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

Percentage Accurate: 86.8% → 99.1%

Time: 12.9s

Alternatives: 15

Speedup: 1.3×

• 24.0% 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: 86.8% 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

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

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(Float64(-2.0 + 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[(N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.4%

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

   1. +-commutative 85.4%

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

   2. remove-double-neg 85.4%

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

   3. distribute-frac-neg 85.4%

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

   4. unsub-neg 85.4%

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

   5. *-commutative 85.4%

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

   6. associate-*r* 85.4%

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

   7. distribute-rgt1-in 85.4%

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

   8. associate-/l* 85.3%

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

   9. fma-neg 85.3%

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

   10. *-commutative 85.3%

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

   11. fma-define 85.3%

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

   12. *-commutative 85.3%

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

   13. distribute-frac-neg 85.3%

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

   14. remove-double-neg 85.3%

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

3. Simplified 85.3%

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

5. Taylor expanded in t around inf 99.9%

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

   1. associate--l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. sub-neg 99.9%

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

   4. metadata-eval 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-*r/ 99.9%

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

   7. distribute-lft-in 99.9%

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

   8. metadata-eval 99.9%

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

   9. associate-*r/ 99.9%

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

   10. metadata-eval 99.9%

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

7. Simplified 99.9%

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

8. Final simplification 99.9%

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

Alternative 2: 87.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+155) (not (<= (/ x y) 1.0)))
   (+ (/ 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) <= -2e+155) || !((x / y) <= 1.0)) {
		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) <= (-2d+155)) .or. (.not. ((x / y) <= 1.0d0))) 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) <= -2e+155) || !((x / y) <= 1.0)) {
		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) <= -2e+155) or not ((x / y) <= 1.0):
		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) <= -2e+155) || !(Float64(x / y) <= 1.0))
		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) <= -2e+155) || ~(((x / y) <= 1.0)))
		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], -2e+155], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.0]], $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) < -2.00000000000000001e155 or 1 < (/.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 91.3%

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

      1. div-sub 91.3%

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

      2. sub-neg 91.3%

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

      3. *-inverses 91.3%

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

      4. metadata-eval 91.3%

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

      5. distribute-lft-in 91.3%

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

      6. associate-*r/ 91.3%

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

      7. metadata-eval 91.3%

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

      8. metadata-eval 91.3%

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

   5. Simplified 91.3%

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

   if -2.00000000000000001e155 < (/.f64 x y) < 1

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. remove-double-neg 84.6%

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

      3. distribute-frac-neg 84.6%

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

      4. unsub-neg 84.6%

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

      5. *-commutative 84.6%

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

      6. associate-*r* 84.6%

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

      7. distribute-rgt1-in 84.6%

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

      8. associate-/l* 84.5%

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

      9. fma-neg 84.5%

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

      10. *-commutative 84.5%

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

      11. fma-define 84.5%

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

      12. *-commutative 84.5%

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

      13. distribute-frac-neg 84.5%

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

      14. remove-double-neg 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 94.2%

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

      1. associate--l+ 94.2%

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

      2. associate-*r/ 94.2%

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

      3. metadata-eval 94.2%

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

      4. associate-*r/ 94.2%

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

      5. metadata-eval 94.2%

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

      6. associate-/l/ 94.1%

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

      7. sub-neg 94.1%

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

      8. *-rgt-identity 94.1%

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

      9. associate-*r/ 94.1%

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

      10. metadata-eval 94.1%

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

      11. associate-+l+ 94.1%

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

      12. metadata-eval 94.1%

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

      13. associate-*r/ 94.1%

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

      14. distribute-rgt-in 94.1%

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

      15. associate-*l/ 94.1%

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

      16. *-lft-identity 94.1%

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

      17. +-commutative 94.1%

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

   10. Simplified 94.1%

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

4. Final simplification 93.0%

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

Alternative 3: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+58) (not (<= (/ x y) 100000000000.0)))
   (+ (/ x y) (/ 2.0 (* z 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) <= -4e+58) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + (2.0 / (z * 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) <= (-4d+58)) .or. (.not. ((x / y) <= 100000000000.0d0))) then
        tmp = (x / y) + (2.0d0 / (z * 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) <= -4e+58) || !((x / y) <= 100000000000.0)) {
		tmp = (x / y) + (2.0 / (z * 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) <= -4e+58) or not ((x / y) <= 100000000000.0):
		tmp = (x / y) + (2.0 / (z * 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) <= -4e+58) || !(Float64(x / y) <= 100000000000.0))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * 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) <= -4e+58) || ~(((x / y) <= 100000000000.0)))
		tmp = (x / y) + (2.0 / (z * 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], -4e+58], N[Not[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * 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) < -3.99999999999999978e58 or 1e11 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 95.0%

