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

Percentage Accurate: 86.7% → 99.2%

Time: 10.4s

Alternatives: 12

Speedup: 1.3×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

   1. +-commutative 85.4%

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

   2. remove-double-neg 85.4%

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

   3. distribute-frac-neg 85.4%

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

   4. unsub-neg 85.4%

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

   5. *-commutative 85.4%

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

   6. associate-*r* 85.4%

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

   7. distribute-rgt1-in 85.4%

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

   8. associate-/l* 85.4%

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

   9. fma-neg 85.4%

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

   10. *-commutative 85.4%

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

   11. fma-define 85.4%

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

   12. *-commutative 85.4%

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

   13. distribute-frac-neg 85.4%

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

   14. remove-double-neg 85.4%

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

3. Simplified 85.4%

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

5. Taylor expanded in t around inf 99.1%

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

   1. associate--l+ 99.1%

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

   2. +-commutative 99.1%

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

   3. sub-neg 99.1%

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

   4. metadata-eval 99.1%

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

   5. +-commutative 99.1%

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

   6. associate-*r/ 99.1%

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

   7. distribute-lft-in 99.1%

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

   8. metadata-eval 99.1%

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

   9. associate-*r/ 99.1%

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

   10. metadata-eval 99.1%

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

7. Simplified 99.1%

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

8. Final simplification 99.1%

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

Alternative 2: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -5e-21)
     t_2
     (if (<= t 5.7e-121)
       t_1
       (if (<= t 2.8e-97) (/ x y) (if (<= t 3e-63) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -5e-21) {
		tmp = t_2;
	} else if (t <= 5.7e-121) {
		tmp = t_1;
	} else if (t <= 2.8e-97) {
		tmp = x / y;
	} else if (t <= 3e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (x / y) - 2.0d0
    if (t <= (-5d-21)) then
        tmp = t_2
    else if (t <= 5.7d-121) then
        tmp = t_1
    else if (t <= 2.8d-97) then
        tmp = x / y
    else if (t <= 3d-63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -5e-21) {
		tmp = t_2;
	} else if (t <= 5.7e-121) {
		tmp = t_1;
	} else if (t <= 2.8e-97) {
		tmp = x / y;
	} else if (t <= 3e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -5e-21:
		tmp = t_2
	elif t <= 5.7e-121:
		tmp = t_1
	elif t <= 2.8e-97:
		tmp = x / y
	elif t <= 3e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -5e-21)
		tmp = t_2;
	elseif (t <= 5.7e-121)
		tmp = t_1;
	elseif (t <= 2.8e-97)
		tmp = Float64(x / y);
	elseif (t <= 3e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -5e-21)
		tmp = t_2;
	elseif (t <= 5.7e-121)
		tmp = t_1;
	elseif (t <= 2.8e-97)
		tmp = x / y;
	elseif (t <= 3e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -5e-21], t$95$2, If[LessEqual[t, 5.7e-121], t$95$1, If[LessEqual[t, 2.8e-97], N[(x / y), $MachinePrecision], If[LessEqual[t, 3e-63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.99999999999999973e-21 or 2.99999999999999979e-63 < t

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 76.9%

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

   if -4.99999999999999973e-21 < t < 5.70000000000000014e-121 or 2.8000000000000002e-97 < t < 2.99999999999999979e-63

