Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Percentage Accurate: 97.8% → 98.0%

Time: 7.5s

Alternatives: 15

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \frac{z - t}{\frac{y}{x}} \end{array} \]

FPCore

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

C

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

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 = t + ((z - t) / (y / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. *-commutative 98.4%

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

   2. clear-num 98.4%

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

   3. un-div-inv 98.7%

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

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

   \[\leadsto t + \frac{z - t}{\frac{y}{x}} \]
6. Add Preprocessing

Alternative 2: 65.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ t_2 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -40000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+221} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))) (t_2 (* t (/ x (- y)))))
   (if (<= (/ x y) -2e+166)
     t_1
     (if (<= (/ x y) -5e+125)
       t_2
       (if (<= (/ x y) -5e+40)
         t_1
         (if (<= (/ x y) -40000000000.0)
           t_2
           (if (<= (/ x y) -5e-19)
             t_1
             (if (<= (/ x y) -5e-29)
               t
               (if (<= (/ x y) -1e-58)
                 t_1
                 (if (<= (/ x y) 5e-49)
                   t
                   (if (or (<= (/ x y) 2e+221) (not (<= (/ x y) 4e+299)))
                     (/ z (/ y x))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = t * (x / -y);
	double tmp;
	if ((x / y) <= -2e+166) {
		tmp = t_1;
	} else if ((x / y) <= -5e+125) {
		tmp = t_2;
	} else if ((x / y) <= -5e+40) {
		tmp = t_1;
	} else if ((x / y) <= -40000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else if (((x / y) <= 2e+221) || !((x / y) <= 4e+299)) {
		tmp = z / (y / x);
	} 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 = z * (x / y)
    t_2 = t * (x / -y)
    if ((x / y) <= (-2d+166)) then
        tmp = t_1
    else if ((x / y) <= (-5d+125)) then
        tmp = t_2
    else if ((x / y) <= (-5d+40)) then
        tmp = t_1
    else if ((x / y) <= (-40000000000.0d0)) then
        tmp = t_2
    else if ((x / y) <= (-5d-19)) then
        tmp = t_1
    else if ((x / y) <= (-5d-29)) then
        tmp = t
    else if ((x / y) <= (-1d-58)) then
        tmp = t_1
    else if ((x / y) <= 5d-49) then
        tmp = t
    else if (((x / y) <= 2d+221) .or. (.not. ((x / y) <= 4d+299))) then
        tmp = z / (y / x)
    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 = z * (x / y);
	double t_2 = t * (x / -y);
	double tmp;
	if ((x / y) <= -2e+166) {
		tmp = t_1;
	} else if ((x / y) <= -5e+125) {
		tmp = t_2;
	} else if ((x / y) <= -5e+40) {
		tmp = t_1;
	} else if ((x / y) <= -40000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else if (((x / y) <= 2e+221) || !((x / y) <= 4e+299)) {
		tmp = z / (y / x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	t_2 = t * (x / -y)
	tmp = 0
	if (x / y) <= -2e+166:
		tmp = t_1
	elif (x / y) <= -5e+125:
		tmp = t_2
	elif (x / y) <= -5e+40:
		tmp = t_1
	elif (x / y) <= -40000000000.0:
		tmp = t_2
	elif (x / y) <= -5e-19:
		tmp = t_1
	elif (x / y) <= -5e-29:
		tmp = t
	elif (x / y) <= -1e-58:
		tmp = t_1
	elif (x / y) <= 5e-49:
		tmp = t
	elif ((x / y) <= 2e+221) or not ((x / y) <= 4e+299):
		tmp = z / (y / x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	t_2 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (Float64(x / y) <= -2e+166)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e+125)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e+40)
		tmp = t_1;
	elseif (Float64(x / y) <= -40000000000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e-19)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e-29)
		tmp = t;
	elseif (Float64(x / y) <= -1e-58)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-49)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+221) || !(Float64(x / y) <= 4e+299))
		tmp = Float64(z / Float64(y / x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	t_2 = t * (x / -y);
	tmp = 0.0;
	if ((x / y) <= -2e+166)
		tmp = t_1;
	elseif ((x / y) <= -5e+125)
		tmp = t_2;
	elseif ((x / y) <= -5e+40)
		tmp = t_1;
	elseif ((x / y) <= -40000000000.0)
		tmp = t_2;
	elseif ((x / y) <= -5e-19)
		tmp = t_1;
	elseif ((x / y) <= -5e-29)
		tmp = t;
	elseif ((x / y) <= -1e-58)
		tmp = t_1;
	elseif ((x / y) <= 5e-49)
		tmp = t;
	elseif (((x / y) <= 2e+221) || ~(((x / y) <= 4e+299)))
		tmp = z / (y / x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+166], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e+125], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e+40], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -40000000000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e-19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e-29], t, If[LessEqual[N[(x / y), $MachinePrecision], -1e-58], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-49], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+221], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+299]], $MachinePrecision]], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -1.99999999999999988e166 or -4.99999999999999962e125 < (/.f64 x y) < -5.00000000000000003e40 or -4e10 < (/.f64 x y) < -5.0000000000000004e-19 or -4.99999999999999986e-29 < (/.f64 x y) < -1e-58

