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

Percentage Accurate: 86.5% → 99.1%

Time: 10.7s

Alternatives: 13

Speedup: 1.3×

• 22.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

   1. +-commutative 89.3%

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

   2. remove-double-neg 89.3%

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

   3. distribute-frac-neg 89.3%

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

   4. unsub-neg 89.3%

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

   5. *-commutative 89.3%

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

   6. associate-*r* 89.3%

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

   7. distribute-rgt1-in 89.3%

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

   8. associate-/l* 89.6%

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

   9. fma-neg 89.6%

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

   10. *-commutative 89.6%

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

   11. fma-define 89.6%

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

   12. *-commutative 89.6%

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

   13. distribute-frac-neg 89.6%

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

   14. remove-double-neg 89.6%

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

3. Simplified 89.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
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. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. metadata-eval 99.9%

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

   4. associate-+l+ 99.9%

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

   5. associate-*r/ 99.9%

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

   6. distribute-lft-in 99.9%

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

   7. metadata-eval 99.9%

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

   8. associate-*r/ 99.9%

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

   9. metadata-eval 99.9%

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

7. Simplified 99.9%

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

Alternative 2: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-12} \lor \neg \left(t \leq 1.9 \cdot 10^{-23}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -2.1e+82)
     t_1
     (if (<= t -9.2e+39)
       (+ -2.0 (/ 2.0 (* z t)))
       (if (or (<= t -3.2e-12) (not (<= t 1.9e-23)))
         t_1
         (/ (+ 2.0 (/ 2.0 z)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.1e+82) {
		tmp = t_1;
	} else if (t <= -9.2e+39) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if ((t <= -3.2e-12) || !(t <= 1.9e-23)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-2.1d+82)) then
        tmp = t_1
    else if (t <= (-9.2d+39)) then
        tmp = (-2.0d0) + (2.0d0 / (z * t))
    else if ((t <= (-3.2d-12)) .or. (.not. (t <= 1.9d-23))) then
        tmp = t_1
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -2.1e+82) {
		tmp = t_1;
	} else if (t <= -9.2e+39) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if ((t <= -3.2e-12) || !(t <= 1.9e-23)) {
		tmp = t_1;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -2.1e+82:
		tmp = t_1
	elif t <= -9.2e+39:
		tmp = -2.0 + (2.0 / (z * t))
	elif (t <= -3.2e-12) or not (t <= 1.9e-23):
		tmp = t_1
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -2.1e+82)
		tmp = t_1;
	elseif (t <= -9.2e+39)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	elseif ((t <= -3.2e-12) || !(t <= 1.9e-23))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -2.1e+82)
		tmp = t_1;
	elseif (t <= -9.2e+39)
		tmp = -2.0 + (2.0 / (z * t));
	elseif ((t <= -3.2e-12) || ~((t <= 1.9e-23)))
		tmp = t_1;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -2.1e+82], t$95$1, If[LessEqual[t, -9.2e+39], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.2e-12], N[Not[LessEqual[t, 1.9e-23]], $MachinePrecision]], t$95$1, N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e82 or -9.20000000000000047e39 < t < -3.2000000000000001e-12 or 1.90000000000000006e-23 < t

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf 88.2%

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

   if -2.1e82 < t < -9.20000000000000047e39

   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 inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-commutative 99.8%

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

      5. div-sub 99.8%

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

      6. sub-neg 99.8%

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

      7. *-inverses 99.8%

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

      8. metadata-eval 99.8%

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

      9. distribute-lft-in 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

      13. *-commutative 99.8%

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

      14. +-commutative 99.8%

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

      15. associate-/l/ 99.7%

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

      16. metadata-eval 99.7%

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

      17. associate-*r/ 99.7%

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

      18. *-rgt-identity 99.7%

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

      19. associate-*r/ 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in x around 0 88.8%

