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

   4. Simplified 92.7%

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

   if -2e11 < (/.f64 x y) < 5e15

   1. Initial program 86.3%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-/l/ 99.9%

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

      11. associate-*r/ 99.9%

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

      12. associate-*r/ 99.9%

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

      13. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in t around 0 98.5%

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

      1. associate-*r/ 98.5%

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

      2. metadata-eval 98.5%

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

   7. Simplified 98.5%

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

   if 5e15 < (/.f64 x y) < 3.99999999999999987e118

   1. Initial program 89.9%

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

   2. Taylor expanded in z around inf 85.7%

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

      1. div-sub 85.7%

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

      2. sub-neg 85.7%

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

      3. *-inverses 85.7%

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

      4. metadata-eval 85.7%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in x around 0 85.7%

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

      1. +-commutative 85.7%

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

      2. sub-neg 85.7%

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

      3. metadata-eval 85.7%

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

      4. distribute-lft-in 85.7%

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

      5. associate-*r/ 85.7%

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

      6. metadata-eval 85.7%

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

      7. metadata-eval 85.7%

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

   7. Simplified 85.7%

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

   if 3.99999999999999987e118 < (/.f64 x y)

   1. Initial program 84.3%

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

   2. Taylor expanded in z around 0 97.9%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000000000:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+118}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 6: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+155} \lor \neg \left(\frac{x}{y} \leq 1.7 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+155) (not (<= (/ x y) 1.7e+17)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+155) || !((x / y) <= 1.7e+17)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+155)) .or. (.not. ((x / y) <= 1.7d+17))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+155) || !((x / y) <= 1.7e+17)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+155) or not ((x / y) <= 1.7e+17):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+155) || !(Float64(x / y) <= 1.7e+17))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+155) || ~(((x / y) <= 1.7e+17)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+155], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.7e+17]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000001e155 or 1.7e17 < (/.f64 x y)

   1. Initial program 86.8%

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

   2. Taylor expanded in z around inf 85.5%

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

      1. div-sub 85.5%

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

      2. sub-neg 85.5%

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

      3. *-inverses 85.5%

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

      4. metadata-eval 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in x around 0 85.5%

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

      1. +-commutative 85.5%

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

      2. sub-neg 85.5%

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

      3. metadata-eval 85.5%

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

      4. distribute-lft-in 85.5%

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

      5. associate-*r/ 85.5%

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

      6. metadata-eval 85.5%

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

      7. metadata-eval 85.5%

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

   7. Simplified 85.5%

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

   if -1.00000000000000001e155 < (/.f64 x y) < 1.7e17

   1. Initial program 87.0%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. associate-/l/ 99.9%

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

      11. associate-*r/ 99.9%

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

      12. associate-*r/ 99.9%

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

      13. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in t around 0 91.2%

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

      1. associate-*r/ 91.2%

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

      2. metadata-eval 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+155} \lor \neg \left(\frac{x}{y} \leq 1.7 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 7: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5.2e+154)
   (/ x y)
   (if (<= (/ x y) 1.16e+120)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.2e+154) {
		tmp = x / y;
	} else if ((x / y) <= 1.16e+120) {
		tmp = -2.0 + ((2.0 + (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) <= (-5.2d+154)) then
        tmp = x / y
    else if ((x / y) <= 1.16d+120) then
        tmp = (-2.0d0) + ((2.0d0 + (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) <= -5.2e+154) {
		tmp = x / y;
	} else if ((x / y) <= 1.16e+120) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5.2e+154:
		tmp = x / y
	elif (x / y) <= 1.16e+120:
		tmp = -2.0 + ((2.0 + (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) <= -5.2e+154)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.16e+120)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + 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) <= -5.2e+154)
		tmp = x / y;
	elseif ((x / y) <= 1.16e+120)
		tmp = -2.0 + ((2.0 + (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], -5.2e+154], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.16e+120], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.19999999999999978e154

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 89.8%

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

   if -5.19999999999999978e154 < (/.f64 x y) < 1.16000000000000003e120

   1. Initial program 87.5%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-/l/ 99.9%

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

      11. associate-*r/ 99.9%

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

      12. associate-*r/ 99.9%

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

      13. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in t around 0 87.9%

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

      1. associate-*r/ 87.9%

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

      2. metadata-eval 87.9%

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

   7. Simplified 87.9%

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

   if 1.16000000000000003e120 < (/.f64 x y)