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 83.4%

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

   4. Taylor expanded in z around inf 60.6%

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

      1. clear-num 60.5%

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

      2. un-div-inv 60.7%

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

   6. Applied egg-rr 60.7%

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

      1. associate-/r/ 73.4%

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

   8. Applied egg-rr 73.4%

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

   if -1.99999999999999988e166 < (/.f64 x y) < -4.99999999999999962e125 or -5.00000000000000003e40 < (/.f64 x y) < -4e10 or 2.0000000000000001e221 < (/.f64 x y) < 4.0000000000000002e299

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. *-commutative 82.5%

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

      2. sub-div 82.7%

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

      3. associate-/r/ 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in z around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. distribute-frac-neg 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. associate-*r/ 77.7%

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

   8. Simplified 77.7%

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

   if -5.0000000000000004e-19 < (/.f64 x y) < -4.99999999999999986e-29 or -1e-58 < (/.f64 x y) < 4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.0%

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

   if 4.9999999999999999e-49 < (/.f64 x y) < 2.0000000000000001e221 or 4.0000000000000002e299 < (/.f64 x y)

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 75.4%

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

   4. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/r/ 63.9%

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

   6. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{z}{\frac{y}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -40000000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+221} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ t_2 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -40000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+221} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))) (t_2 (* t (/ x (- y)))))
   (if (<= (/ x y) -2e+166)
     t_1
     (if (<= (/ x y) -5e+125)
       t_2
       (if (<= (/ x y) -5e+40)
         t_1
         (if (<= (/ x y) -40000000000.0)
           t_2
           (if (<= (/ x y) -5e-19)
             t_1
             (if (<= (/ x y) -5e-29)
               t
               (if (<= (/ x y) -1e-58)
                 t_1
                 (if (<= (/ x y) 5e-49)
                   t
                   (if (or (<= (/ x y) 2e+221) (not (<= (/ x y) 4e+299)))
                     (/ z (/ y x))
                     (* x (/ t (- y))))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = t * (x / -y);
	double tmp;
	if ((x / y) <= -2e+166) {
		tmp = t_1;
	} else if ((x / y) <= -5e+125) {
		tmp = t_2;
	} else if ((x / y) <= -5e+40) {
		tmp = t_1;
	} else if ((x / y) <= -40000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else if (((x / y) <= 2e+221) || !((x / y) <= 4e+299)) {
		tmp = z / (y / x);
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x / y)
    t_2 = t * (x / -y)
    if ((x / y) <= (-2d+166)) then
        tmp = t_1
    else if ((x / y) <= (-5d+125)) then
        tmp = t_2
    else if ((x / y) <= (-5d+40)) then
        tmp = t_1
    else if ((x / y) <= (-40000000000.0d0)) then
        tmp = t_2
    else if ((x / y) <= (-5d-19)) then
        tmp = t_1
    else if ((x / y) <= (-5d-29)) then
        tmp = t
    else if ((x / y) <= (-1d-58)) then
        tmp = t_1
    else if ((x / y) <= 5d-49) then
        tmp = t
    else if (((x / y) <= 2d+221) .or. (.not. ((x / y) <= 4d+299))) then
        tmp = z / (y / x)
    else
        tmp = x * (t / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = t * (x / -y);
	double tmp;
	if ((x / y) <= -2e+166) {
		tmp = t_1;
	} else if ((x / y) <= -5e+125) {
		tmp = t_2;
	} else if ((x / y) <= -5e+40) {
		tmp = t_1;
	} else if ((x / y) <= -40000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else if (((x / y) <= 2e+221) || !((x / y) <= 4e+299)) {
		tmp = z / (y / x);
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	t_2 = t * (x / -y)
	tmp = 0
	if (x / y) <= -2e+166:
		tmp = t_1
	elif (x / y) <= -5e+125:
		tmp = t_2
	elif (x / y) <= -5e+40:
		tmp = t_1
	elif (x / y) <= -40000000000.0:
		tmp = t_2
	elif (x / y) <= -5e-19:
		tmp = t_1
	elif (x / y) <= -5e-29:
		tmp = t
	elif (x / y) <= -1e-58:
		tmp = t_1
	elif (x / y) <= 5e-49:
		tmp = t
	elif ((x / y) <= 2e+221) or not ((x / y) <= 4e+299):
		tmp = z / (y / x)
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	t_2 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (Float64(x / y) <= -2e+166)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e+125)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e+40)
		tmp = t_1;
	elseif (Float64(x / y) <= -40000000000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e-19)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e-29)
		tmp = t;
	elseif (Float64(x / y) <= -1e-58)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-49)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+221) || !(Float64(x / y) <= 4e+299))
		tmp = Float64(z / Float64(y / x));
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	t_2 = t * (x / -y);
	tmp = 0.0;
	if ((x / y) <= -2e+166)
		tmp = t_1;
	elseif ((x / y) <= -5e+125)
		tmp = t_2;
	elseif ((x / y) <= -5e+40)
		tmp = t_1;
	elseif ((x / y) <= -40000000000.0)
		tmp = t_2;
	elseif ((x / y) <= -5e-19)
		tmp = t_1;
	elseif ((x / y) <= -5e-29)
		tmp = t;
	elseif ((x / y) <= -1e-58)
		tmp = t_1;
	elseif ((x / y) <= 5e-49)
		tmp = t;
	elseif (((x / y) <= 2e+221) || ~(((x / y) <= 4e+299)))
		tmp = z / (y / x);
	else
		tmp = x * (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+166], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e+125], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e+40], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -40000000000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e-19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e-29], t, If[LessEqual[N[(x / y), $MachinePrecision], -1e-58], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-49], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+221], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+299]], $MachinePrecision]], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -1.99999999999999988e166 or -4.99999999999999962e125 < (/.f64 x y) < -5.00000000000000003e40 or -4e10 < (/.f64 x y) < -5.0000000000000004e-19 or -4.99999999999999986e-29 < (/.f64 x y) < -1e-58