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

       1. sub-neg 88.8%

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

       2. metadata-eval 88.8%

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

       3. associate-*r/ 88.8%

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

       4. metadata-eval 88.8%

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

       5. associate-/l/ 88.6%

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

       6. +-commutative 88.6%

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

       7. associate-/l/ 88.8%

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

   11. Simplified 88.8%

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

   if -3.2000000000000001e-12 < t < 1.90000000000000006e-23

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0 81.8%

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

      1. associate-*r/ 81.8%

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

      2. metadata-eval 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-12} \lor \neg \left(t \leq 1.9 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -8 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -8e+83)
     t_1
     (if (<= t -8.5e+39)
       (+ -2.0 (/ 2.0 (* z t)))
       (if (<= t -1.7e-9)
         (/ (+ x (* y -2.0)) y)
         (if (<= t 2.1e-23) (/ (+ 2.0 (/ 2.0 z)) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -8e+83) {
		tmp = t_1;
	} else if (t <= -8.5e+39) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if (t <= -1.7e-9) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 2.1e-23) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-8d+83)) then
        tmp = t_1
    else if (t <= (-8.5d+39)) then
        tmp = (-2.0d0) + (2.0d0 / (z * t))
    else if (t <= (-1.7d-9)) then
        tmp = (x + (y * (-2.0d0))) / y
    else if (t <= 2.1d-23) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -8e+83) {
		tmp = t_1;
	} else if (t <= -8.5e+39) {
		tmp = -2.0 + (2.0 / (z * t));
	} else if (t <= -1.7e-9) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 2.1e-23) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -8e+83:
		tmp = t_1
	elif t <= -8.5e+39:
		tmp = -2.0 + (2.0 / (z * t))
	elif t <= -1.7e-9:
		tmp = (x + (y * -2.0)) / y
	elif t <= 2.1e-23:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -8e+83)
		tmp = t_1;
	elseif (t <= -8.5e+39)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	elseif (t <= -1.7e-9)
		tmp = Float64(Float64(x + Float64(y * -2.0)) / y);
	elseif (t <= 2.1e-23)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -8e+83)
		tmp = t_1;
	elseif (t <= -8.5e+39)
		tmp = -2.0 + (2.0 / (z * t));
	elseif (t <= -1.7e-9)
		tmp = (x + (y * -2.0)) / y;
	elseif (t <= 2.1e-23)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -8e+83], t$95$1, If[LessEqual[t, -8.5e+39], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-9], N[(N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.1e-23], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.00000000000000025e83 or 2.1000000000000001e-23 < t

   1. Initial program 79.0%

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

   3. Taylor expanded in t around inf 90.0%

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

   if -8.00000000000000025e83 < t < -8.49999999999999971e39

   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 inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-commutative 99.8%

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

      5. div-sub 99.8%

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

      6. sub-neg 99.8%

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

      7. *-inverses 99.8%

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

      8. metadata-eval 99.8%

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

      9. distribute-lft-in 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

      13. *-commutative 99.8%

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

      14. +-commutative 99.8%

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

      15. associate-/l/ 99.7%

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

      16. metadata-eval 99.7%

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

      17. associate-*r/ 99.7%

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

      18. *-rgt-identity 99.7%

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

      19. associate-*r/ 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in x around 0 88.8%

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

       1. sub-neg 88.8%

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

       2. metadata-eval 88.8%

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

       3. associate-*r/ 88.8%

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

       4. metadata-eval 88.8%

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

       5. associate-/l/ 88.6%

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

       6. +-commutative 88.6%

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

       7. associate-/l/ 88.8%

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

   11. Simplified 88.8%

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

   if -8.49999999999999971e39 < t < -1.6999999999999999e-9

   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 inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.8%

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

      16. metadata-eval 99.8%

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

      17. associate-*r/ 99.8%

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

      18. *-rgt-identity 99.8%

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

      19. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-/r* 90.0%

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

      3. associate-*r/ 90.0%

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

      4. associate-*l/ 90.0%

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

      5. distribute-rgt-in 90.0%

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

      6. metadata-eval 90.0%

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

      7. associate-*l/ 90.0%

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

      8. *-lft-identity 90.0%

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

      9. +-commutative 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in t around inf 76.3%

