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

Percentage Accurate: 86.5% → 99.2%

Time: 16.2s

Alternatives: 13

Speedup: 1.3×

• 23.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

2. Taylor expanded in t around 0 99.9%

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

   1. associate--l+ 99.9%

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

   2. associate-*r/ 99.9%

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

   3. metadata-eval 99.9%

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

4. Simplified 99.9%

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

5. Taylor expanded in t around 0 99.9%

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

   1. associate--l+ 99.9%

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

   2. associate-*r/ 99.9%

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

   3. metadata-eval 99.9%

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

   4. +-commutative 99.9%

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

   5. sub-neg 99.9%

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

   6. metadata-eval 99.9%

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

   7. associate-+r+ 99.9%

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

   8. +-commutative 99.9%

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

   9. +-commutative 99.9%

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

   10. +-commutative 99.9%

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

   11. associate-+l+ 99.9%

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

   12. metadata-eval 99.9%

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

   13. associate-*l/ 99.9%

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

   14. metadata-eval 99.9%

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

   15. associate-*l/ 99.9%

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

   16. associate-/r/ 99.9%

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

   17. associate-/l* 99.9%

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

   18. metadata-eval 99.9%

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

   19. associate-*r/ 99.9%

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

   20. associate-/r/ 99.9%

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

   21. distribute-lft-in 99.9%

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

   22. associate-*r/ 99.9%

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

7. Simplified 99.9%

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

8. Final simplification 99.9%

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

Alternative 2: 91.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-53} \lor \neg \left(z \leq 160000000000\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.3e-53) (not (<= z 160000000000.0)))
   (+ (/ 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 <= -5.3e-53) || !(z <= 160000000000.0)) {
		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 <= (-5.3d-53)) .or. (.not. (z <= 160000000000.0d0))) 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 <= -5.3e-53) || !(z <= 160000000000.0)) {
		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 <= -5.3e-53) or not (z <= 160000000000.0):
		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 <= -5.3e-53) || !(z <= 160000000000.0))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.3e-53) || ~((z <= 160000000000.0)))
		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, -5.3e-53], N[Not[LessEqual[z, 160000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3e-53 or 1.6e11 < z

   1. Initial program 81.3%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 97.2%

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

      1. sub-neg 97.2%

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

      2. associate-*r/ 97.2%

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

      3. metadata-eval 97.2%

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

      4. metadata-eval 97.2%

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

      5. +-commutative 97.2%

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

   7. Simplified 97.2%

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

   if -5.3e-53 < z < 1.6e11

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 92.3%

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

      1. associate-*r/ 92.3%

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

      2. metadata-eval 92.3%

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

   7. Simplified 92.3%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-53} \lor \neg \left(z \leq 160000000000\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 3: 62.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\frac{1}{t} + -1\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (/ 1.0 t) -1.0))))
   (if (<= z -6.2e+124)
     t_1
     (if (<= z -2.35e-122)
       (- (/ x y) 2.0)
       (if (<= z 4e-28) (/ (/ 2.0 t) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((1.0 / t) + -1.0);
	double tmp;
	if (z <= -6.2e+124) {
		tmp = t_1;
	} else if (z <= -2.35e-122) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4e-28) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((1.0d0 / t) + (-1.0d0))
    if (z <= (-6.2d+124)) then
        tmp = t_1
    else if (z <= (-2.35d-122)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 4d-28) then
        tmp = (2.0d0 / t) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((1.0 / t) + -1.0);
	double tmp;
	if (z <= -6.2e+124) {
		tmp = t_1;
	} else if (z <= -2.35e-122) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4e-28) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((1.0 / t) + -1.0)
	tmp = 0
	if z <= -6.2e+124:
		tmp = t_1
	elif z <= -2.35e-122:
		tmp = (x / y) - 2.0
	elif z <= 4e-28:
		tmp = (2.0 / t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(1.0 / t) + -1.0))
	tmp = 0.0
	if (z <= -6.2e+124)
		tmp = t_1;
	elseif (z <= -2.35e-122)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 4e-28)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((1.0 / t) + -1.0);
	tmp = 0.0;
	if (z <= -6.2e+124)
		tmp = t_1;
	elseif (z <= -2.35e-122)
		tmp = (x / y) - 2.0;
	elseif (z <= 4e-28)
		tmp = (2.0 / t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(1.0 / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+124], t$95$1, If[LessEqual[z, -2.35e-122], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 4e-28], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000004e124 or 3.99999999999999988e-28 < z