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 83.4%

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

   4. Taylor expanded in z around inf 60.6%

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

      1. clear-num 60.5%

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

      2. un-div-inv 60.7%

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

   6. Applied egg-rr 60.7%

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

      1. associate-/r/ 73.4%

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

   8. Applied egg-rr 73.4%

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

   if -1.99999999999999988e166 < (/.f64 x y) < -4.99999999999999962e125 or -5.00000000000000003e40 < (/.f64 x y) < -4e10

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. sub-div 75.9%

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

      3. associate-/r/ 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-frac-neg 60.4%

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

      3. distribute-rgt-neg-in 60.4%

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

      4. associate-*r/ 74.4%

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

   8. Simplified 74.4%

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

   if -5.0000000000000004e-19 < (/.f64 x y) < -4.99999999999999986e-29 or -1e-58 < (/.f64 x y) < 4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.0%

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

   if 4.9999999999999999e-49 < (/.f64 x y) < 2.0000000000000001e221 or 4.0000000000000002e299 < (/.f64 x y)

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 75.4%

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

   4. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/r/ 63.9%

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

   6. Applied egg-rr 63.9%

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

   if 2.0000000000000001e221 < (/.f64 x y) < 4.0000000000000002e299

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in z around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. neg-mul-1 86.1%

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

   6. Simplified 86.1%

      \[\leadsto x \cdot \color{blue}{\frac{-t}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -40000000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+221} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+125}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -40000000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+221} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -2e+166)
     t_1
     (if (<= (/ x y) -5e+125)
       (/ (* t x) (- y))
       (if (<= (/ x y) -5e+40)
         t_1
         (if (<= (/ x y) -40000000000.0)
           (* t (/ x (- y)))
           (if (<= (/ x y) -5e-19)
             t_1
             (if (<= (/ x y) -5e-29)
               t
               (if (<= (/ x y) -1e-58)
                 t_1
                 (if (<= (/ x y) 5e-49)
                   t
                   (if (or (<= (/ x y) 2e+221) (not (<= (/ x y) 4e+299)))
                     (/ z (/ y x))
                     (* x (/ t (- y))))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -2e+166) {
		tmp = t_1;
	} else if ((x / y) <= -5e+125) {
		tmp = (t * x) / -y;
	} else if ((x / y) <= -5e+40) {
		tmp = t_1;
	} else if ((x / y) <= -40000000000.0) {
		tmp = t * (x / -y);
	} else if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else if (((x / y) <= 2e+221) || !((x / y) <= 4e+299)) {
		tmp = z / (y / x);
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x / y)
    if ((x / y) <= (-2d+166)) then
        tmp = t_1
    else if ((x / y) <= (-5d+125)) then
        tmp = (t * x) / -y
    else if ((x / y) <= (-5d+40)) then
        tmp = t_1
    else if ((x / y) <= (-40000000000.0d0)) then
        tmp = t * (x / -y)
    else if ((x / y) <= (-5d-19)) then
        tmp = t_1
    else if ((x / y) <= (-5d-29)) then
        tmp = t
    else if ((x / y) <= (-1d-58)) then
        tmp = t_1
    else if ((x / y) <= 5d-49) then
        tmp = t
    else if (((x / y) <= 2d+221) .or. (.not. ((x / y) <= 4d+299))) then
        tmp = z / (y / x)
    else
        tmp = x * (t / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -2e+166) {
		tmp = t_1;
	} else if ((x / y) <= -5e+125) {
