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

Percentage Accurate: 86.4% → 99.0%

Time: 11.4s

Alternatives: 11

Speedup: 1.1×

• 24.2% 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: 86.4% 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: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x / y) + (-2.0 + ((1.0 / t) * (2.0 + (2.0 / 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) + ((1.0d0 / t) * (2.0d0 + (2.0d0 / z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

3. Taylor expanded in t around 0 98.7%

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

   1. sub-neg 98.7%

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

   2. metadata-eval 98.7%

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

   3. associate-*r/ 98.7%

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

   4. +-commutative 98.7%

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

   5. associate-*r/ 98.7%

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

   6. metadata-eval 98.7%

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

   7. metadata-eval 98.7%

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

   8. +-commutative 98.7%

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

   9. associate-/l/ 98.7%

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

   10. metadata-eval 98.7%

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

   11. associate-*r/ 98.7%

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

   12. *-rgt-identity 98.7%

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

   13. associate-*r/ 98.7%

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

   14. distribute-rgt-out 98.7%

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

   15. associate-*r/ 98.7%

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

   16. metadata-eval 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 2: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-13}:\\ \;\;\;\;-2 + t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 3.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.32 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)))
   (if (<= (/ x y) -3.8e+73)
     (/ x y)
     (if (<= (/ x y) 1e-13)
       (+ -2.0 t_1)
       (if (<= (/ x y) 3.7e+126)
         (+ (/ x y) -2.0)
         (if (<= (/ x y) 1.32e+156) t_1 (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double tmp;
	if ((x / y) <= -3.8e+73) {
		tmp = x / y;
	} else if ((x / y) <= 1e-13) {
		tmp = -2.0 + t_1;
	} else if ((x / y) <= 3.7e+126) {
		tmp = (x / y) + -2.0;
	} else if ((x / y) <= 1.32e+156) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    if ((x / y) <= (-3.8d+73)) then
        tmp = x / y
    else if ((x / y) <= 1d-13) then
        tmp = (-2.0d0) + t_1
    else if ((x / y) <= 3.7d+126) then
        tmp = (x / y) + (-2.0d0)
    else if ((x / y) <= 1.32d+156) then
        tmp = t_1
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double tmp;
	if ((x / y) <= -3.8e+73) {
		tmp = x / y;
	} else if ((x / y) <= 1e-13) {
		tmp = -2.0 + t_1;
	} else if ((x / y) <= 3.7e+126) {
		tmp = (x / y) + -2.0;
	} else if ((x / y) <= 1.32e+156) {
		tmp = t_1;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	tmp = 0
	if (x / y) <= -3.8e+73:
		tmp = x / y
	elif (x / y) <= 1e-13:
		tmp = -2.0 + t_1
	elif (x / y) <= 3.7e+126:
		tmp = (x / y) + -2.0
	elif (x / y) <= 1.32e+156:
		tmp = t_1
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	tmp = 0.0
	if (Float64(x / y) <= -3.8e+73)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1e-13)
		tmp = Float64(-2.0 + t_1);
	elseif (Float64(x / y) <= 3.7e+126)
		tmp = Float64(Float64(x / y) + -2.0);
	elseif (Float64(x / y) <= 1.32e+156)
		tmp = t_1;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	tmp = 0.0;
	if ((x / y) <= -3.8e+73)
		tmp = x / y;
	elseif ((x / y) <= 1e-13)
		tmp = -2.0 + t_1;
	elseif ((x / y) <= 3.7e+126)
		tmp = (x / y) + -2.0;
	elseif ((x / y) <= 1.32e+156)
		tmp = t_1;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -3.8e+73], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-13], N[(-2.0 + t$95$1), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.7e+126], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.32e+156], t$95$1, N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -3.80000000000000022e73 or 1.3199999999999999e156 < (/.f64 x y)