   1. Initial program 78.6%

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

   2. Taylor expanded in z around inf 95.7%

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

      1. div-sub 95.8%

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

      2. sub-neg 95.8%

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

      3. *-inverses 95.8%

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

      4. metadata-eval 95.8%

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

   4. Simplified 95.8%

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

   5. Taylor expanded in x around 0 70.1%

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

   if -6.2000000000000004e124 < z < -2.35e-122

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 68.4%

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

   if -2.35e-122 < z < 3.99999999999999988e-28

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. +-commutative 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+l+ 99.8%

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

      12. metadata-eval 99.8%

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

      13. associate-*l/ 99.8%

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

      14. metadata-eval 99.8%

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

      15. associate-*l/ 99.8%

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

      16. associate-/r/ 99.8%

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

      17. associate-/l* 99.7%

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

      18. metadata-eval 99.7%

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

      19. associate-*r/ 99.7%

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

      20. associate-/r/ 99.8%

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

      21. distribute-lft-in 99.8%

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

      22. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 72.7%

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

      1. associate-/r* 72.7%

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

   10. Simplified 72.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+124}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \end{array} \]

Alternative 4: 65.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+25)
   (+ (/ x y) (/ 2.0 t))
   (if (<= z -1.05e-121)
     (- (/ x y) 2.0)
     (if (<= z 4.6e-33) (/ (/ 2.0 t) z) (* 2.0 (+ (/ 1.0 t) -1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+25) {
		tmp = (x / y) + (2.0 / t);
	} else if (z <= -1.05e-121) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4.6e-33) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = 2.0 * ((1.0 / t) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.7d+25)) then
        tmp = (x / y) + (2.0d0 / t)
    else if (z <= (-1.05d-121)) then
        tmp = (x / y) - 2.0d0
    else if (z <= 4.6d-33) then
        tmp = (2.0d0 / t) / z
    else
        tmp = 2.0d0 * ((1.0d0 / t) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+25) {
		tmp = (x / y) + (2.0 / t);
	} else if (z <= -1.05e-121) {
		tmp = (x / y) - 2.0;
	} else if (z <= 4.6e-33) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = 2.0 * ((1.0 / t) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+25:
		tmp = (x / y) + (2.0 / t)
	elif z <= -1.05e-121:
		tmp = (x / y) - 2.0
	elif z <= 4.6e-33:
		tmp = (2.0 / t) / z
	else:
		tmp = 2.0 * ((1.0 / t) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+25)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (z <= -1.05e-121)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 4.6e-33)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = Float64(2.0 * Float64(Float64(1.0 / t) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e+25)
		tmp = (x / y) + (2.0 / t);
	elseif (z <= -1.05e-121)
		tmp = (x / y) - 2.0;
	elseif (z <= 4.6e-33)
		tmp = (2.0 / t) / z;
	else
		tmp = 2.0 * ((1.0 / t) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+25], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e-121], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 4.6e-33], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], N[(2.0 * N[(N[(1.0 / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7e25

   1. Initial program 80.8%

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

      1. associate-/r* 58.7%

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

      2. div-inv 58.7%

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

      3. +-commutative 58.7%

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

      4. *-commutative 58.7%

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

      5. associate-*l* 58.7%

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

      6. fma-def 58.7%

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

   3. Applied egg-rr 58.7%

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

   4. Taylor expanded in t around 0 82.1%

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

      1. *-commutative 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in z around inf 82.3%