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

   if -3.99999999999999978e58 < (/.f64 x y) < 1e11

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. remove-double-neg 84.6%

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

      3. distribute-frac-neg 84.6%

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

      4. unsub-neg 84.6%

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

      5. *-commutative 84.6%

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

      6. associate-*r* 84.6%

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

      7. distribute-rgt1-in 84.6%

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

      8. associate-/l* 84.5%

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

      9. fma-neg 84.5%

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

      10. *-commutative 84.5%

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

      11. fma-define 84.5%

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

      12. *-commutative 84.5%

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

      13. distribute-frac-neg 84.5%

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

      14. remove-double-neg 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 96.7%

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

      1. associate--l+ 96.7%

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

      2. associate-*r/ 96.7%

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

      3. metadata-eval 96.7%

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

      4. associate-*r/ 96.7%

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

      5. metadata-eval 96.7%

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

      6. associate-/l/ 96.7%

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

      7. sub-neg 96.7%

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

      8. *-rgt-identity 96.7%

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

      9. associate-*r/ 96.7%

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

      10. metadata-eval 96.7%

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

      11. associate-+l+ 96.7%

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

      12. metadata-eval 96.7%

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

      13. associate-*r/ 96.7%

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

      14. distribute-rgt-in 96.6%

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

      15. associate-*l/ 96.7%

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

      16. *-lft-identity 96.7%

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

      17. +-commutative 96.7%

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

   10. Simplified 96.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+155)
   (/ x y)
   (if (<= (/ x y) 100000000000.0)
     (+ -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) <= -2e+155) {
		tmp = x / y;
	} else if ((x / y) <= 100000000000.0) {
		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) <= (-2d+155)) then
        tmp = x / y
    else if ((x / y) <= 100000000000.0d0) 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) <= -2e+155) {
		tmp = x / y;
	} else if ((x / y) <= 100000000000.0) {
		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) <= -2e+155:
		tmp = x / y
	elif (x / y) <= 100000000000.0:
		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) <= -2e+155)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 100000000000.0)
		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) <= -2e+155)
		tmp = x / y;
	elseif ((x / y) <= 100000000000.0)
		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], -2e+155], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0], 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) < -2.00000000000000001e155

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf 90.4%

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

   if -2.00000000000000001e155 < (/.f64 x y) < 1e11

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. remove-double-neg 84.5%

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

      3. distribute-frac-neg 84.5%

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

      4. unsub-neg 84.5%

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

      5. *-commutative 84.5%

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

      6. associate-*r* 84.5%

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

      7. distribute-rgt1-in 84.5%

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

      8. associate-/l* 84.4%

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

      9. fma-neg 84.4%

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

      10. *-commutative 84.4%

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

      11. fma-define 84.4%

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

      12. *-commutative 84.4%

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

      13. distribute-frac-neg 84.4%

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

      14. remove-double-neg 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 93.6%

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

      1. associate--l+ 93.6%

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

      2. associate-*r/ 93.6%

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

      3. metadata-eval 93.6%

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

      4. associate-*r/ 93.6%

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

      5. metadata-eval 93.6%

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

      6. associate-/l/ 93.6%

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

      7. sub-neg 93.6%

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

      8. *-rgt-identity 93.6%

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

      9. associate-*r/ 93.5%

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

      10. metadata-eval 93.5%

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

      11. associate-+l+ 93.5%

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

      12. metadata-eval 93.5%

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

      13. associate-*r/ 93.5%

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

      14. distribute-rgt-in 93.5%

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

      15. associate-*l/ 93.6%

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

      16. *-lft-identity 93.6%

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

      17. +-commutative 93.6%

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

   10. Simplified 93.6%

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

   if 1e11 < (/.f64 x y)

   1. Initial program 83.2%

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

   3. Taylor expanded in t around inf 85.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e+58)
   (+ (/ x y) (/ 2.0 (* z t)))
   (if (<= (/ x y) 100000000000.0)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (/ (/ 2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+58) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if ((x / y) <= 100000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4d+58)) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else if ((x / y) <= 100000000000.0d0) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+58) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if ((x / y) <= 100000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4e+58:
		tmp = (x / y) + (2.0 / (z * t))
	elif (x / y) <= 100000000000.0:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4e+58)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	elseif (Float64(x / y) <= 100000000000.0)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4e+58)
		tmp = (x / y) + (2.0 / (z * t));
	elseif ((x / y) <= 100000000000.0)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4e+58], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.99999999999999978e58