   1. Initial program 82.3%

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

   3. Taylor expanded in x around inf 85.0%

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

   if -3.80000000000000022e73 < (/.f64 x y) < 1e-13

   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 t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-/l/ 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*r/ 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. associate-*r/ 99.9%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   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 95.6%

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

      1. sub-neg 95.6%

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

      2. associate-/r* 95.6%

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

      3. associate-*r/ 95.6%

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

      4. associate-*l/ 95.5%

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

      5. distribute-rgt-in 95.6%

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

      6. associate-*l/ 95.6%

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

      7. associate-*r/ 95.6%

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

      8. *-lft-identity 95.6%

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

      9. metadata-eval 95.6%

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

      10. +-commutative 95.6%

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

   8. Simplified 95.6%

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

   if 1e-13 < (/.f64 x y) < 3.6999999999999998e126

   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 t around inf 66.9%

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

   if 3.6999999999999998e126 < (/.f64 x y) < 1.3199999999999999e156

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 87.7%

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

      1. associate-*r/ 87.7%

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

      2. metadata-eval 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-13}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.32 \cdot 10^{+156}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+215} \lor \neg \left(z \leq 7.6 \cdot 10^{+283}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -1.05e+145)
     t_2
     (if (<= z -2.7e-162)
       t_1
       (if (<= z 8.2e+26)
         (/ 2.0 (* t z))
         (if (or (<= z 5.5e+215) (not (<= z 7.6e+283))) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.05e+145) {
		tmp = t_2;
	} else if (z <= -2.7e-162) {
		tmp = t_1;
	} else if (z <= 8.2e+26) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 5.5e+215) || !(z <= 7.6e+283)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    t_2 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-1.05d+145)) then
        tmp = t_2
    else if (z <= (-2.7d-162)) then
        tmp = t_1
    else if (z <= 8.2d+26) then
        tmp = 2.0d0 / (t * z)
    else if ((z <= 5.5d+215) .or. (.not. (z <= 7.6d+283))) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.05e+145) {
		tmp = t_2;
	} else if (z <= -2.7e-162) {
		tmp = t_1;
	} else if (z <= 8.2e+26) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 5.5e+215) || !(z <= 7.6e+283)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -1.05e+145:
		tmp = t_2
	elif z <= -2.7e-162:
		tmp = t_1
	elif z <= 8.2e+26:
		tmp = 2.0 / (t * z)
	elif (z <= 5.5e+215) or not (z <= 7.6e+283):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.05e+145)
		tmp = t_2;
	elseif (z <= -2.7e-162)
		tmp = t_1;
	elseif (z <= 8.2e+26)
		tmp = Float64(2.0 / Float64(t * z));
	elseif ((z <= 5.5e+215) || !(z <= 7.6e+283))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.05e+145)
		tmp = t_2;
	elseif (z <= -2.7e-162)
		tmp = t_1;
	elseif (z <= 8.2e+26)
		tmp = 2.0 / (t * z);
	elseif ((z <= 5.5e+215) || ~((z <= 7.6e+283)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+145], t$95$2, If[LessEqual[z, -2.7e-162], t$95$1, If[LessEqual[z, 8.2e+26], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 5.5e+215], N[Not[LessEqual[z, 7.6e+283]], $MachinePrecision]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999995e145 or 5.5e215 < z < 7.6000000000000004e283

   1. Initial program 58.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 79.0%

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

      1. sub-neg 79.0%

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

      2. associate-/r* 79.0%

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

      3. associate-*r/ 79.0%

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

      4. associate-*l/ 79.0%

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

      5. distribute-rgt-in 79.0%

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

      6. associate-*l/ 79.0%

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

      7. associate-*r/ 79.0%

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

      8. *-lft-identity 79.0%

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

      9. metadata-eval 79.0%

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

      10. +-commutative 79.0%

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

   8. Simplified 79.0%

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

      1. *-un-lft-identity 79.0%

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

      2. associate-*l/ 79.0%

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

   10. Applied egg-rr 79.0%

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

   11. Taylor expanded in z around inf 79.0%

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

   if -1.04999999999999995e145 < z < -2.69999999999999984e-162 or 8.19999999999999967e26 < z < 5.5e215 or 7.6000000000000004e283 < z

