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

Percentage Accurate: 86.6% → 99.1%

Time: 10.8s

Alternatives: 13

Speedup: 1.3×

• 23.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.1× 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 83.8%

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

3. Taylor expanded in z around inf 98.7%

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

   1. +-commutative 98.7%

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

   2. associate-*r/ 98.7%

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

   3. metadata-eval 98.7%

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

   4. *-commutative 98.7%

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

   5. div-sub 98.7%

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

   6. sub-neg 98.7%

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

   7. *-inverses 98.7%

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

   8. metadata-eval 98.7%

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

   9. distribute-lft-in 98.7%

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

   10. metadata-eval 98.7%

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

   11. associate-+l+ 98.7%

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

   12. +-commutative 98.7%

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

   13. *-commutative 98.7%

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

   14. +-commutative 98.7%

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

   15. associate-/l/ 98.7%

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

   16. metadata-eval 98.7%

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

   17. associate-*r/ 98.7%

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

   18. *-rgt-identity 98.7%

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

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: 80.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -6.3:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-18}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+25} \lor \neg \left(t \leq 1.6 \cdot 10^{+61}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -6.3)
     t_1
     (if (<= t 4e-18)
       (/ (+ 2.0 (/ 2.0 z)) t)
       (if (or (<= t 1.75e+25) (not (<= t 1.6e+61)))
         t_1
         (- -2.0 (/ (/ -2.0 z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -6.3) {
		tmp = t_1;
	} else if (t <= 4e-18) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 1.75e+25) || !(t <= 1.6e+61)) {
		tmp = t_1;
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-6.3d0)) then
        tmp = t_1
    else if (t <= 4d-18) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if ((t <= 1.75d+25) .or. (.not. (t <= 1.6d+61))) then
        tmp = t_1
    else
        tmp = (-2.0d0) - (((-2.0d0) / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -6.3) {
		tmp = t_1;
	} else if (t <= 4e-18) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((t <= 1.75e+25) || !(t <= 1.6e+61)) {
		tmp = t_1;
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -6.3:
		tmp = t_1
	elif t <= 4e-18:
		tmp = (2.0 + (2.0 / z)) / t
	elif (t <= 1.75e+25) or not (t <= 1.6e+61):
		tmp = t_1
	else:
		tmp = -2.0 - ((-2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -6.3)
		tmp = t_1;
	elseif (t <= 4e-18)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif ((t <= 1.75e+25) || !(t <= 1.6e+61))
		tmp = t_1;
	else
		tmp = Float64(-2.0 - Float64(Float64(-2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -6.3)
		tmp = t_1;
	elseif (t <= 4e-18)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif ((t <= 1.75e+25) || ~((t <= 1.6e+61)))
		tmp = t_1;
	else
		tmp = -2.0 - ((-2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -6.3], t$95$1, If[LessEqual[t, 4e-18], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[t, 1.75e+25], N[Not[LessEqual[t, 1.6e+61]], $MachinePrecision]], t$95$1, N[(-2.0 - N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.29999999999999982 or 4.0000000000000003e-18 < t < 1.75e25 or 1.5999999999999999e61 < t

   1. Initial program 69.4%

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

   3. Taylor expanded in t around inf 85.1%

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

   if -6.29999999999999982 < t < 4.0000000000000003e-18

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. metadata-eval 77.2%

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

   5. Simplified 77.2%

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

   if 1.75e25 < t < 1.5999999999999999e61

   1. Initial program 85.0%

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

   3. Taylor expanded in z around inf 99.3%

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

      1. +-commutative 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. *-commutative 99.3%

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

      5. div-sub 99.3%

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

      6. sub-neg 99.3%

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

      7. *-inverses 99.3%

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

      8. metadata-eval 99.3%

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

      9. distribute-lft-in 99.3%

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

      10. metadata-eval 99.3%

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

      11. associate-+l+ 99.3%

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

      12. +-commutative 99.3%

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

      13. *-commutative 99.3%

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

      14. +-commutative 99.3%

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

      15. associate-/l/ 99.8%

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

      16. metadata-eval 99.8%

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

      17. associate-*r/ 99.8%

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

      18. *-rgt-identity 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 99.3%

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

      1. associate--l+ 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. sub-neg 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.8%

