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

Percentage Accurate: 86.8% → 99.3%

Time: 15.1s

Alternatives: 13

Speedup: 1.3×

• 24.5% 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: 86.8% 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: 99.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.3%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

   4. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

   5. *-rgt-identity N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

   6. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

   8. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

   9. div-sub N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   11. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

3. Simplified 98.7%

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

Alternative 2: 91.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{2 \cdot \frac{y}{t}}{z}}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{t} + \left(-2 + \frac{2}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* 2.0 (/ y t)) z)) y)))
   (if (<= (/ x y) -5e+23)
     t_1
     (if (<= (/ x y) 4e-27) (+ (/ 2.0 t) (+ -2.0 (/ 2.0 (* z t)))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + ((2.0 * (y / t)) / z)) / y;
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_1;
	} else if ((x / y) <= 4e-27) {
		tmp = (2.0 / t) + (-2.0 + (2.0 / (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((2.0d0 * (y / t)) / z)) / y
    if ((x / y) <= (-5d+23)) then
        tmp = t_1
    else if ((x / y) <= 4d-27) then
        tmp = (2.0d0 / t) + ((-2.0d0) + (2.0d0 / (z * t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + ((2.0 * (y / t)) / z)) / y;
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_1;
	} else if ((x / y) <= 4e-27) {
		tmp = (2.0 / t) + (-2.0 + (2.0 / (z * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + ((2.0 * (y / t)) / z)) / y
	tmp = 0
	if (x / y) <= -5e+23:
		tmp = t_1
	elif (x / y) <= 4e-27:
		tmp = (2.0 / t) + (-2.0 + (2.0 / (z * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(2.0 * Float64(y / t)) / z)) / y)
	tmp = 0.0
	if (Float64(x / y) <= -5e+23)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-27)
		tmp = Float64(Float64(2.0 / t) + Float64(-2.0 + Float64(2.0 / Float64(z * t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + ((2.0 * (y / t)) / z)) / y;
	tmp = 0.0;
	if ((x / y) <= -5e+23)
		tmp = t_1;
	elseif ((x / y) <= 4e-27)
		tmp = (2.0 / t) + (-2.0 + (2.0 / (z * t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(2.0 * N[(y / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+23], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-27], N[(N[(2.0 / t), $MachinePrecision] + N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e23 or 4.0000000000000002e-27 < (/.f64 x y)

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\color{blue}{\left(2 + 2 \cdot z\right)}, \mathsf{*.f64}\left(t, z\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(2 \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{t}, z\right)\right)\right) \]

      2. *-lowering-*.f64 96.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{*.f64}\left(2, z\right)\right), \mathsf{*.f64}\left(t, z\right)\right)\right) \]

   5. Simplified 96.8%

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

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + y \cdot \left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)\right), \color{blue}{y}\right) \]

   8. Simplified 97.5%

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

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \color{blue}{\left(2 \cdot \frac{y}{t \cdot z}\right)}\right), y\right) \]
   10. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(2 \cdot \frac{\frac{y}{t}}{z}\right)\right), y\right) \]

       2. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{2 \cdot \frac{y}{t}}{z}\right)\right), y\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(2 \cdot \frac{y}{t}\right), z\right)\right), y\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{y}{t}\right)\right), z\right)\right), y\right) \]

       5. /-lowering-/.f64 95.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(y, t\right)\right), z\right)\right), y\right) \]

   11. Simplified 95.4%

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

   if -4.9999999999999999e23 < (/.f64 x y) < 4.0000000000000002e-27

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 99.0%

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

      1. +-commutative N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{\left(\frac{1}{t} \cdot \frac{2}{z} + -2\right)}\right) \]

      8. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), \left(\color{blue}{\frac{1}{t} \cdot \frac{2}{z}} + -2\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \left(\color{blue}{\frac{1}{t} \cdot \frac{2}{z}} + -2\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\left(\frac{1}{t} \cdot \frac{2}{z}\right), \color{blue}{-2}\right)\right) \]

      11. frac-times N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\left(\frac{1 \cdot 2}{t \cdot z}\right), -2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\left(\frac{2}{t \cdot z}\right), -2\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, \left(t \cdot z\right)\right), -2\right)\right) \]

      14. *-lowering-*.f64 99.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, z\right)\right), -2\right)\right) \]