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf 76.3%

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

   if -2.69999999999999984e-162 < z < 8.19999999999999967e26

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 96.7%

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

      1. sub-neg 96.7%

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

      2. metadata-eval 96.7%

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

      3. associate-*r/ 96.7%

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

      4. +-commutative 96.7%

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

      5. associate-*r/ 96.7%

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

      6. metadata-eval 96.7%

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

      7. metadata-eval 96.7%

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

      8. +-commutative 96.7%

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

      9. associate-/l/ 96.7%

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

      10. metadata-eval 96.7%

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

      11. associate-*r/ 96.7%

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

      12. *-rgt-identity 96.7%

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

      13. associate-*r/ 96.7%

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

      14. distribute-rgt-out 96.7%

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

      15. associate-*r/ 96.7%

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

      16. metadata-eval 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in z around 0 69.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+145}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+215} \lor \neg \left(z \leq 7.6 \cdot 10^{+283}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+215} \lor \neg \left(z \leq 2.5 \cdot 10^{+284}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)) (t_2 (+ -2.0 (/ 2.0 t))))
   (if (<= z -7e+144)
     t_2
     (if (<= z -1.25e-161)
       t_1
       (if (<= z 8.2e+26)
         (/ (/ 2.0 z) t)
         (if (or (<= z 5.5e+215) (not (<= z 2.5e+284))) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -7e+144) {
		tmp = t_2;
	} else if (z <= -1.25e-161) {
		tmp = t_1;
	} else if (z <= 8.2e+26) {
		tmp = (2.0 / z) / t;
	} else if ((z <= 5.5e+215) || !(z <= 2.5e+284)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    t_2 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-7d+144)) then
        tmp = t_2
    else if (z <= (-1.25d-161)) then
        tmp = t_1
    else if (z <= 8.2d+26) then
        tmp = (2.0d0 / z) / t
    else if ((z <= 5.5d+215) .or. (.not. (z <= 2.5d+284))) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -7e+144) {
		tmp = t_2;
	} else if (z <= -1.25e-161) {
		tmp = t_1;
	} else if (z <= 8.2e+26) {
		tmp = (2.0 / z) / t;
	} else if ((z <= 5.5e+215) || !(z <= 2.5e+284)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	t_2 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -7e+144:
		tmp = t_2
	elif z <= -1.25e-161:
		tmp = t_1
	elif z <= 8.2e+26:
		tmp = (2.0 / z) / t
	elif (z <= 5.5e+215) or not (z <= 2.5e+284):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	t_2 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -7e+144)
		tmp = t_2;
	elseif (z <= -1.25e-161)
		tmp = t_1;
	elseif (z <= 8.2e+26)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif ((z <= 5.5e+215) || !(z <= 2.5e+284))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	t_2 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -7e+144)
		tmp = t_2;
	elseif (z <= -1.25e-161)
		tmp = t_1;
	elseif (z <= 8.2e+26)
		tmp = (2.0 / z) / t;
	elseif ((z <= 5.5e+215) || ~((z <= 2.5e+284)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+144], t$95$2, If[LessEqual[z, -1.25e-161], t$95$1, If[LessEqual[z, 8.2e+26], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 5.5e+215], N[Not[LessEqual[z, 2.5e+284]], $MachinePrecision]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999996e144 or 5.5e215 < z < 2.5e284

   1. Initial program 58.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-/l/ 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-*r/ 100.0%