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

      9. *-rgt-identity 99.8%

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

      10. associate-*r/ 99.8%

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

      11. metadata-eval 99.8%

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

      12. associate-+l+ 99.8%

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

      13. metadata-eval 99.8%

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

      14. associate-*r/ 99.8%

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

      15. distribute-rgt-in 99.8%

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

      16. associate-*l/ 99.8%

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

      17. *-lft-identity 99.8%

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

      18. +-commutative 99.8%

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

      19. remove-double-neg 99.8%

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

      20. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in z around 0 99.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-18}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+25} \lor \neg \left(t \leq 1.6 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-92}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 10500 \lor \neg \left(z \leq 1.25 \cdot 10^{+36}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -6.2e-72)
     t_1
     (if (<= z 1.9e-92)
       (/ 2.0 (* t z))
       (if (or (<= z 10500.0) (not (<= z 1.25e+36)))
         t_1
         (- -2.0 (/ -2.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -6.2e-72) {
		tmp = t_1;
	} else if (z <= 1.9e-92) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 10500.0) || !(z <= 1.25e+36)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-6.2d-72)) then
        tmp = t_1
    else if (z <= 1.9d-92) then
        tmp = 2.0d0 / (t * z)
    else if ((z <= 10500.0d0) .or. (.not. (z <= 1.25d+36))) then
        tmp = t_1
    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 t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -6.2e-72) {
		tmp = t_1;
	} else if (z <= 1.9e-92) {
		tmp = 2.0 / (t * z);
	} else if ((z <= 10500.0) || !(z <= 1.25e+36)) {
		tmp = t_1;
	} else {
		tmp = -2.0 - (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -6.2e-72:
		tmp = t_1
	elif z <= 1.9e-92:
		tmp = 2.0 / (t * z)
	elif (z <= 10500.0) or not (z <= 1.25e+36):
		tmp = t_1
	else:
		tmp = -2.0 - (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -6.2e-72)
		tmp = t_1;
	elseif (z <= 1.9e-92)
		tmp = Float64(2.0 / Float64(t * z));
	elseif ((z <= 10500.0) || !(z <= 1.25e+36))
		tmp = t_1;
	else
		tmp = Float64(-2.0 - Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -6.2e-72)
		tmp = t_1;
	elseif (z <= 1.9e-92)
		tmp = 2.0 / (t * z);
	elseif ((z <= 10500.0) || ~((z <= 1.25e+36)))
		tmp = t_1;
	else
		tmp = -2.0 - (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -6.2e-72], t$95$1, If[LessEqual[z, 1.9e-92], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 10500.0], N[Not[LessEqual[z, 1.25e+36]], $MachinePrecision]], t$95$1, N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999996e-72 or 1.9e-92 < z < 10500 or 1.24999999999999994e36 < z

   1. Initial program 73.3%

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

   3. Taylor expanded in t around inf 70.6%

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

   if -6.1999999999999996e-72 < z < 1.9e-92

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-*r/ 97.8%

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

      3. metadata-eval 97.8%

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

      4. *-commutative 97.8%

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

      5. div-sub 97.8%

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

      6. sub-neg 97.8%

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

      7. *-inverses 97.8%

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

      8. metadata-eval 97.8%

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

      9. distribute-lft-in 97.8%

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

      10. metadata-eval 97.8%

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

      11. associate-+l+ 97.8%

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

      12. +-commutative 97.8%

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

      13. *-commutative 97.8%

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

      14. +-commutative 97.8%

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

      15. associate-/l/ 97.8%

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

      16. metadata-eval 97.8%

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

      17. associate-*r/ 97.8%

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

      18. *-rgt-identity 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in z around 0 71.1%

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

   if 10500 < z < 1.24999999999999994e36

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. div-sub 100.0%

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

      6. sub-neg 100.0%

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

      7. *-inverses 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-lft-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-+l+ 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. +-commutative 100.0%

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

      15. associate-/l/ 100.0%

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

      16. metadata-eval 100.0%

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

      17. associate-*r/ 100.0%

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

      18. *-rgt-identity 100.0%

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

   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 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. *-commutative 100.0%