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

       1. *-commutative 76.3%

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

   11. Simplified 76.3%

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

   if -1.6999999999999999e-9 < t < 2.1000000000000001e-23

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0 81.8%

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

      1. associate-*r/ 81.8%

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

      2. metadata-eval 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-9} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-9) (not (<= (/ x y) 2e+42)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-9) || !((x / y) <= 2e+42)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d-9)) .or. (.not. ((x / y) <= 2d+42))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-9) || !((x / y) <= 2e+42)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-9) or not ((x / y) <= 2e+42):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-9) || !(Float64(x / y) <= 2e+42))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-9) || ~(((x / y) <= 2e+42)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-9], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+42]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000006e-9 or 2.00000000000000009e42 < (/.f64 x y)

   1. Initial program 90.7%

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

   3. Taylor expanded in z around inf 90.3%

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

      1. div-sub 90.3%

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

      2. sub-neg 90.3%

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

      3. *-inverses 90.3%

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

      4. metadata-eval 90.3%

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

      5. distribute-lft-in 90.3%

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

      6. associate-*r/ 90.3%

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

      7. metadata-eval 90.3%

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

      8. metadata-eval 90.3%

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

   5. Simplified 90.3%

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

   if -1.00000000000000006e-9 < (/.f64 x y) < 2.00000000000000009e42

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 96.2%

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

      1. sub-neg 96.2%

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

      2. associate-/r* 96.2%

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

      3. associate-*r/ 96.2%

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

      4. associate-*l/ 96.2%

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

      5. distribute-rgt-in 96.2%

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

      6. metadata-eval 96.2%

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

      7. associate-*l/ 96.2%

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

      8. *-lft-identity 96.2%

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

      9. +-commutative 96.2%

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

   8. Simplified 96.2%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-9} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.2 \cdot 10^{+40} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.2e+40) (not (<= (/ x y) 2e+42)))
   (/ x y)
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.2e+40) || !((x / y) <= 2e+42)) {
		tmp = x / y;
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.2d+40)) .or. (.not. ((x / y) <= 2d+42))) then
        tmp = x / y
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.2e+40) || !((x / y) <= 2e+42)) {
		tmp = x / y;
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.2e+40) or not ((x / y) <= 2e+42):
		tmp = x / y
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.2e+40) || !(Float64(x / y) <= 2e+42))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.2e+40) || ~(((x / y) <= 2e+42)))
		tmp = x / y;
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.2e+40], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+42]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.1999999999999999e40 or 2.00000000000000009e42 < (/.f64 x y)

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 81.9%

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

   if -2.1999999999999999e40 < (/.f64 x y) < 2.00000000000000009e42

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 94.6%

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

      1. sub-neg 94.6%

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

      2. associate-/r* 94.5%

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

      3. associate-*r/ 94.5%

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

      4. associate-*l/ 94.5%

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

      5. distribute-rgt-in 94.5%

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

      6. metadata-eval 94.5%

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

      7. associate-*l/ 94.5%

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

      8. *-lft-identity 94.5%

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

      9. +-commutative 94.5%

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

   8. Simplified 94.5%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.2 \cdot 10^{+40} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.2e+40)
   (+ (/ x y) (/ 2.0 (* z t)))
   (if (<= (/ x y) 2e+42)
     (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)
     (+ (/ x y) (+ -2.0 (/ 2.0 t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.2e+40) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if ((x / y) <= 2e+42) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2.2d+40)) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else if ((x / y) <= 2d+42) then
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    else
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.2e+40) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if ((x / y) <= 2e+42) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.2e+40:
		tmp = (x / y) + (2.0 / (z * t))
	elif (x / y) <= 2e+42:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	else:
		tmp = (x / y) + (-2.0 + (2.0 / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.2e+40)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	elseif (Float64(x / y) <= 2e+42)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.2e+40)
		tmp = (x / y) + (2.0 / (z * t));
	elseif ((x / y) <= 2e+42)
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	else
		tmp = (x / y) + (-2.0 + (2.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.2e+40], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+42], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.1999999999999999e40