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0 90.8%

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

      1. associate-*r/ 90.8%

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

      2. metadata-eval 90.8%

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

   5. Simplified 90.8%

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

   if 5.70000000000000014e-121 < t < 2.8000000000000002e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 96.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-121}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-63}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-119}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 29 \lor \neg \left(z \leq 4.5 \cdot 10^{+55}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -6.5e-121)
     t_1
     (if (<= z 2.7e-119)
       (/ 2.0 (* z t))
       (if (or (<= z 29.0) (not (<= z 4.5e+55))) 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 <= -6.5e-121) {
		tmp = t_1;
	} else if (z <= 2.7e-119) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 29.0) || !(z <= 4.5e+55)) {
		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 <= (-6.5d-121)) then
        tmp = t_1
    else if (z <= 2.7d-119) then
        tmp = 2.0d0 / (z * t)
    else if ((z <= 29.0d0) .or. (.not. (z <= 4.5d+55))) 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 <= -6.5e-121) {
		tmp = t_1;
	} else if (z <= 2.7e-119) {
		tmp = 2.0 / (z * t);
	} else if ((z <= 29.0) || !(z <= 4.5e+55)) {
		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 <= -6.5e-121:
		tmp = t_1
	elif z <= 2.7e-119:
		tmp = 2.0 / (z * t)
	elif (z <= 29.0) or not (z <= 4.5e+55):
		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 <= -6.5e-121)
		tmp = t_1;
	elseif (z <= 2.7e-119)
		tmp = Float64(2.0 / Float64(z * t));
	elseif ((z <= 29.0) || !(z <= 4.5e+55))
		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 <= -6.5e-121)
		tmp = t_1;
	elseif (z <= 2.7e-119)
		tmp = 2.0 / (z * t);
	elseif ((z <= 29.0) || ~((z <= 4.5e+55)))
		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, -6.5e-121], t$95$1, If[LessEqual[z, 2.7e-119], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 29.0], N[Not[LessEqual[z, 4.5e+55]], $MachinePrecision]], t$95$1, N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5000000000000003e-121 or 2.70000000000000027e-119 < z < 29 or 4.49999999999999998e55 < z

   1. Initial program 78.7%

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

   3. Taylor expanded in t around inf 70.9%

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

   if -6.5000000000000003e-121 < z < 2.70000000000000027e-119

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. remove-double-neg 97.4%

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

      3. distribute-frac-neg 97.4%

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

      4. unsub-neg 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*r* 97.4%

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

      7. distribute-rgt1-in 97.4%

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

      8. associate-/l* 97.4%

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

      9. fma-neg 97.4%

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

      10. *-commutative 97.4%

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

      11. fma-define 97.4%

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

      12. *-commutative 97.4%

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

      13. distribute-frac-neg 97.4%

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

      14. remove-double-neg 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around inf 97.4%

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

      1. associate--l+ 97.4%

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

      2. +-commutative 97.4%

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

      3. sub-neg 97.4%

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

      4. metadata-eval 97.4%

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

      5. +-commutative 97.4%

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

      6. associate-*r/ 97.4%

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

      7. distribute-lft-in 97.4%

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

      8. metadata-eval 97.4%

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

      9. associate-*r/ 97.4%

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

      10. metadata-eval 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in z around 0 79.4%

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

   if 29 < z < 4.49999999999999998e55

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. remove-double-neg 99.8%

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

      3. distribute-frac-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.8%

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

      7. distribute-rgt1-in 99.8%

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

      8. associate-/l* 99.5%

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

      9. fma-neg 99.5%

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

      10. *-commutative 99.5%

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

      11. fma-define 99.5%

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

      12. *-commutative 99.5%

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

      13. distribute-frac-neg 99.5%

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

      14. remove-double-neg 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-*r/ 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. associate-*r/ 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-lft-out 100.0%

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

      5. associate-/l/ 100.0%

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

      6. *-lft-identity 100.0%

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

      7. associate-*l/ 100.0%

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

      8. distribute-lft-out 100.0%

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

      9. *-commutative 100.0%

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

      10. associate-*r* 100.0%

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

      11. associate-*r/ 100.0%

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

      12. metadata-eval 100.0%

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

      13. distribute-rgt-in 100.0%

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

      14. associate-*l/ 99.8%

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

      15. *-lft-identity 99.8%

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

   10. Simplified 99.8%

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

   11. Taylor expanded in z around inf 91.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-119}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;z \leq 29 \lor \neg \left(z \leq 4.5 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -800000000 \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -800000000.0) (not (<= (/ x y) 3.5e+68)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -800000000.0) || !((x / y) <= 3.5e+68)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-800000000.0d0)) .or. (.not. ((x / y) <= 3.5d+68))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -800000000.0) || !((x / y) <= 3.5e+68)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -800000000.0) or not ((x / y) <= 3.5e+68):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -800000000.0) || !(Float64(x / y) <= 3.5e+68))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -800000000.0) || ~(((x / y) <= 3.5e+68)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -800000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.5e+68]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -8e8 or 3.49999999999999977e68 < (/.f64 x y)