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

      8. associate-/r* 100.0%

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

      9. *-rgt-identity 100.0%

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

      10. associate-*r/ 100.0%

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

      11. metadata-eval 100.0%

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

      12. associate-+l+ 100.0%

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

      13. metadata-eval 100.0%

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

      14. associate-*r/ 100.0%

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

      15. distribute-rgt-in 100.0%

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

      16. associate-*l/ 100.0%

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

      17. *-lft-identity 100.0%

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

      18. +-commutative 100.0%

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

      19. remove-double-neg 100.0%

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

      20. distribute-neg-frac2 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 94.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-92}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 10500 \lor \neg \left(z \leq 1.25 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 17000000000 \lor \neg \left(z \leq 6.4 \cdot 10^{+38}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -5.4e-72)
     t_1
     (if (<= z 7.2e-113)
       (/ (/ 2.0 t) z)
       (if (or (<= z 17000000000.0) (not (<= z 6.4e+38)))
         t_1
         (- -2.0 (/ -2.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -5.4e-72) {
		tmp = t_1;
	} else if (z <= 7.2e-113) {
		tmp = (2.0 / t) / z;
	} else if ((z <= 17000000000.0) || !(z <= 6.4e+38)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-5.4d-72)) then
        tmp = t_1
    else if (z <= 7.2d-113) then
        tmp = (2.0d0 / t) / z
    else if ((z <= 17000000000.0d0) .or. (.not. (z <= 6.4d+38))) then
        tmp = t_1
    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 t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -5.4e-72) {
		tmp = t_1;
	} else if (z <= 7.2e-113) {
		tmp = (2.0 / t) / z;
	} else if ((z <= 17000000000.0) || !(z <= 6.4e+38)) {
		tmp = t_1;
	} else {
		tmp = -2.0 - (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -5.4e-72:
		tmp = t_1
	elif z <= 7.2e-113:
		tmp = (2.0 / t) / z
	elif (z <= 17000000000.0) or not (z <= 6.4e+38):
		tmp = t_1
	else:
		tmp = -2.0 - (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -5.4e-72)
		tmp = t_1;
	elseif (z <= 7.2e-113)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif ((z <= 17000000000.0) || !(z <= 6.4e+38))
		tmp = t_1;
	else
		tmp = Float64(-2.0 - Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -5.4e-72)
		tmp = t_1;
	elseif (z <= 7.2e-113)
		tmp = (2.0 / t) / z;
	elseif ((z <= 17000000000.0) || ~((z <= 6.4e+38)))
		tmp = t_1;
	else
		tmp = -2.0 - (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -5.4e-72], t$95$1, If[LessEqual[z, 7.2e-113], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, 17000000000.0], N[Not[LessEqual[z, 6.4e+38]], $MachinePrecision]], t$95$1, N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4e-72 or 7.1999999999999995e-113 < z < 1.7e10 or 6.3999999999999997e38 < z

   1. Initial program 74.0%

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

   3. Taylor expanded in t around inf 70.1%

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

   if -5.4e-72 < z < 7.1999999999999995e-113

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-*r/ 97.8%

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

      3. metadata-eval 97.8%

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

      4. *-commutative 97.8%

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

      5. div-sub 97.8%

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

      6. sub-neg 97.8%

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

      7. *-inverses 97.8%

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

      8. metadata-eval 97.8%

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

      9. distribute-lft-in 97.8%

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

      10. metadata-eval 97.8%

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

      11. associate-+l+ 97.8%

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

      12. +-commutative 97.8%

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

      13. *-commutative 97.8%

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

      14. +-commutative 97.8%

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

      15. associate-/l/ 97.7%

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

      16. metadata-eval 97.7%

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

      17. associate-*r/ 97.7%

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

      18. *-rgt-identity 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in z around 0 71.9%

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

      1. associate-/r* 72.0%

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

   8. Simplified 72.0%

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

   if 1.7e10 < z < 6.3999999999999997e38

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. div-sub 100.0%

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

      6. sub-neg 100.0%

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

      7. *-inverses 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-lft-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. associate-+l+ 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. +-commutative 100.0%

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

      15. associate-/l/ 100.0%

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

      16. metadata-eval 100.0%

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

      17. associate-*r/ 100.0%

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

      18. *-rgt-identity 100.0%

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

   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 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. *-commutative 100.0%