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 94.5%

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

   if -2.1999999999999999e40 < (/.f64 x y) < 2.00000000000000009e42

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 94.6%

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

      1. sub-neg 94.6%

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

      2. associate-/r* 94.5%

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

      3. associate-*r/ 94.5%

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

      4. associate-*l/ 94.5%

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

      5. distribute-rgt-in 94.5%

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

      6. metadata-eval 94.5%

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

      7. associate-*l/ 94.5%

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

      8. *-lft-identity 94.5%

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

      9. +-commutative 94.5%

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

   8. Simplified 94.5%

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

   if 2.00000000000000009e42 < (/.f64 x y)

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf 94.0%

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

      1. div-sub 94.0%

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

      2. sub-neg 94.0%

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

      3. *-inverses 94.0%

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

      4. metadata-eval 94.0%

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

      5. distribute-lft-in 94.0%

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

      6. associate-*r/ 94.0%

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

      7. metadata-eval 94.0%

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

      8. metadata-eval 94.0%

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

   5. Simplified 94.0%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.25 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{z \cdot t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.25e-8)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (+ -2.0 (/ 2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.25e-8)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-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 ((z <= (-1.0d0)) .or. (.not. (z <= 1.25d-8))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((-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 ((z <= -1.0) || !(z <= 1.25e-8)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.25e-8):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (-2.0 + (2.0 / (z * t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.25e-8))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.25e-8)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (-2.0 + (2.0 / (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.25e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.2499999999999999e-8 < z

   1. Initial program 80.3%

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

   3. Taylor expanded in z around inf 99.1%

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

      1. div-sub 99.1%

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

      2. sub-neg 99.1%

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

      3. *-inverses 99.1%

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

      4. metadata-eval 99.1%

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

      5. distribute-lft-in 99.1%

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

      6. associate-*r/ 99.1%

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

      7. metadata-eval 99.1%

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

      8. metadata-eval 99.1%

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

   5. Simplified 99.1%

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

   if -1 < z < 1.2499999999999999e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.8%

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

      16. metadata-eval 99.8%

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

      17. associate-*r/ 99.8%

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

      18. *-rgt-identity 99.8%

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

      19. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 99.5%

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

      1. *-commutative 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.25 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{z \cdot t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8.5 \cdot 10^{-10} \lor \neg \left(\frac{x}{y} \leq 0.047\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -8.5e-10) (not (<= (/ x y) 0.047)))
   (- (/ x y) 2.0)
   (+ -2.0 (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -8.5e-10) || !((x / y) <= 0.047)) {
		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 (((x / y) <= (-8.5d-10)) .or. (.not. ((x / y) <= 0.047d0))) 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 (((x / y) <= -8.5e-10) || !((x / y) <= 0.047)) {
		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 ((x / y) <= -8.5e-10) or not ((x / y) <= 0.047):
		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 ((Float64(x / y) <= -8.5e-10) || !(Float64(x / y) <= 0.047))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -8.5e-10) || ~(((x / y) <= 0.047)))
		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[N[(x / y), $MachinePrecision], -8.5e-10], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.047]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -8.4999999999999996e-10 or 0.047 < (/.f64 x y)

   1. Initial program 90.1%

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

   3. Taylor expanded in t around inf 75.0%

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

   if -8.4999999999999996e-10 < (/.f64 x y) < 0.047

   1. Initial program 88.6%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 76.4%

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

      1. *-commutative 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around 0 75.9%