		tmp = (t * x) / -y;
	} else if ((x / y) <= -5e+40) {
		tmp = t_1;
	} else if ((x / y) <= -40000000000.0) {
		tmp = t * (x / -y);
	} else if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else if (((x / y) <= 2e+221) || !((x / y) <= 4e+299)) {
		tmp = z / (y / x);
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -2e+166:
		tmp = t_1
	elif (x / y) <= -5e+125:
		tmp = (t * x) / -y
	elif (x / y) <= -5e+40:
		tmp = t_1
	elif (x / y) <= -40000000000.0:
		tmp = t * (x / -y)
	elif (x / y) <= -5e-19:
		tmp = t_1
	elif (x / y) <= -5e-29:
		tmp = t
	elif (x / y) <= -1e-58:
		tmp = t_1
	elif (x / y) <= 5e-49:
		tmp = t
	elif ((x / y) <= 2e+221) or not ((x / y) <= 4e+299):
		tmp = z / (y / x)
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e+166)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e+125)
		tmp = Float64(Float64(t * x) / Float64(-y));
	elseif (Float64(x / y) <= -5e+40)
		tmp = t_1;
	elseif (Float64(x / y) <= -40000000000.0)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (Float64(x / y) <= -5e-19)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e-29)
		tmp = t;
	elseif (Float64(x / y) <= -1e-58)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-49)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+221) || !(Float64(x / y) <= 4e+299))
		tmp = Float64(z / Float64(y / x));
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -2e+166)
		tmp = t_1;
	elseif ((x / y) <= -5e+125)
		tmp = (t * x) / -y;
	elseif ((x / y) <= -5e+40)
		tmp = t_1;
	elseif ((x / y) <= -40000000000.0)
		tmp = t * (x / -y);
	elseif ((x / y) <= -5e-19)
		tmp = t_1;
	elseif ((x / y) <= -5e-29)
		tmp = t;
	elseif ((x / y) <= -1e-58)
		tmp = t_1;
	elseif ((x / y) <= 5e-49)
		tmp = t;
	elseif (((x / y) <= 2e+221) || ~(((x / y) <= 4e+299)))
		tmp = z / (y / x);
	else
		tmp = x * (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+166], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e+125], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -5e+40], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -40000000000.0], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -5e-19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e-29], t, If[LessEqual[N[(x / y), $MachinePrecision], -1e-58], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-49], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+221], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+299]], $MachinePrecision]], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 x y) < -1.99999999999999988e166 or -4.99999999999999962e125 < (/.f64 x y) < -5.00000000000000003e40 or -4e10 < (/.f64 x y) < -5.0000000000000004e-19 or -4.99999999999999986e-29 < (/.f64 x y) < -1e-58

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 83.4%

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

   4. Taylor expanded in z around inf 60.6%

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

      1. clear-num 60.5%

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

      2. un-div-inv 60.7%

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

   6. Applied egg-rr 60.7%

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

      1. associate-/r/ 73.4%

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

   8. Applied egg-rr 73.4%

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

   if -1.99999999999999988e166 < (/.f64 x y) < -4.99999999999999962e125

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 85.8%

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

      1. *-commutative 85.8%

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

      2. sub-div 85.8%

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

      3. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. associate-*l/ 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

   8. Simplified 72.1%

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

      1. associate-*l/ 85.9%

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

      2. frac-2neg 85.9%

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

      3. add-sqr-sqrt 28.8%

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

      4. sqrt-unprod 29.5%

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

      5. sqr-neg 29.5%

         \[\leadsto \frac{-t \cdot \sqrt{\color{blue}{x \cdot x}}}{-y} \]