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

      1. associate-*r/ 82.3%

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

      2. metadata-eval 82.3%

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

   9. Simplified 82.3%

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

   if -2.7e25 < z < -1.0499999999999999e-121

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 72.6%

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

   if -1.0499999999999999e-121 < z < 4.59999999999999971e-33

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. +-commutative 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+l+ 99.8%

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

      12. metadata-eval 99.8%

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

      13. associate-*l/ 99.8%

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

      14. metadata-eval 99.8%

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

      15. associate-*l/ 99.8%

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

      16. associate-/r/ 99.8%

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

      17. associate-/l* 99.7%

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

      18. metadata-eval 99.7%

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

      19. associate-*r/ 99.7%

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

      20. associate-/r/ 99.8%

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

      21. distribute-lft-in 99.8%

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

      22. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 72.7%

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

      1. associate-/r* 72.7%

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

   10. Simplified 72.7%

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

   if 4.59999999999999971e-33 < z

   1. Initial program 79.8%

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

   2. Taylor expanded in z around inf 93.0%

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

      1. div-sub 93.0%

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

      2. sub-neg 93.0%

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

      3. *-inverses 93.0%

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

      4. metadata-eval 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in x around 0 68.2%

      \[\leadsto \color{blue}{2 \cdot \left(\frac{1}{t} - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \end{array} \]

Alternative 5: 80.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0029 \lor \neg \left(t \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.0029) (not (<= t 6.5e+18)))
   (- (/ x y) 2.0)
   (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0029) || !(t <= 6.5e+18)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-0.0029d0)) .or. (.not. (t <= 6.5d+18))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) * (1.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0029) || !(t <= 6.5e+18)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.0029) or not (t <= 6.5e+18):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) * (1.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.0029) || !(t <= 6.5e+18))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.0029) || ~((t <= 6.5e+18)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.0029], N[Not[LessEqual[t, 6.5e+18]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0029 or 6.5e18 < t

   1. Initial program 79.5%

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

   2. Taylor expanded in t around inf 82.1%

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

   if -0.0029 < t < 6.5e18

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 85.8%

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

      1. associate-*r/ 85.8%

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

      2. metadata-eval 85.8%

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

   4. Simplified 85.8%

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

      1. div-inv 85.8%

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

   6. Applied egg-rr 85.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0029 \lor \neg \left(t \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \]

Alternative 6: 80.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-17} \lor \neg \left(t \leq 7.5 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e-17) (not (<= t 7.5e-53)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-17) || !(t <= 7.5e-53)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.2d-17)) .or. (.not. (t <= 7.5d-53))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-17) || !(t <= 7.5e-53)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e-17) or not (t <= 7.5e-53):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e-17) || !(t <= 7.5e-53))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.2e-17) || ~((t <= 7.5e-53)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e-17], N[Not[LessEqual[t, 7.5e-53]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000006e-17 or 7.5000000000000001e-53 < t

   1. Initial program 81.0%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. sub-neg 81.0%

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

      2. associate-*r/ 81.0%

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

      3. metadata-eval 81.0%

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

      4. metadata-eval 81.0%

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

      5. +-commutative 81.0%

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

   7. Simplified 81.0%

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

   if -5.20000000000000006e-17 < t < 7.5000000000000001e-53

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. associate-*r/ 87.4%

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

      2. metadata-eval 87.4%

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

   4. Simplified 87.4%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-17} \lor \neg \left(t \leq 7.5 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 7: 92.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-53} \lor \neg \left(z \leq 1.35 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.3e-53) (not (<= z 1.35e-30)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e-53) || !(z <= 1.35e-30)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.3d-53)) .or. (.not. (z <= 1.35d-30))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + (2.0d0 / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e-53) || !(z <= 1.35e-30)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.3e-53) or not (z <= 1.35e-30):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.3e-53) || !(z <= 1.35e-30))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.3e-53) || ~((z <= 1.35e-30)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.3e-53], N[Not[LessEqual[z, 1.35e-30]], $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[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3e-53 or 1.34999999999999994e-30 < z