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

       1. sub-neg 75.9%

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

       2. metadata-eval 75.9%

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

       3. associate-*r/ 75.9%

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

       4. metadata-eval 75.9%

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

       5. associate-/l/ 75.9%

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

       6. +-commutative 75.9%

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

       7. associate-/l/ 75.9%

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

   11. Simplified 75.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8.5 \cdot 10^{-10} \lor \neg \left(\frac{x}{y} \leq 0.047\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.05 \cdot 10^{+40} \lor \neg \left(\frac{x}{y} \leq 26000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.05e+40) (not (<= (/ x y) 26000000.0)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.05e+40) || !((x / y) <= 26000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.05d+40)) .or. (.not. ((x / y) <= 26000000.0d0))) then
        tmp = x / y
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.05e+40) || !((x / y) <= 26000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.05e+40) or not ((x / y) <= 26000000.0):
		tmp = x / y
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.05e+40) || !(Float64(x / y) <= 26000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.05e+40) || ~(((x / y) <= 26000000.0)))
		tmp = x / y;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.05e+40], N[Not[LessEqual[N[(x / y), $MachinePrecision], 26000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0500000000000001e40 or 2.6e7 < (/.f64 x y)

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 77.3%

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

   if -2.0500000000000001e40 < (/.f64 x y) < 2.6e7

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 96.9%

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

      1. sub-neg 96.9%

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

      2. associate-/r* 96.9%

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

      3. associate-*r/ 96.9%

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

      4. associate-*l/ 96.9%

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

      5. distribute-rgt-in 96.9%

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

      6. metadata-eval 96.9%

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

      7. associate-*l/ 96.9%

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

      8. *-lft-identity 96.9%

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

      9. +-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in z around inf 67.2%

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

       1. sub-neg 67.2%

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

       2. associate-*r/ 67.2%

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

       3. metadata-eval 67.2%

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

       4. metadata-eval 67.2%

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

       5. +-commutative 67.2%

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

   11. Simplified 67.2%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.05 \cdot 10^{+40} \lor \neg \left(\frac{x}{y} \leq 26000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.05 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 30500000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.05e+40)
   (/ x y)
   (if (<= (/ x y) 30500000.0) (+ -2.0 (/ 2.0 t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.05e+40) {
		tmp = x / y;
	} else if ((x / y) <= 30500000.0) {
		tmp = -2.0 + (2.0 / 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) <= (-2.05d+40)) then
        tmp = x / y
    else if ((x / y) <= 30500000.0d0) then
        tmp = (-2.0d0) + (2.0d0 / 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) <= -2.05e+40) {
		tmp = x / y;
	} else if ((x / y) <= 30500000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.05e+40:
		tmp = x / y
	elif (x / y) <= 30500000.0:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.05e+40)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 30500000.0)
		tmp = Float64(-2.0 + Float64(2.0 / 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) <= -2.05e+40)
		tmp = x / y;
	elseif ((x / y) <= 30500000.0)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.05e+40], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 30500000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.0500000000000001e40

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 79.6%

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

   if -2.0500000000000001e40 < (/.f64 x y) < 3.05e7

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 96.9%

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

      1. sub-neg 96.9%

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

      2. associate-/r* 96.9%

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

      3. associate-*r/ 96.9%

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

      4. associate-*l/ 96.9%

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

      5. distribute-rgt-in 96.9%

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

      6. metadata-eval 96.9%

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

      7. associate-*l/ 96.9%

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

      8. *-lft-identity 96.9%

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

      9. +-commutative 96.9%

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

   8. Simplified 96.9%

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

   9. Taylor expanded in z around inf 67.2%

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

       1. sub-neg 67.2%

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

       2. associate-*r/ 67.2%

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

       3. metadata-eval 67.2%

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

       4. metadata-eval 67.2%

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

       5. +-commutative 67.2%

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

   11. Simplified 67.2%

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

   if 3.05e7 < (/.f64 x y)

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf 76.2%

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

Alternative 11: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 24000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.0) (not (<= (/ x y) 24000000.0))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 24000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.0d0)) .or. (.not. ((x / y) <= 24000000.0d0))) then
        tmp = x / y
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 24000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.0) or not ((x / y) <= 24000000.0):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.0) || !(Float64(x / y) <= 24000000.0))
		tmp = Float64(x / y);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.0) || ~(((x / y) <= 24000000.0)))
		tmp = x / y;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 24000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 2.4e7 < (/.f64 x y)