   1. Initial program 83.6%

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

   2. Taylor expanded in t around inf 84.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.16 \cdot 10^{+120}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 8: 50.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -28200000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.4 \cdot 10^{-42}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.45 \cdot 10^{+119}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -28200000.0)
   (/ x y)
   (if (<= (/ x y) 1.4e-42)
     -2.0
     (if (<= (/ x y) 1.45e+119) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -28200000.0) {
		tmp = x / y;
	} else if ((x / y) <= 1.4e-42) {
		tmp = -2.0;
	} else if ((x / y) <= 1.45e+119) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-28200000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 1.4d-42) then
        tmp = -2.0d0
    else if ((x / y) <= 1.45d+119) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -28200000.0) {
		tmp = x / y;
	} else if ((x / y) <= 1.4e-42) {
		tmp = -2.0;
	} else if ((x / y) <= 1.45e+119) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -28200000.0:
		tmp = x / y
	elif (x / y) <= 1.4e-42:
		tmp = -2.0
	elif (x / y) <= 1.45e+119:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -28200000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.4e-42)
		tmp = -2.0;
	elseif (Float64(x / y) <= 1.45e+119)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -28200000.0)
		tmp = x / y;
	elseif ((x / y) <= 1.4e-42)
		tmp = -2.0;
	elseif ((x / y) <= 1.45e+119)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -28200000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.4e-42], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 1.45e+119], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.82e7 or 1.45000000000000004e119 < (/.f64 x y)

   1. Initial program 87.3%

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

   2. Taylor expanded in x around inf 71.1%

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

   if -2.82e7 < (/.f64 x y) < 1.39999999999999999e-42

   1. Initial program 84.6%

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

   2. Taylor expanded in z around inf 66.3%

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

      1. div-sub 66.3%

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

      2. sub-neg 66.3%

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

      3. *-inverses 66.3%

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

      4. metadata-eval 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in x around 0 64.8%

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

      1. sub-neg 64.8%

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

      2. metadata-eval 64.8%

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

      3. distribute-lft-in 64.8%

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

      4. associate-*r/ 64.8%

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

      5. metadata-eval 64.8%

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

      6. metadata-eval 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in t around inf 42.1%

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

   if 1.39999999999999999e-42 < (/.f64 x y) < 1.45000000000000004e119

   1. Initial program 93.8%

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

   2. Taylor expanded in t around 0 74.1%

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

      1. associate-*r/ 74.1%

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

      2. metadata-eval 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in z around inf 44.6%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -28200000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.4 \cdot 10^{-42}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.45 \cdot 10^{+119}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 9: 97.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+15} \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+15) (not (<= z 0.26)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ -2.0 (+ (/ x y) (/ (/ 2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+15) || !(z <= 0.26)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((x / y) + ((2.0 / z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.2d+15)) .or. (.not. (z <= 0.26d0))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (-2.0d0) + ((x / y) + ((2.0d0 / z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+15) || !(z <= 0.26)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((x / y) + ((2.0 / z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+15) or not (z <= 0.26):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = -2.0 + ((x / y) + ((2.0 / z) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+15) || !(z <= 0.26))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+15) || ~((z <= 0.26)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = -2.0 + ((x / y) + ((2.0 / z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+15], N[Not[LessEqual[z, 0.26]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e15 or 0.26000000000000001 < z

   1. Initial program 71.5%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. *-inverses 100.0%

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

      4. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   if -6.2e15 < z < 0.26000000000000001

   1. Initial program 99.1%

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

   2. Taylor expanded in t around 0 99.1%

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

      1. sub-neg 99.1%

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

      2. metadata-eval 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+r+ 99.1%

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

      5. metadata-eval 99.1%

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

      6. associate-*r/ 99.1%

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

      7. +-commutative 99.1%

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

      8. associate-*r/ 99.1%

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

      9. metadata-eval 99.1%

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

      10. associate-/l/ 99.2%

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

      11. associate-*r/ 99.2%

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

      12. associate-*r/ 99.2%

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

      13. metadata-eval 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in z around 0 99.1%

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

      1. associate-+r+ 99.1%

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

      2. associate-*r/ 99.1%

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

      3. metadata-eval 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

      6. *-commutative 99.1%

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

      7. metadata-eval 99.1%

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

      8. associate-*r/ 99.1%

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

      9. associate-/r* 99.2%

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

      10. *-rgt-identity 99.2%

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

      11. associate-*r/ 99.1%

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

      12. distribute-rgt-in 99.1%

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

      13. +-commutative 99.1%

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

      14. associate-*l/ 99.2%

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

      15. *-lft-identity 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in z around 0 98.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+15} \lor \neg \left(z \leq 0.26\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \]

Alternative 10: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -190000000000 \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -190000000000.0) (not (<= (/ x y) 3.5e+27)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -190000000000.0) || !((x / y) <= 3.5e+27)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (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) <= (-190000000000.0d0)) .or. (.not. ((x / y) <= 3.5d+27))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (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) <= -190000000000.0) || !((x / y) <= 3.5e+27)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -190000000000.0) or not ((x / y) <= 3.5e+27):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -190000000000.0) || !(Float64(x / y) <= 3.5e+27))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -190000000000.0) || ~(((x / y) <= 3.5e+27)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -190000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.5e+27]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.9e11 or 3.5000000000000002e27 < (/.f64 x y)

