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

Percentage Accurate: 97.7% → 98.4%

Time: 7.4s

Alternatives: 14

Speedup: 0.6×

• 25.6% 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: 97.7% 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: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) (- INFINITY)) (* x (/ (- z t) y)) (fma (/ x y) (- z t) t)))

C

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

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = fma(Float64(x / y), Float64(z - t), t);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -inf.0

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around -inf 99.9%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -inf.0 < (/.f64 x y)

   1. Initial program 99.4%

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

      1. fma-define 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+159}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= (/ x y) -4e+159)
     (/ (* x t) (- y))
     (if (<= (/ x y) -2e-101)
       t_1
       (if (<= (/ x y) 4e-41)
         t
         (if (<= (/ x y) 2e+30) t_1 (* (/ x y) (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -4e+159) {
		tmp = (x * t) / -y;
	} else if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else if ((x / y) <= 2e+30) {
		tmp = t_1;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * z
    if ((x / y) <= (-4d+159)) then
        tmp = (x * t) / -y
    else if ((x / y) <= (-2d-101)) then
        tmp = t_1
    else if ((x / y) <= 4d-41) then
        tmp = t
    else if ((x / y) <= 2d+30) then
        tmp = t_1
    else
        tmp = (x / y) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -4e+159) {
		tmp = (x * t) / -y;
	} else if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else if ((x / y) <= 2e+30) {
		tmp = t_1;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if (x / y) <= -4e+159:
		tmp = (x * t) / -y
	elif (x / y) <= -2e-101:
		tmp = t_1
	elif (x / y) <= 4e-41:
		tmp = t
	elif (x / y) <= 2e+30:
		tmp = t_1
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -4e+159)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (Float64(x / y) <= -2e-101)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-41)
		tmp = t;
	elseif (Float64(x / y) <= 2e+30)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -4e+159)
		tmp = (x * t) / -y;
	elseif ((x / y) <= -2e-101)
		tmp = t_1;
	elseif ((x / y) <= 4e-41)
		tmp = t;
	elseif ((x / y) <= 2e+30)
		tmp = t_1;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4e+159], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e-101], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-41], t, If[LessEqual[N[(x / y), $MachinePrecision], 2e+30], t$95$1, N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -3.9999999999999997e159

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. *-rgt-identity 64.5%

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

      4. associate-/l* 58.9%

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

      5. distribute-lft-out-- 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-frac-neg2 58.9%

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

   8. Simplified 58.9%

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

      1. *-commutative 58.9%

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

      2. distribute-frac-neg2 58.9%

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

      3. distribute-frac-neg 58.9%

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

      4. associate-*l/ 64.5%

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

   10. Applied egg-rr 64.5%

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

   if -3.9999999999999997e159 < (/.f64 x y) < -2.0000000000000001e-101 or 4.00000000000000002e-41 < (/.f64 x y) < 2e30

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 86.1%

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

   4. Taylor expanded in x around -inf 76.8%

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

   5. Taylor expanded in z around inf 59.1%

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

      1. associate-*l/ 78.2%

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

      2. *-commutative 78.2%

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

   7. Simplified 72.6%

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

   if -2.0000000000000001e-101 < (/.f64 x y) < 4.00000000000000002e-41

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 79.5%

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

   if 2e30 < (/.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

      3. *-rgt-identity 58.5%

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

      4. associate-/l* 65.2%

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

      5. distribute-lft-out-- 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-frac-neg2 65.2%

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

   8. Simplified 65.2%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+159}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+159}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= (/ x y) -4e+159)
     (/ t (/ y (- x)))
     (if (<= (/ x y) -2e-101)
       t_1
       (if (<= (/ x y) 4e-41)
         t
         (if (<= (/ x y) 2e+30) t_1 (* (/ x y) (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -4e+159) {
		tmp = t / (y / -x);
	} else if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else if ((x / y) <= 2e+30) {
		tmp = t_1;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * z
    if ((x / y) <= (-4d+159)) then
        tmp = t / (y / -x)
    else if ((x / y) <= (-2d-101)) then
        tmp = t_1
    else if ((x / y) <= 4d-41) then
        tmp = t
    else if ((x / y) <= 2d+30) then
        tmp = t_1
    else
        tmp = (x / y) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -4e+159) {
		tmp = t / (y / -x);
	} else if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else if ((x / y) <= 2e+30) {
		tmp = t_1;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if (x / y) <= -4e+159:
		tmp = t / (y / -x)
	elif (x / y) <= -2e-101:
		tmp = t_1
	elif (x / y) <= 4e-41:
		tmp = t
	elif (x / y) <= 2e+30:
		tmp = t_1
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -4e+159)
		tmp = Float64(t / Float64(y / Float64(-x)));
	elseif (Float64(x / y) <= -2e-101)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-41)
		tmp = t;
	elseif (Float64(x / y) <= 2e+30)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -4e+159)
		tmp = t / (y / -x);
	elseif ((x / y) <= -2e-101)
		tmp = t_1;
	elseif ((x / y) <= 4e-41)
		tmp = t;
	elseif ((x / y) <= 2e+30)
		tmp = t_1;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4e+159], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e-101], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-41], t, If[LessEqual[N[(x / y), $MachinePrecision], 2e+30], t$95$1, N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -3.9999999999999997e159