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 75.0%

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

   if -2 < (/.f64 x y) < 2.4e7

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-/r* 98.0%

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

      3. associate-*r/ 98.0%

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

      4. associate-*l/ 98.0%

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

      5. distribute-rgt-in 98.0%

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

      6. metadata-eval 98.0%

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

      7. associate-*l/ 98.0%

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

      8. *-lft-identity 98.0%

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

      9. +-commutative 98.0%

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

   8. Simplified 98.0%

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

   9. Taylor expanded in t around inf 42.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 24000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -500:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -500.0) -2.0 (if (<= t 2.4e-18) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -500.0) {
		tmp = -2.0;
	} else if (t <= 2.4e-18) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-500.0d0)) then
        tmp = -2.0d0
    else if (t <= 2.4d-18) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -500.0) {
		tmp = -2.0;
	} else if (t <= 2.4e-18) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -500.0:
		tmp = -2.0
	elif t <= 2.4e-18:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -500.0)
		tmp = -2.0;
	elseif (t <= 2.4e-18)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -500.0)
		tmp = -2.0;
	elseif (t <= 2.4e-18)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -500.0], -2.0, If[LessEqual[t, 2.4e-18], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -500 or 2.39999999999999994e-18 < t

   1. Initial program 82.1%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.9%

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

      16. metadata-eval 99.9%

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

      17. associate-*r/ 99.9%

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

      18. *-rgt-identity 99.9%

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

      19. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 56.3%

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

      1. sub-neg 56.3%

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

      2. associate-/r* 56.3%

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

      3. associate-*r/ 56.3%

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

      4. associate-*l/ 56.3%

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

      5. distribute-rgt-in 56.3%

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

      6. metadata-eval 56.3%

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

      7. associate-*l/ 56.3%

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

      8. *-lft-identity 56.3%

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

      9. +-commutative 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in t around inf 41.0%

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

   if -500 < t < 2.39999999999999994e-18

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 66.2%

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

      1. div-sub 66.2%

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

      2. sub-neg 66.2%

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

      3. *-inverses 66.2%

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

      4. metadata-eval 66.2%

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

      5. distribute-lft-in 66.2%

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

      6. associate-*r/ 66.2%

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

      7. metadata-eval 66.2%

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

      8. metadata-eval 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in t around 0 42.7%

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

Alternative 13: 19.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in z around inf 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-*r/ 99.9%

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

   3. metadata-eval 99.9%

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

   4. *-commutative 99.9%

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

   5. div-sub 99.9%

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

   6. sub-neg 99.9%

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

   7. *-inverses 99.9%

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

   8. metadata-eval 99.9%

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

   9. distribute-lft-in 99.9%

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

   10. metadata-eval 99.9%

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

   11. associate-+l+ 99.9%

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

   12. +-commutative 99.9%

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

   13. *-commutative 99.9%

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

   14. +-commutative 99.9%

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

   15. associate-/l/ 99.9%

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

   16. metadata-eval 99.9%

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

   17. associate-*r/ 99.9%

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

   18. *-rgt-identity 99.9%

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

   19. associate-*r/ 99.9%

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

5. Simplified 99.9%

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

6. Taylor expanded in x around 0 65.8%

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

   1. sub-neg 65.8%

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

   2. associate-/r* 65.8%

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

   3. associate-*r/ 65.8%

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

   4. associate-*l/ 65.8%

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

   5. distribute-rgt-in 65.8%

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

   6. metadata-eval 65.8%

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

   7. associate-*l/ 65.8%

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

   8. *-lft-identity 65.8%

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

   9. +-commutative 65.8%

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

8. Simplified 65.8%

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

9. Taylor expanded in t around inf 24.5%

   \[\leadsto \color{blue}{-2} \]
10. 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 2024086 
(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))))