      6. sqrt-unprod 0.8%

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

      7. add-sqr-sqrt 1.2%

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

      8. distribute-rgt-neg-out 1.2%

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

      9. *-commutative 1.2%

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

      10. add-sqr-sqrt 0.4%

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

      11. sqrt-unprod 29.9%

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

      12. sqr-neg 29.9%

          \[\leadsto \frac{\sqrt{\color{blue}{x \cdot x}} \cdot t}{-y} \]

      13. sqrt-unprod 56.3%

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

      14. add-sqr-sqrt 85.9%

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

   10. Applied egg-rr 85.9%

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

   if -5.00000000000000003e40 < (/.f64 x y) < -4e10

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. sub-div 69.6%

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

      3. associate-/r/ 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in z around 0 44.2%

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

      1. mul-1-neg 44.2%

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

      2. distribute-frac-neg 44.2%

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

      3. distribute-rgt-neg-in 44.2%

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

      4. associate-*r/ 67.3%

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

   8. Simplified 67.3%

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

   if -5.0000000000000004e-19 < (/.f64 x y) < -4.99999999999999986e-29 or -1e-58 < (/.f64 x y) < 4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.0%

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

   if 4.9999999999999999e-49 < (/.f64 x y) < 2.0000000000000001e221 or 4.0000000000000002e299 < (/.f64 x y)

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 75.4%

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

   4. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/r/ 63.9%

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

   6. Applied egg-rr 63.9%

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

   if 2.0000000000000001e221 < (/.f64 x y) < 4.0000000000000002e299

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in z around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. neg-mul-1 86.1%

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

   6. Simplified 86.1%

      \[\leadsto x \cdot \color{blue}{\frac{-t}{y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+125}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -40000000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+221} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-61} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ x y))))
   (if (<= (/ x y) -5e-19)
     t_1
     (if (<= (/ x y) -5e-29)
       t
       (if (or (<= (/ x y) -2e-61) (not (<= (/ x y) 5e-49)))
         t_1
         (* t (- 1.0 (/ x y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if (((x / y) <= -2e-61) || !((x / y) <= 5e-49)) {
		tmp = t_1;
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (x / y)
    if ((x / y) <= (-5d-19)) then
        tmp = t_1
    else if ((x / y) <= (-5d-29)) then
        tmp = t
    else if (((x / y) <= (-2d-61)) .or. (.not. ((x / y) <= 5d-49))) then
        tmp = t_1
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if (((x / y) <= -2e-61) || !((x / y) <= 5e-49)) {
		tmp = t_1;
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z - t) * (x / y)
	tmp = 0
	if (x / y) <= -5e-19:
		tmp = t_1
	elif (x / y) <= -5e-29:
		tmp = t
	elif ((x / y) <= -2e-61) or not ((x / y) <= 5e-49):
		tmp = t_1
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z - t) * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e-19)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e-29)
		tmp = t;
	elseif ((Float64(x / y) <= -2e-61) || !(Float64(x / y) <= 5e-49))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z - t) * (x / y);
	tmp = 0.0;
	if ((x / y) <= -5e-19)
		tmp = t_1;
	elseif ((x / y) <= -5e-29)
		tmp = t;
	elseif (((x / y) <= -2e-61) || ~(((x / y) <= 5e-49)))
		tmp = t_1;
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e-29], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-61], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-49]], $MachinePrecision]], t$95$1, N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000004e-19 or -4.99999999999999986e-29 < (/.f64 x y) < -2.0000000000000001e-61 or 4.9999999999999999e-49 < (/.f64 x y)

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 79.6%

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

      1. *-commutative 79.6%

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

      2. sub-div 84.2%

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

      3. associate-/r/ 91.9%

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

   5. Applied egg-rr 91.9%

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

   6. Taylor expanded in z around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*r/ 78.5%

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

      4. mul-1-neg 78.5%

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

      5. associate-*r/ 81.5%

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

      6. sub-neg 81.5%

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

      7. distribute-rgt-out-- 91.5%

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

   8. Simplified 91.5%

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

   if -5.0000000000000004e-19 < (/.f64 x y) < -4.99999999999999986e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   if -2.0000000000000001e-61 < (/.f64 x y) < 4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