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

      12. *-rgt-identity 100.0%

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

      13. associate-*r/ 100.0%

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

      14. distribute-rgt-out 100.0%

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

      15. associate-*r/ 100.0%

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

      16. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 79.0%

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

      1. sub-neg 79.0%

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

      2. associate-/r* 79.0%

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

      3. associate-*r/ 79.0%

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

      4. associate-*l/ 79.0%

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

      5. distribute-rgt-in 79.0%

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

      6. associate-*l/ 79.0%

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

      7. associate-*r/ 79.0%

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

      8. *-lft-identity 79.0%

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

      9. metadata-eval 79.0%

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

      10. +-commutative 79.0%

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

   8. Simplified 79.0%

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

      1. *-un-lft-identity 79.0%

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

      2. associate-*l/ 79.0%

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

   10. Applied egg-rr 79.0%

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

   11. Taylor expanded in z around inf 79.0%

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

   if -6.9999999999999996e144 < z < -1.25e-161 or 8.19999999999999967e26 < z < 5.5e215 or 2.5e284 < z

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf 76.3%

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

   if -1.25e-161 < z < 8.19999999999999967e26

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. remove-double-neg 96.7%

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

      3. distribute-frac-neg 96.7%

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

      4. unsub-neg 96.7%

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

      5. *-commutative 96.7%

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

      6. associate-*r* 96.7%

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

      7. distribute-rgt1-in 96.7%

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

      8. associate-*r/ 96.7%

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

      9. /-rgt-identity 96.7%

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

      10. fma-neg 96.7%

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

      11. /-rgt-identity 96.7%

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

      12. *-commutative 96.7%

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

      13. fma-def 96.7%

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

      14. *-commutative 96.7%

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

      15. distribute-frac-neg 96.7%

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

      16. remove-double-neg 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in x around 0 77.5%

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

   6. Taylor expanded in z around 0 69.3%

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

      1. associate-/r* 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in t around 0 69.3%

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

       1. associate-/l/ 69.3%

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

   11. Simplified 69.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+144}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+215} \lor \neg \left(z \leq 2.5 \cdot 10^{+284}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4200000000000 \lor \neg \left(\frac{x}{y} \leq 245\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4200000000000.0) (not (<= (/ x y) 245.0)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4200000000000.0) || !((x / y) <= 245.0)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4200000000000.0d0)) .or. (.not. ((x / y) <= 245.0d0))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4200000000000.0) || !((x / y) <= 245.0)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4200000000000.0) or not ((x / y) <= 245.0):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4200000000000.0) || !(Float64(x / y) <= 245.0))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4200000000000.0) || ~(((x / y) <= 245.0)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4200000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 245.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.2e12 or 245 < (/.f64 x y)

   1. Initial program 86.9%

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

   3. Taylor expanded in z around 0 90.6%

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

   if -4.2e12 < (/.f64 x y) < 245

   1. Initial program 86.3%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-/l/ 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*r/ 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. associate-*r/ 99.9%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   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 98.8%

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

      1. sub-neg 98.8%

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

      2. associate-/r* 98.8%

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

      3. associate-*r/ 98.8%

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

      4. associate-*l/ 98.8%

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

      5. distribute-rgt-in 98.8%

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

      6. associate-*l/ 98.8%

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

      7. associate-*r/ 98.8%

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

      8. *-lft-identity 98.8%

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

      9. metadata-eval 98.8%

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

      10. +-commutative 98.8%

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

   8. Simplified 98.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4200000000000 \lor \neg \left(\frac{x}{y} \leq 245\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4200000000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 3550:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4200000000000.0)
   (+ (/ x y) (/ 2.0 (* t z)))
   (if (<= (/ x y) 3550.0)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (/ (/ 2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4200000000000.0) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 3550.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4200000000000.0d0)) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else if ((x / y) <= 3550.0d0) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4200000000000.0) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 3550.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4200000000000.0:
		tmp = (x / y) + (2.0 / (t * z))
	elif (x / y) <= 3550.0:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4200000000000.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	elseif (Float64(x / y) <= 3550.0)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4200000000000.0)
		tmp = (x / y) + (2.0 / (t * z));
	elseif ((x / y) <= 3550.0)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4200000000000.0], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3550.0], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.2e12