   1. Initial program 82.5%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 94.2%

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

      1. sub-neg 94.2%

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

      2. associate-*r/ 94.2%

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

      3. metadata-eval 94.2%

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

      4. metadata-eval 94.2%

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

      5. +-commutative 94.2%

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

   7. Simplified 94.2%

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

   if -5.3e-53 < z < 1.34999999999999994e-30

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 92.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-53} \lor \neg \left(z \leq 1.35 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 8: 92.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-53} \lor \neg \left(z \leq 3.85 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.3e-53) (not (<= z 3.85e-28)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e-53) || !(z <= 3.85e-28)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.3d-53)) .or. (.not. (z <= 3.85d-28))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e-53) || !(z <= 3.85e-28)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.3e-53) or not (z <= 3.85e-28):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.3e-53) || !(z <= 3.85e-28))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.3e-53) || ~((z <= 3.85e-28)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.3e-53], N[Not[LessEqual[z, 3.85e-28]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3e-53 or 3.85e-28 < z

   1. Initial program 82.5%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 94.2%

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

      1. sub-neg 94.2%

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

      2. associate-*r/ 94.2%

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

      3. metadata-eval 94.2%

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

      4. metadata-eval 94.2%

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

      5. +-commutative 94.2%

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

   7. Simplified 94.2%

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

   if -5.3e-53 < z < 3.85e-28

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 92.6%

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

      1. *-commutative 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in x around 0 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. metadata-eval 92.6%

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

      4. associate-/r* 92.6%

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

   10. Simplified 92.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-53} \lor \neg \left(z \leq 3.85 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]

Alternative 9: 60.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+125}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-122} \lor \neg \left(z \leq 3.3 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e+125)
   (/ 2.0 t)
   (if (or (<= z -8.5e-122) (not (<= z 3.3e-19)))
     (- (/ x y) 2.0)
     (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+125) {
		tmp = 2.0 / t;
	} else if ((z <= -8.5e-122) || !(z <= 3.3e-19)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.65d+125)) then
        tmp = 2.0d0 / t
    else if ((z <= (-8.5d-122)) .or. (.not. (z <= 3.3d-19))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+125) {
		tmp = 2.0 / t;
	} else if ((z <= -8.5e-122) || !(z <= 3.3e-19)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+125:
		tmp = 2.0 / t
	elif (z <= -8.5e-122) or not (z <= 3.3e-19):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e+125)
		tmp = Float64(2.0 / t);
	elseif ((z <= -8.5e-122) || !(z <= 3.3e-19))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.65e+125)
		tmp = 2.0 / t;
	elseif ((z <= -8.5e-122) || ~((z <= 3.3e-19)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e+125], N[(2.0 / t), $MachinePrecision], If[Or[LessEqual[z, -8.5e-122], N[Not[LessEqual[z, 3.3e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000003e125

   1. Initial program 76.8%

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

   2. Taylor expanded in t around 0 56.0%

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

      1. associate-*r/ 56.0%

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

      2. metadata-eval 56.0%

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

   4. Simplified 56.0%

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

      1. div-inv 56.0%

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

   6. Applied egg-rr 56.0%

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

   7. Taylor expanded in z around inf 56.0%

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

   if -1.65000000000000003e125 < z < -8.50000000000000003e-122 or 3.2999999999999998e-19 < z

   1. Initial program 85.8%

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

   2. Taylor expanded in t around inf 61.7%

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

   if -8.50000000000000003e-122 < z < 3.2999999999999998e-19

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. +-commutative 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. associate-+r+ 99.8%