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

      8. associate-/r* 100.0%

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

      9. *-rgt-identity 100.0%

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

      10. associate-*r/ 100.0%

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

      11. metadata-eval 100.0%

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

      12. associate-+l+ 100.0%

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

      13. metadata-eval 100.0%

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

      14. associate-*r/ 100.0%

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

      15. distribute-rgt-in 100.0%

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

      16. associate-*l/ 100.0%

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

      17. *-lft-identity 100.0%

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

      18. +-commutative 100.0%

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

      19. remove-double-neg 100.0%

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

      20. distribute-neg-frac2 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 94.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 17000000000 \lor \neg \left(z \leq 6.4 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -950000 \lor \neg \left(\frac{x}{y} \leq 3.9 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z} - -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -950000.0) (not (<= (/ x y) 3.9e+27)))
   (+ (/ x y) (/ (/ 2.0 t) z))
   (+ -2.0 (/ (- (/ 2.0 z) -2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -950000.0) || !((x / y) <= 3.9e+27)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = -2.0 + (((2.0 / z) - -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) <= (-950000.0d0)) .or. (.not. ((x / y) <= 3.9d+27))) then
        tmp = (x / y) + ((2.0d0 / t) / z)
    else
        tmp = (-2.0d0) + (((2.0d0 / z) - (-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) <= -950000.0) || !((x / y) <= 3.9e+27)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = -2.0 + (((2.0 / z) - -2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -950000.0) or not ((x / y) <= 3.9e+27):
		tmp = (x / y) + ((2.0 / t) / z)
	else:
		tmp = -2.0 + (((2.0 / z) - -2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -950000.0) || !(Float64(x / y) <= 3.9e+27))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	else
		tmp = Float64(-2.0 + Float64(Float64(Float64(2.0 / z) - -2.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -950000.0) || ~(((x / y) <= 3.9e+27)))
		tmp = (x / y) + ((2.0 / t) / z);
	else
		tmp = -2.0 + (((2.0 / z) - -2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -950000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.9e+27]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.5e5 or 3.8999999999999999e27 < (/.f64 x y)

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 92.0%

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

      1. associate-/r* 92.0%

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

   5. Simplified 92.0%

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

   if -9.5e5 < (/.f64 x y) < 3.8999999999999999e27

   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 z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.8%

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

      16. metadata-eval 99.8%

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

      17. associate-*r/ 99.8%

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

      18. *-rgt-identity 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 98.0%

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

      1. associate--l+ 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. associate-*r/ 98.0%

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

      5. metadata-eval 98.0%

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

      6. sub-neg 98.0%

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

      7. *-commutative 98.0%

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

      8. associate-/r* 98.0%

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

      9. *-rgt-identity 98.0%

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

      10. associate-*r/ 98.0%

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

      11. metadata-eval 98.0%

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

      12. associate-+l+ 98.0%

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

      13. metadata-eval 98.0%

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

      14. associate-*r/ 98.0%

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

      15. distribute-rgt-in 98.0%

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

      16. associate-*l/ 98.0%

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

      17. *-lft-identity 98.0%

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

      18. +-commutative 98.0%

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

      19. remove-double-neg 98.0%

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

      20. distribute-neg-frac2 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -950000 \lor \neg \left(\frac{x}{y} \leq 3.9 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{\frac{2}{z} - -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.3 \cdot 10^{+36} \lor \neg \left(\frac{x}{y} \leq 3.7 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3.3e+36) (not (<= (/ x y) 3.7e+56)))
   (/ x y)
   (- -2.0 (/ (/ -2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.3e+36) || !((x / y) <= 3.7e+56)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-3.3d+36)) .or. (.not. ((x / y) <= 3.7d+56))) then
        tmp = x / y
    else
        tmp = (-2.0d0) - (((-2.0d0) / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.3e+36) || !((x / y) <= 3.7e+56)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - ((-2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3.3e+36) or not ((x / y) <= 3.7e+56):
		tmp = x / y
	else:
		tmp = -2.0 - ((-2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3.3e+36) || !(Float64(x / y) <= 3.7e+56))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 - Float64(Float64(-2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3.3e+36) || ~(((x / y) <= 3.7e+56)))
		tmp = x / y;
	else
		tmp = -2.0 - ((-2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3.3e+36], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.7e+56]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 - N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.2999999999999999e36 or 3.69999999999999997e56 < (/.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 79.4%