   9. Applied egg-rr 99.1%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + \frac{2 \cdot \frac{y}{t}}{z}}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{t} + \left(-2 + \frac{2}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{2 \cdot \frac{y}{t}}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} + t\_1\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{t} + \left(-2 + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))) (t_2 (+ (/ x y) t_1)))
   (if (<= (/ x y) -5e+23)
     t_2
     (if (<= (/ x y) 4e-27) (+ (/ 2.0 t) (+ -2.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double t_2 = (x / y) + t_1;
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_2;
	} else if ((x / y) <= 4e-27) {
		tmp = (2.0 / t) + (-2.0 + 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 / (z * t)
    t_2 = (x / y) + t_1
    if ((x / y) <= (-5d+23)) then
        tmp = t_2
    else if ((x / y) <= 4d-27) then
        tmp = (2.0d0 / t) + ((-2.0d0) + 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 / (z * t);
	double t_2 = (x / y) + t_1;
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_2;
	} else if ((x / y) <= 4e-27) {
		tmp = (2.0 / t) + (-2.0 + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (z * t)
	t_2 = (x / y) + t_1
	tmp = 0
	if (x / y) <= -5e+23:
		tmp = t_2
	elif (x / y) <= 4e-27:
		tmp = (2.0 / t) + (-2.0 + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	t_2 = Float64(Float64(x / y) + t_1)
	tmp = 0.0
	if (Float64(x / y) <= -5e+23)
		tmp = t_2;
	elseif (Float64(x / y) <= 4e-27)
		tmp = Float64(Float64(2.0 / t) + Float64(-2.0 + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (z * t);
	t_2 = (x / y) + t_1;
	tmp = 0.0;
	if ((x / y) <= -5e+23)
		tmp = t_2;
	elseif ((x / y) <= 4e-27)
		tmp = (2.0 / t) + (-2.0 + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+23], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 4e-27], N[(N[(2.0 / t), $MachinePrecision] + N[(-2.0 + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e23 or 4.0000000000000002e-27 < (/.f64 x y)

   1. Initial program 82.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t \cdot z}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      2. *-lowering-*.f64 93.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 93.1%

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

   if -4.9999999999999999e23 < (/.f64 x y) < 4.0000000000000002e-27

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 99.0%

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

      1. +-commutative N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{\left(\frac{1}{t} \cdot \frac{2}{z} + -2\right)}\right) \]

      8. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), \left(\color{blue}{\frac{1}{t} \cdot \frac{2}{z}} + -2\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \left(\color{blue}{\frac{1}{t} \cdot \frac{2}{z}} + -2\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\left(\frac{1}{t} \cdot \frac{2}{z}\right), \color{blue}{-2}\right)\right) \]

      11. frac-times N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\left(\frac{1 \cdot 2}{t \cdot z}\right), -2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\left(\frac{2}{t \cdot z}\right), -2\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, \left(t \cdot z\right)\right), -2\right)\right) \]

      14. *-lowering-*.f64 99.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, z\right)\right), -2\right)\right) \]

   9. Applied egg-rr 99.1%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{t} + \left(-2 + \frac{2}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -4.7 \cdot 10^{-34}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3 \cdot 10^{-11}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5.8e+19)
   (/ x y)
   (if (<= (/ x y) -4.7e-34) (/ 2.0 t) (if (<= (/ x y) 3e-11) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.8e+19) {
		tmp = x / y;
	} else if ((x / y) <= -4.7e-34) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 3e-11) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5.8d+19)) then
        tmp = x / y
    else if ((x / y) <= (-4.7d-34)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 3d-11) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.8e+19) {
		tmp = x / y;
	} else if ((x / y) <= -4.7e-34) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 3e-11) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5.8e+19:
		tmp = x / y
	elif (x / y) <= -4.7e-34:
		tmp = 2.0 / t
	elif (x / y) <= 3e-11:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5.8e+19)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -4.7e-34)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 3e-11)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5.8e+19)
		tmp = x / y;
	elseif ((x / y) <= -4.7e-34)
		tmp = 2.0 / t;
	elseif ((x / y) <= 3e-11)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5.8e+19], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -4.7e-34], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3e-11], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.8e19 or 3e-11 < (/.f64 x y)

   1. Initial program 82.5%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 78.7%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 78.7%

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

   if -5.8e19 < (/.f64 x y) < -4.70000000000000002e-34

   1. Initial program 81.0%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 93.5%

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

   8. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 57.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   10. Simplified 57.8%

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

   11. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 41.5%

          \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{t}\right) \]

   13. Simplified 41.5%

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

   if -4.70000000000000002e-34 < (/.f64 x y) < 3e-11

   1. Initial program 86.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 43.2%

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

Alternative 5: 91.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 (* z t)))))
   (if (<= (/ x y) -5e+23)
     t_1
     (if (<= (/ x y) 4e-27) (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_1;
	} else if ((x / y) <= 4e-27) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / (z * t))
    if ((x / y) <= (-5d+23)) then
        tmp = t_1
    else if ((x / y) <= 4d-27) then
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_1;
	} else if ((x / y) <= 4e-27) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / (z * t))
	tmp = 0
	if (x / y) <= -5e+23:
		tmp = t_1
	elif (x / y) <= 4e-27:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)))
	tmp = 0.0
	if (Float64(x / y) <= -5e+23)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-27)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / (z * t));
	tmp = 0.0;
	if ((x / y) <= -5e+23)
		tmp = t_1;
	elseif ((x / y) <= 4e-27)
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+23], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-27], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e23 or 4.0000000000000002e-27 < (/.f64 x y)