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0 93.1%

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

   if -3.99999999999999978e58 < (/.f64 x y) < 1e11

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. remove-double-neg 84.6%

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

      3. distribute-frac-neg 84.6%

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

      4. unsub-neg 84.6%

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

      5. *-commutative 84.6%

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

      6. associate-*r* 84.6%

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

      7. distribute-rgt1-in 84.6%

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

      8. associate-/l* 84.5%

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

      9. fma-neg 84.5%

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

      10. *-commutative 84.5%

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

      11. fma-define 84.5%

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

      12. *-commutative 84.5%

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

      13. distribute-frac-neg 84.5%

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

      14. remove-double-neg 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 96.7%

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

      1. associate--l+ 96.7%

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

      2. associate-*r/ 96.7%

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

      3. metadata-eval 96.7%

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

      4. associate-*r/ 96.7%

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

      5. metadata-eval 96.7%

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

      6. associate-/l/ 96.7%

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

      7. sub-neg 96.7%

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

      8. *-rgt-identity 96.7%

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

      9. associate-*r/ 96.7%

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

      10. metadata-eval 96.7%

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

      11. associate-+l+ 96.7%

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

      12. metadata-eval 96.7%

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

      13. associate-*r/ 96.7%

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

      14. distribute-rgt-in 96.6%

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

      15. associate-*l/ 96.7%

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

      16. *-lft-identity 96.7%

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

      17. +-commutative 96.7%

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

   10. Simplified 96.7%

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

   if 1e11 < (/.f64 x y)

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 96.6%

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

      1. associate-/r* 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e+58)
   (+ (/ x y) (/ 2.0 (* z t)))
   (if (<= (/ x y) 100000000000.0)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (/ (/ 2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+58) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if ((x / y) <= 100000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / 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) <= (-4d+58)) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else if ((x / y) <= 100000000000.0d0) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / 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) <= -4e+58) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if ((x / y) <= 100000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4e+58:
		tmp = (x / y) + (2.0 / (z * t))
	elif (x / y) <= 100000000000.0:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / 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) <= -4e+58)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	elseif (Float64(x / y) <= 100000000000.0)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = 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 ((x / y) <= -4e+58)
		tmp = (x / y) + (2.0 / (z * t));
	elseif ((x / y) <= 100000000000.0)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / 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], -4e+58], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.99999999999999978e58

   1. Initial program 90.0%

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

   3. Taylor expanded in z around 0 93.1%

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

   if -3.99999999999999978e58 < (/.f64 x y) < 1e11

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. remove-double-neg 84.6%

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

      3. distribute-frac-neg 84.6%

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

      4. unsub-neg 84.6%

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

      5. *-commutative 84.6%

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

      6. associate-*r* 84.6%

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

      7. distribute-rgt1-in 84.6%

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

      8. associate-/l* 84.5%

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

      9. fma-neg 84.5%

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

      10. *-commutative 84.5%

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

      11. fma-define 84.5%

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

      12. *-commutative 84.5%

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

      13. distribute-frac-neg 84.5%

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

      14. remove-double-neg 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 96.7%

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

      1. associate--l+ 96.7%

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

      2. associate-*r/ 96.7%

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

      3. metadata-eval 96.7%

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

      4. associate-*r/ 96.7%

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

      5. metadata-eval 96.7%

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

      6. associate-/l/ 96.7%

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

      7. sub-neg 96.7%

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

      8. *-rgt-identity 96.7%

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

      9. associate-*r/ 96.7%

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

      10. metadata-eval 96.7%

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

      11. associate-+l+ 96.7%

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

      12. metadata-eval 96.7%

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

      13. associate-*r/ 96.7%

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

      14. distribute-rgt-in 96.6%

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

      15. associate-*l/ 96.7%

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

      16. *-lft-identity 96.7%

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

      17. +-commutative 96.7%

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

   10. Simplified 96.7%

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

   if 1e11 < (/.f64 x y)

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 81.6%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in z around 0 96.6%

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

      1. associate-/l/ 96.7%

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

   8. Simplified 96.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -24000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 + \frac{x}{y}\right) + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -24000000000.0) (not (<= z 5.5e-6)))
   (+ (/ 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 <= -24000000000.0) || !(z <= 5.5e-6)) {
		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 <= (-24000000000.0d0)) .or. (.not. (z <= 5.5d-6))) 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 <= -24000000000.0) || !(z <= 5.5e-6)) {
		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 <= -24000000000.0) or not (z <= 5.5e-6):
		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 <= -24000000000.0) || !(z <= 5.5e-6))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(-2.0 + 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 ((z <= -24000000000.0) || ~((z <= 5.5e-6)))
		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, -24000000000.0], N[Not[LessEqual[z, 5.5e-6]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e10 or 5.4999999999999999e-6 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