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

   if -3.2999999999999999e36 < (/.f64 x y) < 3.69999999999999997e56

   1. Initial program 83.1%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.8%

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

      6. sub-neg 99.8%

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

      7. *-inverses 99.8%

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

      8. metadata-eval 99.8%

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

      9. distribute-lft-in 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

      13. *-commutative 99.8%

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

      14. +-commutative 99.8%

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

      15. associate-/l/ 99.8%

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

      16. metadata-eval 99.8%

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

      17. associate-*r/ 99.8%

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

      18. *-rgt-identity 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 96.1%

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

      1. associate--l+ 96.1%

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

      2. associate-*r/ 96.1%

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

      3. metadata-eval 96.1%

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

      4. associate-*r/ 96.1%

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

      5. metadata-eval 96.1%

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

      6. sub-neg 96.1%

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

      7. *-commutative 96.1%

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

      8. associate-/r* 96.1%

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

      9. *-rgt-identity 96.1%

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

      10. associate-*r/ 96.1%

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

      11. metadata-eval 96.1%

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

      12. associate-+l+ 96.1%

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

      13. metadata-eval 96.1%

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

      14. associate-*r/ 96.1%

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

      15. distribute-rgt-in 96.1%

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

      16. associate-*l/ 96.1%

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

      17. *-lft-identity 96.1%

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

      18. +-commutative 96.1%

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

      19. remove-double-neg 96.1%

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

      20. distribute-neg-frac2 96.1%

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

   8. Simplified 96.1%

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

   9. Taylor expanded in z around 0 73.5%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.3 \cdot 10^{+36} \lor \neg \left(\frac{x}{y} \leq 3.7 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -350000000 \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -350000000.0) (not (<= (/ x y) 4.2e+27)))
   (/ x y)
   (- -2.0 (/ -2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -350000000.0) || !((x / y) <= 4.2e+27)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - (-2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-350000000.0d0)) .or. (.not. ((x / y) <= 4.2d+27))) then
        tmp = x / y
    else
        tmp = (-2.0d0) - ((-2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -350000000.0) || !((x / y) <= 4.2e+27)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -350000000.0) or not ((x / y) <= 4.2e+27):
		tmp = x / y
	else:
		tmp = -2.0 - (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -350000000.0) || !(Float64(x / y) <= 4.2e+27))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 - Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -350000000.0) || ~(((x / y) <= 4.2e+27)))
		tmp = x / y;
	else
		tmp = -2.0 - (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -350000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.2e+27]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.5e8 or 4.19999999999999989e27 < (/.f64 x y)

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf 73.6%

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

   if -3.5e8 < (/.f64 x y) < 4.19999999999999989e27

   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 z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.8%

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

      16. metadata-eval 99.8%

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

      17. associate-*r/ 99.8%

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

      18. *-rgt-identity 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 98.0%

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

      1. associate--l+ 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. associate-*r/ 98.0%

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

      5. metadata-eval 98.0%

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

      6. sub-neg 98.0%

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

      7. *-commutative 98.0%

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

      8. associate-/r* 98.0%

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

      9. *-rgt-identity 98.0%

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

      10. associate-*r/ 98.0%

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

      11. metadata-eval 98.0%

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

      12. associate-+l+ 98.0%

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

      13. metadata-eval 98.0%

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

      14. associate-*r/ 98.0%

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

      15. distribute-rgt-in 98.0%

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

      16. associate-*l/ 98.0%

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

      17. *-lft-identity 98.0%

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

      18. +-commutative 98.0%

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

      19. remove-double-neg 98.0%

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

      20. distribute-neg-frac2 98.0%

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

   8. Simplified 98.0%

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

   9. Taylor expanded in z around inf 59.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -350000000 \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3500 \lor \neg \left(\frac{x}{y} \leq 0.25\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3500.0) (not (<= (/ x y) 0.25)))
   (- (/ 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) <= -3500.0) || !((x / y) <= 0.25)) {
		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) <= (-3500.0d0)) .or. (.not. ((x / y) <= 0.25d0))) 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) <= -3500.0) || !((x / y) <= 0.25)) {
		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) <= -3500.0) or not ((x / y) <= 0.25):
		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) <= -3500.0) || !(Float64(x / y) <= 0.25))
		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) <= -3500.0) || ~(((x / y) <= 0.25)))
		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], -3500.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.25]], $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) < -3500 or 0.25 < (/.f64 x y)