   1. Initial program 82.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t \cdot z}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{\left(t \cdot z\right)}\right)\right) \]

      2. *-lowering-*.f64 93.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 93.1%

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

   if -4.9999999999999999e23 < (/.f64 x y) < 4.0000000000000002e-27

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 99.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+67)
   (/ x y)
   (if (<= (/ x y) 5e-11) (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+67) {
		tmp = x / y;
	} else if ((x / y) <= 5e-11) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} 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) <= (-2d+67)) then
        tmp = x / y
    else if ((x / y) <= 5d-11) then
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    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) <= -2e+67) {
		tmp = x / y;
	} else if ((x / y) <= 5e-11) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+67:
		tmp = x / y
	elif (x / y) <= 5e-11:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+67)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-11)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	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) <= -2e+67)
		tmp = x / y;
	elseif ((x / y) <= 5e-11)
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+67], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-11], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999997e67

   1. Initial program 83.0%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 87.0%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 87.0%

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

   if -1.99999999999999997e67 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 86.5%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 97.1%

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

   if 5.00000000000000018e-11 < (/.f64 x y)

   1. Initial program 80.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 82.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+67)
   (/ x y)
   (if (<= (/ x y) 5e-11) (+ -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) <= -2e+67) {
		tmp = x / y;
	} else if ((x / y) <= 5e-11) {
		tmp = -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) <= (-2d+67)) then
        tmp = x / y
    else if ((x / y) <= 5d-11) then
        tmp = (-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) <= -2e+67) {
		tmp = x / y;
	} else if ((x / y) <= 5e-11) {
		tmp = -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) <= -2e+67:
		tmp = x / y
	elif (x / y) <= 5e-11:
		tmp = -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) <= -2e+67)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-11)
		tmp = Float64(-2.0 + Float64(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) <= -2e+67)
		tmp = x / y;
	elseif ((x / y) <= 5e-11)
		tmp = -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], -2e+67], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-11], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999997e67

   1. Initial program 83.0%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 87.0%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 87.0%

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

   if -1.99999999999999997e67 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 86.5%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(-2, \mathsf{/.f64}\left(\color{blue}{\left(\frac{2}{z}\right)}, t\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 73.8%

         \[\leadsto \mathsf{+.f64}\left(-2, \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right)\right) \]

   10. Simplified 73.8%

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

   if 5.00000000000000018e-11 < (/.f64 x y)

   1. Initial program 80.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 82.1%

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

Alternative 8: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+23)
   (/ x y)
   (if (<= (/ x y) 5e-11) (+ -2.0 (/ 2.0 t)) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = x / y;
	} else if ((x / y) <= 5e-11) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+23)) then
        tmp = x / y
    else if ((x / y) <= 5d-11) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = x / y;
	} else if ((x / y) <= 5e-11) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+23:
		tmp = x / y
	elif (x / y) <= 5e-11:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-11)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+23)
		tmp = x / y;
	elseif ((x / y) <= 5e-11)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-11], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999999e23

   1. Initial program 84.1%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 78.2%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 78.2%

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

   if -4.9999999999999999e23 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 86.2%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 99.0%

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

   8. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 62.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   10. Simplified 62.5%

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

   if 5.00000000000000018e-11 < (/.f64 x y)

   1. Initial program 80.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 82.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 620000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6e+20)
   (/ x y)
   (if (<= (/ x y) 620000.0) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6e+20) {
		tmp = x / y;
	} else if ((x / y) <= 620000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-6d+20)) then
        tmp = x / y
    else if ((x / y) <= 620000.0d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6e+20) {
		tmp = x / y;
	} else if ((x / y) <= 620000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6e+20:
		tmp = x / y
	elif (x / y) <= 620000.0:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -6e+20)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 620000.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -6e+20)
		tmp = x / y;
	elseif ((x / y) <= 620000.0)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -6e+20], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 620000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6e20 or 6.2e5 < (/.f64 x y)

   1. Initial program 82.4%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 79.3%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   7. Simplified 79.3%