      3. *-rgt-identity 83.2%

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

      4. associate-/l* 87.1%

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

      5. distribute-lft-out-- 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-61} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-19} \lor \neg \left(\frac{x}{y} \leq -5 \cdot 10^{-29} \lor \neg \left(\frac{x}{y} \leq -1 \cdot 10^{-58}\right) \land \frac{x}{y} \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-19)
         (not
          (or (<= (/ x y) -5e-29)
              (and (not (<= (/ x y) -1e-58)) (<= (/ x y) 5e-49)))))
   (* z (/ x y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-19) || !(((x / y) <= -5e-29) || (!((x / y) <= -1e-58) && ((x / y) <= 5e-49)))) {
		tmp = z * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d-19)) .or. (.not. ((x / y) <= (-5d-29)) .or. (.not. ((x / y) <= (-1d-58))) .and. ((x / y) <= 5d-49))) then
        tmp = z * (x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-19) || !(((x / y) <= -5e-29) || (!((x / y) <= -1e-58) && ((x / y) <= 5e-49)))) {
		tmp = z * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-19) or not (((x / y) <= -5e-29) or (not ((x / y) <= -1e-58) and ((x / y) <= 5e-49))):
		tmp = z * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-19) || !((Float64(x / y) <= -5e-29) || (!(Float64(x / y) <= -1e-58) && (Float64(x / y) <= 5e-49))))
		tmp = Float64(z * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-19) || ~((((x / y) <= -5e-29) || (~(((x / y) <= -1e-58)) && ((x / y) <= 5e-49)))))
		tmp = z * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-19], N[Not[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-29], And[N[Not[LessEqual[N[(x / y), $MachinePrecision], -1e-58]], $MachinePrecision], LessEqual[N[(x / y), $MachinePrecision], 5e-49]]]], $MachinePrecision]], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000004e-19 or -4.99999999999999986e-29 < (/.f64 x y) < -1e-58 or 4.9999999999999999e-49 < (/.f64 x y)

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 79.9%

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

   4. Taylor expanded in z around inf 50.1%

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

      1. clear-num 49.3%

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

      2. un-div-inv 49.4%

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

   6. Applied egg-rr 49.4%

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

      1. associate-/r/ 61.0%

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

   8. Applied egg-rr 61.0%

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

   if -5.0000000000000004e-19 < (/.f64 x y) < -4.99999999999999986e-29 or -1e-58 < (/.f64 x y) < 4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-19} \lor \neg \left(\frac{x}{y} \leq -5 \cdot 10^{-29} \lor \neg \left(\frac{x}{y} \leq -1 \cdot 10^{-58}\right) \land \frac{x}{y} \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -5e-19)
     t_1
     (if (<= (/ x y) -5e-29)
       t
       (if (<= (/ x y) -1e-58) t_1 (if (<= (/ x y) 5e-49) t (/ z (/ y x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	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 = z * (x / y)
    if ((x / y) <= (-5d-19)) then
        tmp = t_1
    else if ((x / y) <= (-5d-29)) then
        tmp = t
    else if ((x / y) <= (-1d-58)) then
        tmp = t_1
    else if ((x / y) <= 5d-49) then
        tmp = t
    else
        tmp = z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -5e-19) {
		tmp = t_1;
	} else if ((x / y) <= -5e-29) {
		tmp = t;
	} else if ((x / y) <= -1e-58) {
		tmp = t_1;
	} else if ((x / y) <= 5e-49) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -5e-19:
		tmp = t_1
	elif (x / y) <= -5e-29:
		tmp = t
	elif (x / y) <= -1e-58:
		tmp = t_1
	elif (x / y) <= 5e-49:
		tmp = t
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e-19)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e-29)
		tmp = t;
	elseif (Float64(x / y) <= -1e-58)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-49)
		tmp = t;
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -5e-19)
		tmp = t_1;
	elseif ((x / y) <= -5e-29)
		tmp = t;
	elseif ((x / y) <= -1e-58)
		tmp = t_1;
	elseif ((x / y) <= 5e-49)
		tmp = t;
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e-29], t, If[LessEqual[N[(x / y), $MachinePrecision], -1e-58], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-49], t, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000004e-19 or -4.99999999999999986e-29 < (/.f64 x y) < -1e-58

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 81.7%

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

   4. Taylor expanded in z around inf 51.5%

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

      1. clear-num 51.5%

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

      2. un-div-inv 51.6%

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

   6. Applied egg-rr 51.6%

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

      1. associate-/r/ 62.7%

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

   8. Applied egg-rr 62.7%

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

   if -5.0000000000000004e-19 < (/.f64 x y) < -4.99999999999999986e-29 or -1e-58 < (/.f64 x y) < 4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.0%

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

   if 4.9999999999999999e-49 < (/.f64 x y)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 77.9%