   1. Initial program 84.5%

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

   3. Taylor expanded in z around inf 82.8%

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

      1. div-sub 82.8%

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

      2. sub-neg 82.8%

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

      3. *-inverses 82.8%

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

      4. metadata-eval 82.8%

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

      5. distribute-lft-in 82.8%

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

      6. metadata-eval 82.8%

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

      7. associate-*r/ 82.8%

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

      8. metadata-eval 82.8%

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

   5. Simplified 82.8%

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

   if -8e8 < (/.f64 x y) < 3.49999999999999977e68

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. remove-double-neg 86.1%

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

      3. distribute-frac-neg 86.1%

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

      4. unsub-neg 86.1%

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

      5. *-commutative 86.1%

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

      6. associate-*r* 86.1%

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

      7. distribute-rgt1-in 86.1%

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

      8. associate-/l* 86.0%

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

      9. fma-neg 86.0%

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

      10. *-commutative 86.0%

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

      11. fma-define 86.0%

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

      12. *-commutative 86.0%

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

      13. distribute-frac-neg 86.0%

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

      14. remove-double-neg 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 96.0%

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

      1. sub-neg 96.0%

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

      2. metadata-eval 96.0%

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

      3. +-commutative 96.0%

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

      4. distribute-lft-out 96.0%

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

      5. associate-/l/ 95.9%

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

      6. *-lft-identity 95.9%

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

      7. associate-*l/ 95.9%

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

      8. distribute-lft-out 95.9%

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

      9. *-commutative 95.9%

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

      10. associate-*r* 95.9%

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

      11. associate-*r/ 95.9%

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

      12. metadata-eval 95.9%

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

      13. distribute-rgt-in 95.9%

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

      14. associate-*l/ 95.9%

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

      15. *-lft-identity 95.9%

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

   10. Simplified 95.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -800000000 \lor \neg \left(\frac{x}{y} \leq 3.5 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+38} \lor \neg \left(\frac{x}{y} \leq 3.4 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4.5e+38) (not (<= (/ x y) 3.4e+21)))
   (+ (/ x y) (/ 2.0 (* z t)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.5e+38) || !((x / y) <= 3.4e+21)) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4.5d+38)) .or. (.not. ((x / y) <= 3.4d+21))) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.5e+38) || !((x / y) <= 3.4e+21)) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4.5e+38) or not ((x / y) <= 3.4e+21):
		tmp = (x / y) + (2.0 / (z * t))
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4.5e+38) || !(Float64(x / y) <= 3.4e+21))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4.5e+38) || ~(((x / y) <= 3.4e+21)))
		tmp = (x / y) + (2.0 / (z * t));
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4.5e+38], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.4e+21]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.4999999999999998e38 or 3.4e21 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in z around 0 93.5%

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

   if -4.4999999999999998e38 < (/.f64 x y) < 3.4e21

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. remove-double-neg 86.0%

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

      3. distribute-frac-neg 86.0%

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

      4. unsub-neg 86.0%

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

      5. *-commutative 86.0%

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

      6. associate-*r* 86.0%

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

      7. distribute-rgt1-in 86.0%

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

      8. associate-/l* 85.9%

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

      9. fma-neg 86.0%

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

      10. *-commutative 86.0%

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

      11. fma-define 86.0%

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

      12. *-commutative 86.0%

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

      13. distribute-frac-neg 86.0%

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

      14. remove-double-neg 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 97.9%