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

      8. +-commutative 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+l+ 99.8%

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

      12. metadata-eval 99.8%

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

      13. associate-*l/ 99.8%

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

      14. metadata-eval 99.8%

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

      15. associate-*l/ 99.8%

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

      16. associate-/r/ 99.8%

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

      17. associate-/l* 99.7%

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

      18. metadata-eval 99.7%

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

      19. associate-*r/ 99.7%

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

      20. associate-/r/ 99.8%

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

      21. distribute-lft-in 99.8%

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

      22. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 72.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+125}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-122} \lor \neg \left(z \leq 3.3 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]

Alternative 10: 80.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0045 \lor \neg \left(t \leq 6.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.0045) (not (<= t 6.4e+18)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0045) || !(t <= 6.4e+18)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-0.0045d0)) .or. (.not. (t <= 6.4d+18))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0045) || !(t <= 6.4e+18)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.0045) or not (t <= 6.4e+18):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.0045) || !(t <= 6.4e+18))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.0045) || ~((t <= 6.4e+18)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.0045], N[Not[LessEqual[t, 6.4e+18]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.00449999999999999966 or 6.4e18 < t

   1. Initial program 79.5%

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

   2. Taylor expanded in t around inf 82.1%

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

   if -0.00449999999999999966 < t < 6.4e18

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 85.8%

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

      1. associate-*r/ 85.8%

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

      2. metadata-eval 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0045 \lor \neg \left(t \leq 6.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 11: 46.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40000000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.65 \cdot 10^{+90}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -40000000000000.0)
   (/ x y)
   (if (<= (/ x y) 3.65e+90) (/ 2.0 t) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -40000000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 3.65e+90) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-40000000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 3.65d+90) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -40000000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 3.65e+90) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -40000000000000.0:
		tmp = x / y
	elif (x / y) <= 3.65e+90:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -40000000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 3.65e+90)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -40000000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 3.65e+90)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -40000000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.65e+90], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4e13 or 3.64999999999999997e90 < (/.f64 x y)

   1. Initial program 90.8%

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

   2. Taylor expanded in x around inf 69.1%

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

   if -4e13 < (/.f64 x y) < 3.64999999999999997e90

   1. Initial program 90.8%

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

   2. Taylor expanded in t around 0 72.2%

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

      1. associate-*r/ 72.2%

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

      2. metadata-eval 72.2%

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

   4. Simplified 72.2%

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

      1. div-inv 72.2%

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

   6. Applied egg-rr 72.2%

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

   7. Taylor expanded in z around inf 30.1%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40000000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.65 \cdot 10^{+90}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 12: 61.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.95 \cdot 10^{-57} \lor \neg \left(t \leq 1.3 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.95e-57) (not (<= t 1.3e-33))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.95e-57) || !(t <= 1.3e-33)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.95d-57)) .or. (.not. (t <= 1.3d-33))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.95e-57) || !(t <= 1.3e-33)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.95e-57) or not (t <= 1.3e-33):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.95e-57) || !(t <= 1.3e-33))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.95e-57) || ~((t <= 1.3e-33)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.95e-57], N[Not[LessEqual[t, 1.3e-33]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9499999999999999e-57 or 1.29999999999999997e-33 < t

   1. Initial program 82.2%

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

   2. Taylor expanded in t around inf 75.5%

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

   if -3.9499999999999999e-57 < t < 1.29999999999999997e-33

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 88.9%

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

      1. associate-*r/ 88.9%

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

      2. metadata-eval 88.9%

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

   4. Simplified 88.9%

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

      1. div-inv 88.9%

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

   6. Applied egg-rr 88.9%

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

   7. Taylor expanded in z around inf 39.3%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.95 \cdot 10^{-57} \lor \neg \left(t \leq 1.3 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 13: 19.8% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

2. Taylor expanded in t around 0 57.0%

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

   1. associate-*r/ 57.0%

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

   2. metadata-eval 57.0%

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

4. Simplified 57.0%

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

   1. div-inv 57.0%

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

6. Applied egg-rr 57.0%

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

7. Taylor expanded in z around inf 22.1%

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

8. Final simplification 22.1%

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

Developer target: 99.2% 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 2023279 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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