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

   4. Taylor expanded in z around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-/r/ 59.1%

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

   6. Applied egg-rr 59.1%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{y}{x}}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+254}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ y x))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= z -1.15e+74)
     t_1
     (if (<= z 7.2e+143)
       t_2
       (if (<= z 1.85e+207) t_1 (if (<= z 3.7e+254) t_2 (/ (* z x) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (z <= -1.15e+74) {
		tmp = t_1;
	} else if (z <= 7.2e+143) {
		tmp = t_2;
	} else if (z <= 1.85e+207) {
		tmp = t_1;
	} else if (z <= 3.7e+254) {
		tmp = t_2;
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z / (y / x)
    t_2 = t * (1.0d0 - (x / y))
    if (z <= (-1.15d+74)) then
        tmp = t_1
    else if (z <= 7.2d+143) then
        tmp = t_2
    else if (z <= 1.85d+207) then
        tmp = t_1
    else if (z <= 3.7d+254) then
        tmp = t_2
    else
        tmp = (z * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (z <= -1.15e+74) {
		tmp = t_1;
	} else if (z <= 7.2e+143) {
		tmp = t_2;
	} else if (z <= 1.85e+207) {
		tmp = t_1;
	} else if (z <= 3.7e+254) {
		tmp = t_2;
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (y / x)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if z <= -1.15e+74:
		tmp = t_1
	elif z <= 7.2e+143:
		tmp = t_2
	elif z <= 1.85e+207:
		tmp = t_1
	elif z <= 3.7e+254:
		tmp = t_2
	else:
		tmp = (z * x) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(y / x))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (z <= -1.15e+74)
		tmp = t_1;
	elseif (z <= 7.2e+143)
		tmp = t_2;
	elseif (z <= 1.85e+207)
		tmp = t_1;
	elseif (z <= 3.7e+254)
		tmp = t_2;
	else
		tmp = Float64(Float64(z * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (y / x);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (z <= -1.15e+74)
		tmp = t_1;
	elseif (z <= 7.2e+143)
		tmp = t_2;
	elseif (z <= 1.85e+207)
		tmp = t_1;
	elseif (z <= 3.7e+254)
		tmp = t_2;
	else
		tmp = (z * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+74], t$95$1, If[LessEqual[z, 7.2e+143], t$95$2, If[LessEqual[z, 1.85e+207], t$95$1, If[LessEqual[z, 3.7e+254], t$95$2, N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e74 or 7.1999999999999998e143 < z < 1.85e207

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 58.1%

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

   4. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/r/ 77.2%

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

   6. Applied egg-rr 77.2%

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

   if -1.1499999999999999e74 < z < 7.1999999999999998e143 or 1.85e207 < z < 3.6999999999999999e254

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. unsub-neg 73.3%

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

      3. *-rgt-identity 73.3%

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

      4. associate-/l* 78.4%

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

      5. distribute-lft-out-- 78.4%

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

   5. Simplified 78.4%

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

   if 3.6999999999999999e254 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 71.2%

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

   4. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+207}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+254}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-20} \lor \neg \left(\frac{x}{y} \leq 50\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-20) (not (<= (/ x y) 50.0)))
   (* (- z t) (/ x y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-20) || !((x / y) <= 50.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x * (z / 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) <= (-2d-20)) .or. (.not. ((x / y) <= 50.0d0))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t + (x * (z / 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) <= -2e-20) || !((x / y) <= 50.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-20) or not ((x / y) <= 50.0):
		tmp = (z - t) * (x / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-20) || !(Float64(x / y) <= 50.0))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-20) || ~(((x / y) <= 50.0)))
		tmp = (z - t) * (x / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 50.0]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999989e-20 or 50 < (/.f64 x y)

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. sub-div 88.4%

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

      3. associate-/r/ 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in z around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-*r/ 79.4%

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

      4. mul-1-neg 79.4%

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

      5. associate-*r/ 82.7%

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

      6. sub-neg 82.7%

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

      7. distribute-rgt-out-- 94.0%

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

   8. Simplified 94.0%

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

   if -1.99999999999999989e-20 < (/.f64 x y) < 50

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 95.5%

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

      1. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-20} \lor \neg \left(\frac{x}{y} \leq 50\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-20} \lor \neg \left(\frac{x}{y} \leq 50\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-20) (not (<= (/ x y) 50.0)))
   (* (- z t) (/ x y))
   (+ t (/ x (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-20) || !((x / y) <= 50.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d-20)) .or. (.not. ((x / y) <= 50.0d0))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t + (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-20) || !((x / y) <= 50.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-20) or not ((x / y) <= 50.0):
		tmp = (z - t) * (x / y)
	else:
		tmp = t + (x / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-20) || !(Float64(x / y) <= 50.0))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-20) || ~(((x / y) <= 50.0)))
		tmp = (z - t) * (x / y);
	else
		tmp = t + (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 50.0]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999989e-20 or 50 < (/.f64 x y)