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

      1. sub-neg 97.9%

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

      2. metadata-eval 97.9%

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

      3. +-commutative 97.9%

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

      4. distribute-lft-out 97.9%

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

      5. associate-/l/ 97.9%

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

      6. *-lft-identity 97.9%

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

      7. associate-*l/ 97.8%

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

      8. distribute-lft-out 97.8%

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

      9. *-commutative 97.8%

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

      10. associate-*r* 97.8%

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

      11. associate-*r/ 97.8%

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

      12. metadata-eval 97.8%

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

      13. distribute-rgt-in 97.8%

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

      14. associate-*l/ 97.9%

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

      15. *-lft-identity 97.9%

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

   10. Simplified 97.9%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+38} \lor \neg \left(\frac{x}{y} \leq 3.4 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.22 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.1 \cdot 10^{+56}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.22e+104)
   (/ x y)
   (if (<= (/ x y) 6.1e+56) (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.22e+104) {
		tmp = x / y;
	} else if ((x / y) <= 6.1e+56) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.22d+104)) then
        tmp = x / y
    else if ((x / y) <= 6.1d+56) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.22e+104) {
		tmp = x / y;
	} else if ((x / y) <= 6.1e+56) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.22e+104:
		tmp = x / y
	elif (x / y) <= 6.1e+56:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.22e+104)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 6.1e+56)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.22e+104)
		tmp = x / y;
	elseif ((x / y) <= 6.1e+56)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.22e+104], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6.1e+56], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.22e104

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 86.8%

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

   if -1.22e104 < (/.f64 x y) < 6.1000000000000001e56

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. remove-double-neg 86.7%

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

      3. distribute-frac-neg 86.7%

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

      4. unsub-neg 86.7%

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

      5. *-commutative 86.7%

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

      6. associate-*r* 86.7%

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

      7. distribute-rgt1-in 86.7%

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

      8. associate-/l* 86.6%

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

      9. fma-neg 86.6%

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

      10. *-commutative 86.6%

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

      11. fma-define 86.6%

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

      12. *-commutative 86.6%

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

      13. distribute-frac-neg 86.6%

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

      14. remove-double-neg 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 92.2%

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

      1. sub-neg 92.2%

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

      2. metadata-eval 92.2%

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

      3. +-commutative 92.2%

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

      4. distribute-lft-out 92.2%

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

      5. associate-/l/ 92.2%

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

      6. *-lft-identity 92.2%

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

      7. associate-*l/ 92.1%

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

      8. distribute-lft-out 92.1%

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

      9. *-commutative 92.1%

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

      10. associate-*r* 92.1%

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

      11. associate-*r/ 92.1%

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

      12. metadata-eval 92.1%

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

      13. distribute-rgt-in 92.1%

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

      14. associate-*l/ 92.2%

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

      15. *-lft-identity 92.2%

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

   10. Simplified 92.2%

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

   if 6.1000000000000001e56 < (/.f64 x y)

   1. Initial program 78.8%

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

   3. Taylor expanded in t around inf 75.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.22 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.1 \cdot 10^{+56}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{x + 2 \cdot \frac{\frac{y}{t}}{z}}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+17}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+42)
   (/ (+ x (* 2.0 (/ (/ y t) z))) y)
   (if (<= (/ x y) 1e+17)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (/ 2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+42) {
		tmp = (x + (2.0 * ((y / t) / z))) / y;
	} else if ((x / y) <= 1e+17) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2d+42)) then
        tmp = (x + (2.0d0 * ((y / t) / z))) / y
    else if ((x / y) <= 1d+17) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + (2.0d0 / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+42) {
		tmp = (x + (2.0 * ((y / t) / z))) / y;
	} else if ((x / y) <= 1e+17) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+42:
		tmp = (x + (2.0 * ((y / t) / z))) / y
	elif (x / y) <= 1e+17:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+42)
		tmp = Float64(Float64(x + Float64(2.0 * Float64(Float64(y / t) / z))) / y);
	elseif (Float64(x / y) <= 1e+17)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+42)
		tmp = (x + (2.0 * ((y / t) / z))) / y;
	elseif ((x / y) <= 1e+17)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+42], N[(N[(x + N[(2.0 * N[(N[(y / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e+17], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0 93.5%

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

      1. associate-/r* 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in y around 0 95.2%