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

   if -6e20 < (/.f64 x y) < 6.2e5

   1. Initial program 86.2%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 99.0%

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

   8. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 62.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   10. Simplified 62.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 620000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= t -8.6e-31) t_1 (if (<= t 6.2e-52) (/ (+ 2.0 (/ 2.0 z)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -8.6e-31) {
		tmp = t_1;
	} else if (t <= 6.2e-52) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (t <= (-8.6d-31)) then
        tmp = t_1
    else if (t <= 6.2d-52) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -8.6e-31) {
		tmp = t_1;
	} else if (t <= 6.2e-52) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -8.6e-31:
		tmp = t_1
	elif t <= 6.2e-52:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -8.6e-31)
		tmp = t_1;
	elseif (t <= 6.2e-52)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -8.6e-31)
		tmp = t_1;
	elseif (t <= 6.2e-52)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -8.6e-31], t$95$1, If[LessEqual[t, 6.2e-52], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6e-31 or 6.1999999999999998e-52 < t

   1. Initial program 76.3%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 81.7%

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

   if -8.6e-31 < t < 6.1999999999999998e-52

   1. Initial program 96.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(2 + 2 \cdot \frac{1}{z}\right), \color{blue}{t}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(2 \cdot \frac{1}{z}\right)\right), t\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(\frac{2 \cdot 1}{z}\right)\right), t\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(\frac{2}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 79.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right) \]

   7. Simplified 79.0%

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

Alternative 11: 64.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-190}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= z -5.8e-69) t_1 (if (<= z 1.3e-190) (/ 2.0 (* z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -5.8e-69) {
		tmp = t_1;
	} else if (z <= 1.3e-190) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (z <= (-5.8d-69)) then
        tmp = t_1
    else if (z <= 1.3d-190) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -5.8e-69) {
		tmp = t_1;
	} else if (z <= 1.3e-190) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if z <= -5.8e-69:
		tmp = t_1
	elif z <= 1.3e-190:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (z <= -5.8e-69)
		tmp = t_1;
	elseif (z <= 1.3e-190)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (z <= -5.8e-69)
		tmp = t_1;
	elseif (z <= 1.3e-190)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -5.8e-69], t$95$1, If[LessEqual[z, 1.3e-190], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999997e-69 or 1.2999999999999999e-190 < z

   1. Initial program 77.4%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 72.0%

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

   if -5.7999999999999997e-69 < z < 1.2999999999999999e-190

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{/.f64}\left(2, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 71.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-190}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -130000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -130000.0) -2.0 (if (<= t 8.5e+20) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -130000.0) {
		tmp = -2.0;
	} else if (t <= 8.5e+20) {
		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 <= (-130000.0d0)) then
        tmp = -2.0d0
    else if (t <= 8.5d+20) 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 <= -130000.0) {
		tmp = -2.0;
	} else if (t <= 8.5e+20) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -130000.0:
		tmp = -2.0
	elif t <= 8.5e+20:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -130000.0)
		tmp = -2.0;
	elseif (t <= 8.5e+20)
		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 <= -130000.0)
		tmp = -2.0;
	elseif (t <= 8.5e+20)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -130000.0], -2.0, If[LessEqual[t, 8.5e+20], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e5 or 8.5e20 < t

   1. Initial program 72.3%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 50.6%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 36.7%

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

   if -1.3e5 < t < 8.5e20

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      5. *-rgt-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

      6. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   3. Simplified 97.4%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 72.5%

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

   8. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 30.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   10. Simplified 30.5%

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

   11. Taylor expanded in t around 0

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

       1. /-lowering-/.f64 29.7%

          \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{t}\right) \]

   13. Simplified 29.7%

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

Alternative 13: 20.2% 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 84.3%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\right)}\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}}{t \cdot z}\right)\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

   4. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(\left(z \cdot 2\right) \cdot 1 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

   5. *-rgt-identity N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + \left(z \cdot 2 + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)\right)}{t \cdot z}\right)\right) \]

   6. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(z \cdot 2\right) \cdot \left(\mathsf{neg}\left(t\right)\right)}{\color{blue}{t} \cdot z}\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) + \left(\mathsf{neg}\left(\left(z \cdot 2\right) \cdot t\right)\right)}{t \cdot z}\right)\right) \]

   8. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\left(2 + z \cdot 2\right) - \left(z \cdot 2\right) \cdot t}{\color{blue}{t} \cdot z}\right)\right) \]

   9. div-sub N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}}\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

   11. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 + z \cdot 2}{t \cdot z}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{\left(z \cdot 2\right) \cdot t}{t \cdot z}\right)\right)}\right)\right) \]

3. Simplified 98.7%

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

5. Taylor expanded in x around 0

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

7. Simplified 61.1%

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

8. Taylor expanded in t around inf

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

10. Simplified 20.4%

    \[\leadsto \color{blue}{-2} \]
11. Add Preprocessing

Developer Target 1: 99.3% 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 2024192 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

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