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. sub-div 88.4%

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

      3. associate-/r/ 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in z around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-*r/ 79.4%

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

      4. mul-1-neg 79.4%

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

      5. associate-*r/ 82.7%

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

      6. sub-neg 82.7%

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

      7. distribute-rgt-out-- 94.0%

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

   8. Simplified 94.0%

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

   if -1.99999999999999989e-20 < (/.f64 x y) < 50

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 95.5%

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

      1. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

      1. clear-num 19.3%

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

      2. un-div-inv 19.6%

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

   7. Applied egg-rr 95.1%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-20} \lor \neg \left(\frac{x}{y} \leq 50\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \lor \neg \left(\frac{x}{y} \leq 50\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.0) (not (<= (/ x y) 50.0)))
   (* (- z t) (/ x y))
   (+ t (/ (* z x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.0) || !((x / y) <= 50.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + ((z * 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) <= (-5.0d0)) .or. (.not. ((x / y) <= 50.0d0))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t + ((z * 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) <= -5.0) || !((x / y) <= 50.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + ((z * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.0) or not ((x / y) <= 50.0):
		tmp = (z - t) * (x / y)
	else:
		tmp = t + ((z * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5.0) || !(Float64(x / y) <= 50.0))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t + Float64(Float64(z * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5.0) || ~(((x / y) <= 50.0)))
		tmp = (z - t) * (x / y);
	else
		tmp = t + ((z * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 50.0]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5 or 50 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. sub-div 90.3%

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

      3. associate-/r/ 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in z around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r/ 80.1%

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

      4. mul-1-neg 80.1%

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

      5. associate-*r/ 83.6%

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

      6. sub-neg 83.6%

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

      7. distribute-rgt-out-- 95.2%

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

   8. Simplified 95.2%

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

   if -5 < (/.f64 x y) < 50

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 95.5%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \lor \neg \left(\frac{x}{y} \leq 50\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 95.1% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.0) (not (<= (/ x y) 2e-5)))
   (/ (- z t) (/ y x))
   (+ t (/ (* z x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.0) || !((x / y) <= 2e-5)) {
		tmp = (z - t) / (y / x);
	} else {
		tmp = t + ((z * 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) <= (-5.0d0)) .or. (.not. ((x / y) <= 2d-5))) then
        tmp = (z - t) / (y / x)
    else
        tmp = t + ((z * 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) <= -5.0) || !((x / y) <= 2e-5)) {
		tmp = (z - t) / (y / x);
	} else {
		tmp = t + ((z * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.0) or not ((x / y) <= 2e-5):
		tmp = (z - t) / (y / x)
	else:
		tmp = t + ((z * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5.0) || !(Float64(x / y) <= 2e-5))
		tmp = Float64(Float64(z - t) / Float64(y / x));
	else
		tmp = Float64(t + Float64(Float64(z * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5.0) || ~(((x / y) <= 2e-5)))
		tmp = (z - t) / (y / x);
	else
		tmp = t + ((z * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-5]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5 or 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 85.0%

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

      1. *-commutative 85.0%

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

      2. sub-div 90.3%

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

      3. associate-/r/ 95.8%

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

   5. Applied egg-rr 95.8%

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

   if -5 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 95.4%

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

4. Final simplification 95.6%

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

Alternative 13: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+42} \lor \neg \left(x \leq 3.1 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.35e+42) (not (<= x 3.1e+92))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.35e+42) || !(x <= 3.1e+92)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.35d+42)) .or. (.not. (x <= 3.1d+92))) then
        tmp = x * (z / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.35e+42) || !(x <= 3.1e+92)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.35e+42) or not (x <= 3.1e+92):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.35e+42) || !(x <= 3.1e+92))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.35e+42) || ~((x <= 3.1e+92)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.35e+42], N[Not[LessEqual[x, 3.1e+92]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -2.34999999999999993e42 or 3.1000000000000002e92 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf 83.9%

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

   4. Taylor expanded in z around inf 54.8%

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

   if -2.34999999999999993e42 < x < 3.1000000000000002e92

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 59.6%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+42} \lor \neg \left(x \leq 3.1 \cdot 10^{+92}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 15: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in x around 0 39.8%

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

4. Final simplification 39.8%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + 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) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + 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) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024075 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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