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

      1. associate-/r* 95.2%

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

   8. Simplified 95.2%

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

   if -2.00000000000000009e42 < (/.f64 x y) < 1e17

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. remove-double-neg 86.0%

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

      3. distribute-frac-neg 86.0%

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

      4. unsub-neg 86.0%

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

      5. *-commutative 86.0%

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

      6. associate-*r* 86.0%

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

      7. distribute-rgt1-in 86.0%

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

      8. associate-/l* 85.9%

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

      9. fma-neg 86.0%

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

      10. *-commutative 86.0%

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

      11. fma-define 86.0%

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

      12. *-commutative 86.0%

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

      13. distribute-frac-neg 86.0%

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

      14. remove-double-neg 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 97.9%

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

      1. sub-neg 97.9%

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

      2. metadata-eval 97.9%

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

      3. +-commutative 97.9%

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

      4. distribute-lft-out 97.9%

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

      5. associate-/l/ 97.9%

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

      6. *-lft-identity 97.9%

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

      7. associate-*l/ 97.8%

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

      8. distribute-lft-out 97.8%

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

      9. *-commutative 97.8%

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

      10. associate-*r* 97.8%

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

      11. associate-*r/ 97.8%

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

      12. metadata-eval 97.8%

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

      13. distribute-rgt-in 97.8%

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

      14. associate-*l/ 97.9%

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

      15. *-lft-identity 97.9%

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

   10. Simplified 97.9%

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

   if 1e17 < (/.f64 x y)

   1. Initial program 80.0%

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

   3. Taylor expanded in z around 0 93.4%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{x + 2 \cdot \frac{\frac{y}{t}}{z}}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+17}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.8 \cdot 10^{+38} \lor \neg \left(\frac{x}{y} \leq 6.8 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.8e+38) (not (<= (/ x y) 6.8e+16)))
   (/ x y)
   (+ -2.0 (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.8e+38) || !((x / y) <= 6.8e+16)) {
		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) <= (-5.8d+38)) .or. (.not. ((x / y) <= 6.8d+16))) 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) <= -5.8e+38) || !((x / y) <= 6.8e+16)) {
		tmp = x / y;
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.8e+38) or not ((x / y) <= 6.8e+16):
		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) <= -5.8e+38) || !(Float64(x / y) <= 6.8e+16))
		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) <= -5.8e+38) || ~(((x / y) <= 6.8e+16)))
		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], -5.8e+38], N[Not[LessEqual[N[(x / y), $MachinePrecision], 6.8e+16]], $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) < -5.80000000000000013e38 or 6.8e16 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 73.8%

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

   if -5.80000000000000013e38 < (/.f64 x y) < 6.8e16

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. remove-double-neg 86.0%

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

      3. distribute-frac-neg 86.0%

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

      4. unsub-neg 86.0%

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

      5. *-commutative 86.0%

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

      6. associate-*r* 86.0%

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

      7. distribute-rgt1-in 86.0%

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

      8. associate-/l* 85.9%

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

      9. fma-neg 86.0%

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

      10. *-commutative 86.0%

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

      11. fma-define 86.0%

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

      12. *-commutative 86.0%

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

      13. distribute-frac-neg 86.0%

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

      14. remove-double-neg 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 97.9%