   1. Initial program 87.2%

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

   2. Taylor expanded in x around inf 68.4%

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

   if -1.9e11 < (/.f64 x y) < 3.5000000000000002e27

   1. Initial program 86.7%

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

   2. Taylor expanded in z around inf 64.1%

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

      1. div-sub 64.1%

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

      2. sub-neg 64.1%

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

      3. *-inverses 64.1%

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

      4. metadata-eval 64.1%

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

   4. Simplified 64.1%

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

   5. Taylor expanded in x around 0 62.0%

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

      1. sub-neg 62.0%

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

      2. metadata-eval 62.0%

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

      3. distribute-lft-in 62.0%

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

      4. associate-*r/ 62.0%

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

      5. metadata-eval 62.0%

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

      6. metadata-eval 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -190000000000 \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 11: 65.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.3 \cdot 10^{-25} \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.3e-25) (not (<= (/ x y) 3.5e+27)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.3e-25) || !((x / y) <= 3.5e+27)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (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) <= (-6.3d-25)) .or. (.not. ((x / y) <= 3.5d+27))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (-2.0d0) + (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) <= -6.3e-25) || !((x / y) <= 3.5e+27)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6.3e-25) or not ((x / y) <= 3.5e+27):
		tmp = (x / y) - 2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6.3e-25) || !(Float64(x / y) <= 3.5e+27))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6.3e-25) || ~(((x / y) <= 3.5e+27)))
		tmp = (x / y) - 2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6.3e-25], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.5e+27]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.29999999999999961e-25 or 3.5000000000000002e27 < (/.f64 x y)

   1. Initial program 86.8%

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

   2. Taylor expanded in t around inf 65.5%

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

   if -6.29999999999999961e-25 < (/.f64 x y) < 3.5000000000000002e27

   1. Initial program 87.1%

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

   2. Taylor expanded in z around inf 66.4%

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

      1. div-sub 66.5%

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

      2. sub-neg 66.5%

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

      3. *-inverses 66.5%

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

      4. metadata-eval 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in x around 0 65.6%

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

      1. sub-neg 65.6%

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

      2. metadata-eval 65.6%

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

      3. distribute-lft-in 65.6%

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

      4. associate-*r/ 65.6%

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

      5. metadata-eval 65.6%

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

      6. metadata-eval 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.3 \cdot 10^{-25} \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 12: 61.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.72 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-234}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -1.72e-71)
     t_1
     (if (<= t 1.05e-234)
       (/ 2.0 (* z t))
       (if (<= t 3.9e-56) (+ -2.0 (/ 2.0 t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.72e-71) {
		tmp = t_1;
	} else if (t <= 1.05e-234) {
		tmp = 2.0 / (z * t);
	} else if (t <= 3.9e-56) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-1.72d-71)) then
        tmp = t_1
    else if (t <= 1.05d-234) then
        tmp = 2.0d0 / (z * t)
    else if (t <= 3.9d-56) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.72e-71) {
		tmp = t_1;
	} else if (t <= 1.05e-234) {
		tmp = 2.0 / (z * t);
	} else if (t <= 3.9e-56) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -1.72e-71:
		tmp = t_1
	elif t <= 1.05e-234:
		tmp = 2.0 / (z * t)
	elif t <= 3.9e-56:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.72e-71)
		tmp = t_1;
	elseif (t <= 1.05e-234)
		tmp = Float64(2.0 / Float64(z * t));
	elseif (t <= 3.9e-56)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.72e-71)
		tmp = t_1;
	elseif (t <= 1.05e-234)
		tmp = 2.0 / (z * t);
	elseif (t <= 3.9e-56)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.72e-71], t$95$1, If[LessEqual[t, 1.05e-234], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-56], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.72e-71 or 3.9e-56 < t

   1. Initial program 80.3%

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

   2. Taylor expanded in t around inf 76.9%

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

   if -1.72e-71 < t < 1.04999999999999996e-234

   1. Initial program 98.1%

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

   2. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/r* 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in x around 0 61.1%

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

   if 1.04999999999999996e-234 < t < 3.9e-56

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 67.9%

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

      1. div-sub 67.9%

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

      2. sub-neg 67.9%

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

      3. *-inverses 67.9%

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

      4. metadata-eval 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. sub-neg 56.0%