   1. Initial program 81.4%

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

   3. Taylor expanded in z around 0 88.9%

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

   if -4.2e12 < (/.f64 x y) < 3550

   1. Initial program 86.3%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-/l/ 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*r/ 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. associate-*r/ 99.9%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   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 98.8%

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

      1. sub-neg 98.8%

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

      2. associate-/r* 98.8%

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

      3. associate-*r/ 98.8%

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

      4. associate-*l/ 98.8%

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

      5. distribute-rgt-in 98.8%

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

      6. associate-*l/ 98.8%

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

      7. associate-*r/ 98.8%

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

      8. *-lft-identity 98.8%

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

      9. metadata-eval 98.8%

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

      10. +-commutative 98.8%

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

   8. Simplified 98.8%

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

   if 3550 < (/.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 0 91.9%

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

      1. associate-/r* 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4200000000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 3550:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -14000000000000 \lor \neg \left(\frac{x}{y} \leq 15500\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -14000000000000.0) (not (<= (/ x y) 15500.0)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -14000000000000.0) || !((x / y) <= 15500.0)) {
		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) <= (-14000000000000.0d0)) .or. (.not. ((x / y) <= 15500.0d0))) 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) <= -14000000000000.0) || !((x / y) <= 15500.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -14000000000000.0) or not ((x / y) <= 15500.0):
		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) <= -14000000000000.0) || !(Float64(x / y) <= 15500.0))
		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) <= -14000000000000.0) || ~(((x / y) <= 15500.0)))
		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], -14000000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 15500.0]], $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) < -1.4e13 or 15500 < (/.f64 x y)

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf 70.8%

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

   if -1.4e13 < (/.f64 x y) < 15500

   1. Initial program 86.3%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-/l/ 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*r/ 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. associate-*r/ 99.9%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   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 98.8%

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

      1. sub-neg 98.8%

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

      2. associate-/r* 98.8%

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

      3. associate-*r/ 98.8%

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

      4. associate-*l/ 98.8%

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

      5. distribute-rgt-in 98.8%

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

      6. associate-*l/ 98.8%

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

      7. associate-*r/ 98.8%

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

      8. *-lft-identity 98.8%

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

      9. metadata-eval 98.8%

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

      10. +-commutative 98.8%

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

   8. Simplified 98.8%

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

      1. *-un-lft-identity 98.8%

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

      2. associate-*l/ 98.8%

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

   10. Applied egg-rr 98.8%

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

   11. Taylor expanded in z around inf 60.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -14000000000000 \lor \neg \left(\frac{x}{y} \leq 15500\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3100000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3100000000000.0) (not (<= (/ x y) 1e-13)))
   (+ (/ x y) -2.0)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3100000000000.0) || !((x / y) <= 1e-13)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-3100000000000.0d0)) .or. (.not. ((x / y) <= 1d-13))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = (-2.0d0) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3100000000000.0) || !((x / y) <= 1e-13)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3100000000000.0) or not ((x / y) <= 1e-13):
		tmp = (x / y) + -2.0
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3100000000000.0) || !(Float64(x / y) <= 1e-13))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3100000000000.0) || ~(((x / y) <= 1e-13)))
		tmp = (x / y) + -2.0;
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3100000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-13]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.1e12 or 1e-13 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf 72.4%

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

   if -3.1e12 < (/.f64 x y) < 1e-13

   1. Initial program 86.8%

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

   3. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-*r/ 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-/l/ 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*r/ 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. associate-*r/ 99.9%

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

      14. distribute-rgt-out 99.9%

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

      15. associate-*r/ 99.9%

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

      16. metadata-eval 99.9%

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

   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 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-/r* 99.5%