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

      1. sub-neg 97.9%

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

      2. metadata-eval 97.9%

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

      3. +-commutative 97.9%

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

      4. distribute-lft-out 97.9%

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

      5. associate-/l/ 97.9%

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

      6. *-lft-identity 97.9%

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

      7. associate-*l/ 97.8%

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

      8. distribute-lft-out 97.8%

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

      9. *-commutative 97.8%

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

      10. associate-*r* 97.8%

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

      11. associate-*r/ 97.8%

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

      12. metadata-eval 97.8%

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

      13. distribute-rgt-in 97.8%

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

      14. associate-*l/ 97.9%

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

      15. *-lft-identity 97.9%

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

   10. Simplified 97.9%

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

   11. Taylor expanded in z around inf 59.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.8 \cdot 10^{+38} \lor \neg \left(\frac{x}{y} \leq 6.8 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.8 \cdot 10^{-24} \lor \neg \left(\frac{x}{y} \leq 1.7 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.8e-24) (not (<= (/ x y) 1.7e+19)))
   (- (/ 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) <= -2.8e-24) || !((x / y) <= 1.7e+19)) {
		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) <= (-2.8d-24)) .or. (.not. ((x / y) <= 1.7d+19))) 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) <= -2.8e-24) || !((x / y) <= 1.7e+19)) {
		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) <= -2.8e-24) or not ((x / y) <= 1.7e+19):
		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) <= -2.8e-24) || !(Float64(x / y) <= 1.7e+19))
		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) <= -2.8e-24) || ~(((x / y) <= 1.7e+19)))
		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], -2.8e-24], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.7e+19]], $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) < -2.8000000000000002e-24 or 1.7e19 < (/.f64 x y)

   1. Initial program 84.2%

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

   3. Taylor expanded in t around inf 71.1%

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

   if -2.8000000000000002e-24 < (/.f64 x y) < 1.7e19

   1. Initial program 86.6%

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

      1. +-commutative 86.6%

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

      2. remove-double-neg 86.6%

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

      3. distribute-frac-neg 86.6%

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

      4. unsub-neg 86.6%

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

      5. *-commutative 86.6%

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

      6. associate-*r* 86.6%

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

      7. distribute-rgt1-in 86.6%

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

      8. associate-/l* 86.5%

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

      9. fma-neg 86.5%

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

      10. *-commutative 86.5%

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

      11. fma-define 86.5%

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

      12. *-commutative 86.5%

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

      13. distribute-frac-neg 86.5%

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

      14. remove-double-neg 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.2%

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

      1. sub-neg 99.2%

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

      2. metadata-eval 99.2%

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

      3. +-commutative 99.2%

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

      4. distribute-lft-out 99.2%

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

      5. associate-/l/ 99.1%

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

      6. *-lft-identity 99.1%

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

      7. associate-*l/ 99.1%

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

      8. distribute-lft-out 99.1%

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

      9. *-commutative 99.1%

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

      10. associate-*r* 99.1%

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

      11. associate-*r/ 99.1%

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

      12. metadata-eval 99.1%

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

      13. distribute-rgt-in 99.1%

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

      14. associate-*l/ 99.1%

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

      15. *-lft-identity 99.1%

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

   10. Simplified 99.1%

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

   11. Taylor expanded in z around inf 62.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.8 \cdot 10^{-24} \lor \neg \left(\frac{x}{y} \leq 1.7 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 320000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.0) (not (<= (/ x y) 320000000000.0))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 320000000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.0d0)) .or. (.not. ((x / y) <= 320000000000.0d0))) then
        tmp = x / y
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 320000000000.0)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.0) or not ((x / y) <= 320000000000.0):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.0) || !(Float64(x / y) <= 320000000000.0))
		tmp = Float64(x / y);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.0) || ~(((x / y) <= 320000000000.0)))
		tmp = x / y;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 320000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 3.2e11 < (/.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 71.3%

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

   if -2 < (/.f64 x y) < 3.2e11

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. remove-double-neg 86.1%

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

      3. distribute-frac-neg 86.1%

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

      4. unsub-neg 86.1%

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

      5. *-commutative 86.1%

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

      6. associate-*r* 86.1%

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

      7. distribute-rgt1-in 86.1%

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

      8. associate-/l* 86.0%

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

      9. fma-neg 86.0%

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

      10. *-commutative 86.0%

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

      11. fma-define 86.0%

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

      12. *-commutative 86.0%

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

      13. distribute-frac-neg 86.0%

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

      14. remove-double-neg 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. metadata-eval 99.3%