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf 72.3%

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

   if -3500 < (/.f64 x y) < 0.25

   1. Initial program 81.8%

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

   3. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-lft-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. *-commutative 99.9%

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

      14. +-commutative 99.9%

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

      15. associate-/l/ 99.8%

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

      16. metadata-eval 99.8%

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

      17. associate-*r/ 99.8%

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

      18. *-rgt-identity 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 98.7%

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

      1. associate--l+ 98.7%

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

      2. associate-*r/ 98.7%

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

      3. metadata-eval 98.7%

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

      4. associate-*r/ 98.7%

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

      5. metadata-eval 98.7%

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

      6. sub-neg 98.7%

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

      7. *-commutative 98.7%

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

      8. associate-/r* 98.7%

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

      9. *-rgt-identity 98.7%

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

      10. associate-*r/ 98.7%

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

      11. metadata-eval 98.7%

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

      12. associate-+l+ 98.7%

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

      13. metadata-eval 98.7%

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

      14. associate-*r/ 98.7%

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

      15. distribute-rgt-in 98.7%

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

      16. associate-*l/ 98.7%

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

      17. *-lft-identity 98.7%

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

      18. +-commutative 98.7%

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

      19. remove-double-neg 98.7%

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

      20. distribute-neg-frac2 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in z around inf 60.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3500 \lor \neg \left(\frac{x}{y} \leq 0.25\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-29} \lor \neg \left(z \leq 9.2 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e-29) (not (<= z 9.2e-62)))
   (+ (/ 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 ((z <= -9.5e-29) || !(z <= 9.2e-62)) {
		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 ((z <= (-9.5d-29)) .or. (.not. (z <= 9.2d-62))) 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 ((z <= -9.5e-29) || !(z <= 9.2e-62)) {
		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 (z <= -9.5e-29) or not (z <= 9.2e-62):
		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 ((z <= -9.5e-29) || !(z <= 9.2e-62))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(-2.0 - Float64(Float64(-2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e-29) || ~((z <= 9.2e-62)))
		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[z, -9.5e-29], N[Not[LessEqual[z, 9.2e-62]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000023e-29 or 9.20000000000000002e-62 < z

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf 97.6%

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

      1. div-sub 97.6%

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

      2. sub-neg 97.6%

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

      3. *-inverses 97.6%

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

      4. metadata-eval 97.6%

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

      5. distribute-lft-in 97.6%

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

      6. metadata-eval 97.6%

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

      7. associate-*r/ 97.6%

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

      8. metadata-eval 97.6%

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

   5. Simplified 97.6%

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

   if -9.50000000000000023e-29 < z < 9.20000000000000002e-62

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-*r/ 97.3%

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

      3. metadata-eval 97.3%

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

      4. *-commutative 97.3%

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

      5. div-sub 97.3%

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

      6. sub-neg 97.3%

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

      7. *-inverses 97.3%

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

      8. metadata-eval 97.3%

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

      9. distribute-lft-in 97.3%

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

      10. metadata-eval 97.3%

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

      11. associate-+l+ 97.3%

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

      12. +-commutative 97.3%

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

      13. *-commutative 97.3%

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

      14. +-commutative 97.3%

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

      15. associate-/l/ 97.3%

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

      16. metadata-eval 97.3%

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

      17. associate-*r/ 97.3%

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

      18. *-rgt-identity 97.3%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in x around 0 75.9%