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

      2. metadata-eval 56.0%

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

      3. distribute-lft-in 56.0%

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

      4. associate-*r/ 56.0%

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

      5. metadata-eval 56.0%

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

      6. metadata-eval 56.0%

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

   7. Simplified 56.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.72 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-234}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 13: 61.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-57}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -7.2e-71)
     t_1
     (if (<= t 1.15e-235)
       (/ (/ 2.0 z) t)
       (if (<= t 9.4e-57) (+ -2.0 (/ 2.0 t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -7.2e-71) {
		tmp = t_1;
	} else if (t <= 1.15e-235) {
		tmp = (2.0 / z) / t;
	} else if (t <= 9.4e-57) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-7.2d-71)) then
        tmp = t_1
    else if (t <= 1.15d-235) then
        tmp = (2.0d0 / z) / t
    else if (t <= 9.4d-57) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -7.2e-71) {
		tmp = t_1;
	} else if (t <= 1.15e-235) {
		tmp = (2.0 / z) / t;
	} else if (t <= 9.4e-57) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -7.2e-71:
		tmp = t_1
	elif t <= 1.15e-235:
		tmp = (2.0 / z) / t
	elif t <= 9.4e-57:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -7.2e-71)
		tmp = t_1;
	elseif (t <= 1.15e-235)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t <= 9.4e-57)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -7.2e-71)
		tmp = t_1;
	elseif (t <= 1.15e-235)
		tmp = (2.0 / z) / t;
	elseif (t <= 9.4e-57)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -7.2e-71], t$95$1, If[LessEqual[t, 1.15e-235], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 9.4e-57], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2e-71 or 9.3999999999999996e-57 < t

   1. Initial program 80.3%

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

   2. Taylor expanded in t around inf 76.9%

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

   if -7.2e-71 < t < 1.14999999999999999e-235

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 91.9%

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

      1. associate-*r/ 91.9%

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

      2. metadata-eval 91.9%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in z around 0 61.2%

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

   if 1.14999999999999999e-235 < t < 9.3999999999999996e-57

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 67.9%

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

      1. div-sub 67.9%

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

      2. sub-neg 67.9%

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

      3. *-inverses 67.9%

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

      4. metadata-eval 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. sub-neg 56.0%

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

      2. metadata-eval 56.0%

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

      3. distribute-lft-in 56.0%

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

      4. associate-*r/ 56.0%

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

      5. metadata-eval 56.0%

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

      6. metadata-eval 56.0%

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

   7. Simplified 56.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-57}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 14: 79.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -13 \lor \neg \left(t \leq 1.5 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -13.0) (not (<= t 1.5e-51)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -13.0) || !(t <= 1.5e-51)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-13.0d0)) .or. (.not. (t <= 1.5d-51))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -13.0) || !(t <= 1.5e-51)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -13.0) or not (t <= 1.5e-51):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -13.0) || !(t <= 1.5e-51))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -13.0) || ~((t <= 1.5e-51)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -13.0], N[Not[LessEqual[t, 1.5e-51]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -13 or 1.50000000000000001e-51 < t

   1. Initial program 77.7%

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

   2. Taylor expanded in t around inf 80.5%

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

   if -13 < t < 1.50000000000000001e-51

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. metadata-eval 84.5%

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

   4. Simplified 84.5%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -13 \lor \neg \left(t \leq 1.5 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 15: 37.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-10}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e-10) -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 <= -4e-10) {
		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 <= (-4d-10)) 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 <= -4e-10) {
		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 <= -4e-10:
		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 <= -4e-10)
		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 <= -4e-10)
		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, -4e-10], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000015e-10 or 1 < t

   1. Initial program 76.4%

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

   2. Taylor expanded in z around inf 82.7%

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

      1. div-sub 82.7%

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

      2. sub-neg 82.7%

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

      3. *-inverses 82.7%

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

      4. metadata-eval 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in x around 0 37.0%

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

      1. sub-neg 37.0%

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

      2. metadata-eval 37.0%

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

      3. distribute-lft-in 37.0%

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

      4. associate-*r/ 37.0%

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

      5. metadata-eval 37.0%

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

      6. metadata-eval 37.0%

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

   7. Simplified 37.0%

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

   8. Taylor expanded in t around inf 35.8%

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

   if -4.00000000000000015e-10 < t < 1

   1. Initial program 98.9%

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

   2. Taylor expanded in t around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. metadata-eval 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in z around inf 36.7%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-10}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 16: 20.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

2. Taylor expanded in z around inf 70.6%

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

   1. div-sub 70.6%

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

   2. sub-neg 70.6%

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

   3. *-inverses 70.6%

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

   4. metadata-eval 70.6%

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

4. Simplified 70.6%

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

5. Taylor expanded in x around 0 36.9%

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

   1. sub-neg 36.9%

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

   2. metadata-eval 36.9%

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

   3. distribute-lft-in 36.9%

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

   4. associate-*r/ 36.9%

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

   5. metadata-eval 36.9%

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

   6. metadata-eval 36.9%

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

7. Simplified 36.9%

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

8. Taylor expanded in t around inf 20.1%

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

9. Final simplification 20.1%

   \[\leadsto -2 \]

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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