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

      3. +-commutative 99.3%

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

      4. distribute-lft-out 99.3%

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

      5. associate-/l/ 99.2%

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

      6. *-lft-identity 99.2%

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

      7. associate-*l/ 99.2%

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

      8. distribute-lft-out 99.2%

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

      9. *-commutative 99.2%

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

      10. associate-*r* 99.2%

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

      11. associate-*r/ 99.2%

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

      12. metadata-eval 99.2%

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

      13. distribute-rgt-in 99.2%

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

      14. associate-*l/ 99.2%

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

      15. *-lft-identity 99.2%

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

   10. Simplified 99.2%

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

   11. Taylor expanded in z around inf 61.3%

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

   12. Taylor expanded in t around inf 37.0%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 320000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 1.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 1.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 1.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1 < t

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. remove-double-neg 73.8%

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

      3. distribute-frac-neg 73.8%

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

      4. unsub-neg 73.8%

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

      5. *-commutative 73.8%

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

      6. associate-*r* 73.8%

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

      7. distribute-rgt1-in 73.8%

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

      8. associate-/l* 73.7%

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

      9. fma-neg 73.8%

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

      10. *-commutative 73.8%

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

      11. fma-define 73.8%

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

      12. *-commutative 73.8%

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

      13. distribute-frac-neg 73.8%

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

      14. remove-double-neg 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. associate-*r/ 99.9%

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

      10. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 54.7%

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

      1. sub-neg 54.7%

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

      2. metadata-eval 54.7%

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

      3. +-commutative 54.7%

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

      4. distribute-lft-out 54.7%

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

      5. associate-/l/ 54.7%

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

      6. *-lft-identity 54.7%

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

      7. associate-*l/ 54.6%

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

      8. distribute-lft-out 54.6%

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

      9. *-commutative 54.6%

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

      10. associate-*r* 54.6%

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

      11. associate-*r/ 54.6%

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

      12. metadata-eval 54.6%

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

      13. distribute-rgt-in 54.6%

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

      14. associate-*l/ 54.7%

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

      15. *-lft-identity 54.7%

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

   10. Simplified 54.7%

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

   11. Taylor expanded in z around inf 36.8%

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

   12. Taylor expanded in t around inf 36.2%

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

   if -1 < t < 1

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. metadata-eval 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in z around inf 32.8%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 20.1% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

   1. +-commutative 85.4%

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

   2. remove-double-neg 85.4%

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

   3. distribute-frac-neg 85.4%

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

   4. unsub-neg 85.4%

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

   5. *-commutative 85.4%

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

   6. associate-*r* 85.4%

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

   7. distribute-rgt1-in 85.4%

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

   8. associate-/l* 85.4%

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

   9. fma-neg 85.4%

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

   10. *-commutative 85.4%

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

   11. fma-define 85.4%

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

   12. *-commutative 85.4%

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

   13. distribute-frac-neg 85.4%

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

   14. remove-double-neg 85.4%

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

3. Simplified 85.4%

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

5. Taylor expanded in t around inf 99.1%

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

   1. associate--l+ 99.1%

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

   2. +-commutative 99.1%

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

   3. sub-neg 99.1%

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

   4. metadata-eval 99.1%

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

   5. +-commutative 99.1%

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

   6. associate-*r/ 99.1%

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

   7. distribute-lft-in 99.1%

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

   8. metadata-eval 99.1%

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

   9. associate-*r/ 99.1%

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

   10. metadata-eval 99.1%

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

7. Simplified 99.1%

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

8. Taylor expanded in x around 0 66.5%

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

   1. sub-neg 66.5%

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

   2. metadata-eval 66.5%

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

   3. +-commutative 66.5%

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

   4. distribute-lft-out 66.5%

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

   5. associate-/l/ 66.4%

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

   6. *-lft-identity 66.4%

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

   7. associate-*l/ 66.4%

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

   8. distribute-lft-out 66.4%

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

   9. *-commutative 66.4%

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

   10. associate-*r* 66.4%

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

   11. associate-*r/ 66.4%

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

   12. metadata-eval 66.4%

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

   13. distribute-rgt-in 66.4%

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

   14. associate-*l/ 66.4%

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

   15. *-lft-identity 66.4%

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

10. Simplified 66.4%

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

11. Taylor expanded in z around inf 35.5%

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

12. Taylor expanded in t around inf 20.2%

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

13. Final simplification 20.2%

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

Developer target: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024059 
(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))))