      5. distribute-lft-in 99.3%

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

      6. associate-*r/ 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -2.4e10 < z < 5.4999999999999999e-6

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. remove-double-neg 99.8%

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

      3. distribute-frac-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.8%

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

      7. distribute-rgt1-in 99.8%

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

      8. associate-/l* 99.8%

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

      9. fma-neg 99.8%

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

      10. *-commutative 99.8%

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

      11. fma-define 99.8%

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

      12. *-commutative 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. remove-double-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 99.1%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 + \frac{x}{y}\right) + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -24000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 + \frac{x}{y}\right) + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -24000000000.0) (not (<= z 5.5e-6)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (+ -2.0 (/ x y)) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -24000000000.0) || !(z <= 5.5e-6)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (-2.0 + (x / y)) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-24000000000.0d0)) .or. (.not. (z <= 5.5d-6))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = ((-2.0d0) + (x / y)) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -24000000000.0) || !(z <= 5.5e-6)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (-2.0 + (x / y)) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -24000000000.0) or not (z <= 5.5e-6):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (-2.0 + (x / y)) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -24000000000.0) || !(z <= 5.5e-6))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(-2.0 + Float64(x / y)) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -24000000000.0) || ~((z <= 5.5e-6)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (-2.0 + (x / y)) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -24000000000.0], N[Not[LessEqual[z, 5.5e-6]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e10 or 5.4999999999999999e-6 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 99.3%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. *-inverses 99.3%

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

      4. metadata-eval 99.3%

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

      5. distribute-lft-in 99.3%

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

      6. associate-*r/ 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -2.4e10 < z < 5.4999999999999999e-6

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around inf 99.2%

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

      1. *-commutative 99.2%

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

   8. Simplified 99.2%

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

   9. Taylor expanded in x around 0 99.1%

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

       1. associate--l+ 99.1%

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

       2. associate-*r/ 99.1%

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

       3. metadata-eval 99.1%

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

       4. associate-/r* 99.2%

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

       5. sub-neg 99.2%

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

       6. metadata-eval 99.2%

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

       7. +-commutative 99.2%

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

   11. Simplified 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-2 + \frac{x}{y}\right) + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+155)
   (/ x y)
   (if (<= (/ x y) 1.0) (+ -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) <= -2e+155) {
		tmp = x / y;
	} else if ((x / y) <= 1.0) {
		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) <= (-2d+155)) then
        tmp = x / y
    else if ((x / y) <= 1.0d0) 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) <= -2e+155) {
		tmp = x / y;
	} else if ((x / y) <= 1.0) {
		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) <= -2e+155:
		tmp = x / y
	elif (x / y) <= 1.0:
		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) <= -2e+155)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.0)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+155)
		tmp = x / y;
	elseif ((x / y) <= 1.0)
		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], -2e+155], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.0], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.00000000000000001e155

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf 90.4%

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

   if -2.00000000000000001e155 < (/.f64 x y) < 1

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. remove-double-neg 84.6%

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

      3. distribute-frac-neg 84.6%

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

      4. unsub-neg 84.6%

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

      5. *-commutative 84.6%

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

      6. associate-*r* 84.6%

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

      7. distribute-rgt1-in 84.6%

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

      8. associate-/l* 84.5%

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

      9. fma-neg 84.5%

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

      10. *-commutative 84.5%

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

      11. fma-define 84.5%

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

      12. *-commutative 84.5%

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

      13. distribute-frac-neg 84.5%

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

      14. remove-double-neg 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 78.3%

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

   9. Taylor expanded in x around 0 72.8%

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

       1. sub-neg 72.8%

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

       2. associate-*r/ 72.8%

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

       3. metadata-eval 72.8%

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

       4. metadata-eval 72.8%

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

       5. +-commutative 72.8%

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

       6. associate-/l/ 72.8%

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

   11. Simplified 72.8%

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

   if 1 < (/.f64 x y)

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 80.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+58) (not (<= (/ x y) 100000000000.0)))
   (/ x y)
   (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+58) || !((x / y) <= 100000000000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4d+58)) .or. (.not. ((x / y) <= 100000000000.0d0))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+58) || !((x / y) <= 100000000000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+58) or not ((x / y) <= 100000000000.0):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+58) || !(Float64(x / y) <= 100000000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4e+58) || ~(((x / y) <= 100000000000.0)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e+58], N[Not[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.99999999999999978e58 or 1e11 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf 78.6%