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

      3. associate-*r/ 99.5%

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

      4. associate-*l/ 99.5%

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

      5. distribute-rgt-in 99.5%

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

      6. associate-*l/ 99.5%

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

      7. associate-*r/ 99.5%

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

      8. *-lft-identity 99.5%

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

      9. metadata-eval 99.5%

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

      10. +-commutative 99.5%

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

   8. Simplified 99.5%

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

      1. *-un-lft-identity 99.5%

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

      2. associate-*l/ 99.5%

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

   10. Applied egg-rr 99.5%

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

   11. Taylor expanded in z around inf 60.6%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3100000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -46000 \lor \neg \left(\frac{x}{y} \leq 2\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -46000.0) (not (<= (/ x y) 2.0))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -46000.0) || !((x / y) <= 2.0)) {
		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) <= (-46000.0d0)) .or. (.not. ((x / y) <= 2.0d0))) 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) <= -46000.0) || !((x / y) <= 2.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -46000.0) or not ((x / y) <= 2.0):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -46000.0) || !(Float64(x / y) <= 2.0))
		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) <= -46000.0) || ~(((x / y) <= 2.0)))
		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], -46000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -46000 or 2 < (/.f64 x y)

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 69.8%

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

   if -46000 < (/.f64 x y) < 2

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. remove-double-neg 86.1%

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

      3. distribute-frac-neg 86.1%

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

      4. unsub-neg 86.1%

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

      5. *-commutative 86.1%

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

      6. associate-*r* 86.1%

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

      7. distribute-rgt1-in 86.1%

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

      8. associate-*r/ 86.0%

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

      9. /-rgt-identity 86.0%

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

      10. fma-neg 86.0%

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

      11. /-rgt-identity 86.0%

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

      12. *-commutative 86.0%

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

      13. fma-def 86.0%

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

      14. *-commutative 86.0%

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

      15. distribute-frac-neg 86.0%

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

      16. remove-double-neg 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around 0 85.2%

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

   6. Taylor expanded in t around inf 39.0%

      \[\leadsto 2 \cdot \color{blue}{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -46000 \lor \neg \left(\frac{x}{y} \leq 2\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-21} \lor \neg \left(t \leq 0.0013\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.5e-21) (not (<= t 0.0013)))
   (+ (/ 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 <= -4.5e-21) || !(t <= 0.0013)) {
		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 <= (-4.5d-21)) .or. (.not. (t <= 0.0013d0))) 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 <= -4.5e-21) || !(t <= 0.0013)) {
		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 <= -4.5e-21) or not (t <= 0.0013):
		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 <= -4.5e-21) || !(t <= 0.0013))
		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 <= -4.5e-21) || ~((t <= 0.0013)))
		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, -4.5e-21], N[Not[LessEqual[t, 0.0013]], $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 < -4.49999999999999968e-21 or 0.0012999999999999999 < t

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf 82.3%

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

   if -4.49999999999999968e-21 < t < 0.0012999999999999999

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. metadata-eval 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-21} \lor \neg \left(t \leq 0.0013\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 20.0% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

   1. +-commutative 86.6%

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

   2. remove-double-neg 86.6%

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

   3. distribute-frac-neg 86.6%

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

   4. unsub-neg 86.6%

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

   5. *-commutative 86.6%

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

   6. associate-*r* 86.6%

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

   7. distribute-rgt1-in 86.6%

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

   8. associate-*r/ 86.5%

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

   9. /-rgt-identity 86.5%

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

   10. fma-neg 86.5%

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

   11. /-rgt-identity 86.5%

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

   12. *-commutative 86.5%

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

   13. fma-def 86.5%

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

   14. *-commutative 86.5%

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

   15. distribute-frac-neg 86.5%

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

   16. remove-double-neg 86.5%

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

3. Simplified 86.5%

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

5. Taylor expanded in x around 0 58.5%

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

6. Taylor expanded in t around inf 20.1%

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

7. Final simplification 20.1%

   \[\leadsto -2 \]
8. Add Preprocessing

Developer target: 99.0% 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 2024031 
(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))))