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

      1. associate--l+ 75.9%

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

      2. associate-*r/ 75.9%

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

      3. metadata-eval 75.9%

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

      4. associate-*r/ 75.9%

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

      5. metadata-eval 75.9%

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

      6. sub-neg 75.9%

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

      7. *-commutative 75.9%

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

      8. associate-/r* 75.9%

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

      9. *-rgt-identity 75.9%

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

      10. associate-*r/ 75.8%

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

      11. metadata-eval 75.8%

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

      12. associate-+l+ 75.8%

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

      13. metadata-eval 75.8%

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

      14. associate-*r/ 75.8%

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

      15. distribute-rgt-in 75.8%

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

      16. associate-*l/ 75.9%

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

      17. *-lft-identity 75.9%

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

      18. +-commutative 75.9%

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

      19. remove-double-neg 75.9%

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

      20. distribute-neg-frac2 75.9%

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

   8. Simplified 75.9%

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

   9. Taylor expanded in z around 0 75.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-29} \lor \neg \left(z \leq 9.2 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \lor \neg \left(z \leq 9.6 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1) (not (<= z 9.6e-61)))
   (+ (/ 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 <= -4.1) || !(z <= 9.6e-61)) {
		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 <= (-4.1d0)) .or. (.not. (z <= 9.6d-61))) 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 <= -4.1) || !(z <= 9.6e-61)) {
		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 <= -4.1) or not (z <= 9.6e-61):
		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 <= -4.1) || !(z <= 9.6e-61))
		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 <= -4.1) || ~((z <= 9.6e-61)))
		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, -4.1], N[Not[LessEqual[z, 9.6e-61]], $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 < -4.0999999999999996 or 9.6000000000000004e-61 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in z around inf 98.3%

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

      1. div-sub 98.3%

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

      2. sub-neg 98.3%

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

      3. *-inverses 98.3%

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

      4. metadata-eval 98.3%

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

      5. distribute-lft-in 98.3%

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

      6. metadata-eval 98.3%

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

      7. associate-*r/ 98.3%

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

      8. metadata-eval 98.3%

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

   5. Simplified 98.3%

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

   if -4.0999999999999996 < z < 9.6000000000000004e-61

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 88.4%

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

      1. associate-/r* 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \lor \neg \left(z \leq 9.6 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -950000 \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -950000.0) (not (<= (/ x y) 4.2e+27))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -950000.0) || !((x / y) <= 4.2e+27)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-950000.0d0)) .or. (.not. ((x / y) <= 4.2d+27))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -950000.0) || !((x / y) <= 4.2e+27)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -950000.0) or not ((x / y) <= 4.2e+27):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -950000.0) || !(Float64(x / y) <= 4.2e+27))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -950000.0) || ~(((x / y) <= 4.2e+27)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -950000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.2e+27]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.5e5 or 4.19999999999999989e27 < (/.f64 x y)

   1. Initial program 85.4%

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

   3. Taylor expanded in x around inf 73.6%

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

   if -9.5e5 < (/.f64 x y) < 4.19999999999999989e27

   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 t around 0 65.2%

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

      1. associate-*r/ 65.2%

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

      2. metadata-eval 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in z around inf 26.8%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -950000 \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.1% accurate, 1.3× speedup

Math

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

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

Derivation

1. Initial program 83.8%

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

   1. +-commutative 83.8%

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

   2. remove-double-neg 83.8%

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

   3. distribute-frac-neg 83.8%

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

   4. unsub-neg 83.8%

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

   5. *-commutative 83.8%

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

   6. associate-*r* 83.8%

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

   7. distribute-rgt1-in 83.8%

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

   8. associate-/l* 83.8%

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

   9. fma-neg 83.8%

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

   10. *-commutative 83.8%

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

   11. fma-define 83.8%

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

   12. *-commutative 83.8%

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

   13. distribute-frac-neg 83.8%

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

   14. remove-double-neg 83.8%

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

3. Simplified 83.8%

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

5. Taylor expanded in t around inf 98.7%

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

   1. associate--l+ 98.7%

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

   2. +-commutative 98.7%

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

   3. sub-neg 98.7%

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

   4. metadata-eval 98.7%

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

   5. +-commutative 98.7%

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

   6. associate-*r/ 98.7%

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

   7. distribute-lft-in 98.7%

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

   8. metadata-eval 98.7%

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

   9. associate-*r/ 98.7%

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

   10. metadata-eval 98.7%

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

7. Simplified 98.7%

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

8. Final simplification 98.7%

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

Alternative 13: 19.2% 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 83.8%

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

3. Taylor expanded in t around 0 48.2%

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

   1. associate-*r/ 48.2%

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

   2. metadata-eval 48.2%

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

5. Simplified 48.2%

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

6. Taylor expanded in z around inf 17.4%

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

7. Final simplification 17.4%

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

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

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

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