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

   if -3.99999999999999978e58 < (/.f64 x y) < 1e11

   1. Initial program 84.6%

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

   3. Taylor expanded in t around 0 63.9%

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

      1. associate-*r/ 63.9%

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

      2. metadata-eval 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in z around inf 26.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+58} \lor \neg \left(\frac{x}{y} \leq 100000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-20} \lor \neg \left(t \leq 9.6\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.2e-20) (not (<= t 9.6)))
   (- (/ 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 <= -9.2e-20) || !(t <= 9.6)) {
		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 <= (-9.2d-20)) .or. (.not. (t <= 9.6d0))) 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 <= -9.2e-20) || !(t <= 9.6)) {
		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 <= -9.2e-20) or not (t <= 9.6):
		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 <= -9.2e-20) || !(t <= 9.6))
		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 <= -9.2e-20) || ~((t <= 9.6)))
		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, -9.2e-20], N[Not[LessEqual[t, 9.6]], $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 < -9.1999999999999997e-20 or 9.59999999999999964 < t

   1. Initial program 72.7%

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

   3. Taylor expanded in t around inf 83.9%

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

   if -9.1999999999999997e-20 < t < 9.59999999999999964

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-20} \lor \neg \left(t \leq 9.6\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 650:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2 \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.2e-20)
   (- (/ x y) 2.0)
   (if (<= t 650.0) (/ (+ 2.0 (/ 2.0 z)) t) (/ (+ x (* -2.0 y)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e-20) {
		tmp = (x / y) - 2.0;
	} else if (t <= 650.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x + (-2.0 * y)) / 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 (t <= (-9.2d-20)) then
        tmp = (x / y) - 2.0d0
    else if (t <= 650.0d0) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = (x + ((-2.0d0) * y)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e-20) {
		tmp = (x / y) - 2.0;
	} else if (t <= 650.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x + (-2.0 * y)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.2e-20:
		tmp = (x / y) - 2.0
	elif t <= 650.0:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = (x + (-2.0 * y)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.2e-20)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (t <= 650.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = Float64(Float64(x + Float64(-2.0 * y)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.2e-20)
		tmp = (x / y) - 2.0;
	elseif (t <= 650.0)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = (x + (-2.0 * y)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.2e-20], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t, 650.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(x + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999997e-20

   1. Initial program 73.8%

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

   3. Taylor expanded in t around inf 79.3%

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

   if -9.1999999999999997e-20 < t < 650

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

   if 650 < t

   1. Initial program 71.5%

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

   3. Taylor expanded in t around inf 88.7%

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

   4. Taylor expanded in y around 0 88.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 650:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2 \cdot y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-34} \lor \neg \left(t \leq 6.5 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.62e-34) (not (<= t 6.5e-93))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.62e-34) || !(t <= 6.5e-93)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.62d-34)) .or. (.not. (t <= 6.5d-93))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.62e-34) || !(t <= 6.5e-93)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.62e-34) or not (t <= 6.5e-93):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.62e-34) || !(t <= 6.5e-93))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.62e-34) || ~((t <= 6.5e-93)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.62e-34], N[Not[LessEqual[t, 6.5e-93]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.62000000000000006e-34 or 6.5e-93 < t

   1. Initial program 75.7%

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

   3. Taylor expanded in t around inf 80.0%

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

   if -1.62000000000000006e-34 < t < 6.5e-93

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. metadata-eval 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in z around inf 37.6%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-34} \lor \neg \left(t \leq 6.5 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-75} \lor \neg \left(z \leq 1.3 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e-75) (not (<= z 1.3e-85)))
   (- (/ x y) 2.0)
   (/ 2.0 (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-75) || !(z <= 1.3e-85)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 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 <= (-3.6d-75)) .or. (.not. (z <= 1.3d-85))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 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 <= -3.6e-75) || !(z <= 1.3e-85)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.6e-75) or not (z <= 1.3e-85):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e-75) || !(z <= 1.3e-85))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.6e-75) || ~((z <= 1.3e-85)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.6e-75], N[Not[LessEqual[z, 1.3e-85]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e-75 or 1.30000000000000006e-85 < z

   1. Initial program 76.9%

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

   3. Taylor expanded in t around inf 69.1%

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

   if -3.6e-75 < z < 1.30000000000000006e-85

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 73.7%

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

      1. associate-*r/ 73.7%

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

      2. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in z around 0 73.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-75} \lor \neg \left(z \leq 1.3 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 19.8% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

3. Taylor expanded in t around 0 47.9%

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

   1. associate-*r/ 47.9%

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

   2. metadata-eval 47.9%

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

5. Simplified 47.9%

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

6. Taylor expanded in z around inf 17.9%

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

7. Final simplification 17.9%

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

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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