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. *-rgt-identity 64.5%

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

      4. associate-/l* 58.9%

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

      5. distribute-lft-out-- 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-frac-neg2 58.9%

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

   8. Simplified 58.9%

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

      1. associate-*r/ 64.5%

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

      2. distribute-frac-neg2 64.5%

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

      3. add-sqr-sqrt 36.6%

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

      4. sqrt-unprod 40.4%

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

      5. sqr-neg 40.4%

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

      6. sqrt-unprod 0.7%

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

      7. add-sqr-sqrt 4.2%

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

      8. associate-*r/ 15.5%

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

      9. clear-num 15.5%

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

      10. un-div-inv 15.5%

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

      11. add-sqr-sqrt 6.4%

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

      12. sqrt-unprod 41.8%

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

      13. sqr-neg 41.8%

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

      14. sqrt-unprod 32.4%

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

      15. add-sqr-sqrt 62.5%

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

   10. Applied egg-rr 62.5%

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

   if -3.9999999999999997e159 < (/.f64 x y) < -2.0000000000000001e-101 or 4.00000000000000002e-41 < (/.f64 x y) < 2e30

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 86.1%

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

   4. Taylor expanded in x around -inf 76.8%

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

   5. Taylor expanded in z around inf 59.1%

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

      1. associate-*l/ 78.2%

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

      2. *-commutative 78.2%

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

   7. Simplified 72.6%

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

   if -2.0000000000000001e-101 < (/.f64 x y) < 4.00000000000000002e-41

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 79.5%

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

   if 2e30 < (/.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

      3. *-rgt-identity 58.5%

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

      4. associate-/l* 65.2%

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

      5. distribute-lft-out-- 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-frac-neg2 65.2%

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

   8. Simplified 65.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+159}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{t}{\frac{y}{-x}}\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (/ t (/ y (- x)))))
   (if (<= (/ x y) -4e+159)
     t_2
     (if (<= (/ x y) -2e-101)
       t_1
       (if (<= (/ x y) 4e-41) t (if (<= (/ x y) 2e+30) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = t / (y / -x);
	double tmp;
	if ((x / y) <= -4e+159) {
		tmp = t_2;
	} else if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else if ((x / y) <= 2e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) * z
    t_2 = t / (y / -x)
    if ((x / y) <= (-4d+159)) then
        tmp = t_2
    else if ((x / y) <= (-2d-101)) then
        tmp = t_1
    else if ((x / y) <= 4d-41) then
        tmp = t
    else if ((x / y) <= 2d+30) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = t / (y / -x);
	double tmp;
	if ((x / y) <= -4e+159) {
		tmp = t_2;
	} else if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else if ((x / y) <= 2e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = t / (y / -x)
	tmp = 0
	if (x / y) <= -4e+159:
		tmp = t_2
	elif (x / y) <= -2e-101:
		tmp = t_1
	elif (x / y) <= 4e-41:
		tmp = t
	elif (x / y) <= 2e+30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(t / Float64(y / Float64(-x)))
	tmp = 0.0
	if (Float64(x / y) <= -4e+159)
		tmp = t_2;
	elseif (Float64(x / y) <= -2e-101)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-41)
		tmp = t;
	elseif (Float64(x / y) <= 2e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = t / (y / -x);
	tmp = 0.0;
	if ((x / y) <= -4e+159)
		tmp = t_2;
	elseif ((x / y) <= -2e-101)
		tmp = t_1;
	elseif ((x / y) <= 4e-41)
		tmp = t;
	elseif ((x / y) <= 2e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4e+159], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -2e-101], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-41], t, If[LessEqual[N[(x / y), $MachinePrecision], 2e+30], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.9999999999999997e159 or 2e30 < (/.f64 x y)

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

      3. *-rgt-identity 60.7%

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

      4. associate-/l* 62.9%

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

      5. distribute-lft-out-- 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-frac-neg2 62.9%

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

   8. Simplified 62.9%

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

      1. associate-*r/ 60.7%

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

      2. distribute-frac-neg2 60.7%

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

      3. add-sqr-sqrt 32.8%

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

      4. sqrt-unprod 34.6%

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

      5. sqr-neg 34.6%

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

      6. sqrt-unprod 1.6%

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

      7. add-sqr-sqrt 4.6%

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

      8. associate-*r/ 9.8%

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

      9. clear-num 9.8%

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

      10. un-div-inv 9.8%

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

      11. add-sqr-sqrt 4.8%

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

      12. sqrt-unprod 37.3%

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

      13. sqr-neg 37.3%

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

      14. sqrt-unprod 32.3%

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

      15. add-sqr-sqrt 64.2%

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

   10. Applied egg-rr 64.2%

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

   if -3.9999999999999997e159 < (/.f64 x y) < -2.0000000000000001e-101 or 4.00000000000000002e-41 < (/.f64 x y) < 2e30

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 86.1%

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

   4. Taylor expanded in x around -inf 76.8%

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

   5. Taylor expanded in z around inf 59.1%

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

      1. associate-*l/ 78.2%

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

      2. *-commutative 78.2%

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

   7. Simplified 72.6%

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

   if -2.0000000000000001e-101 < (/.f64 x y) < 4.00000000000000002e-41

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 79.5%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+159}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -100.0)
     t_1
     (if (<= (/ x y) 4e-41)
       (+ t (* x (/ z y)))
       (if (<= (/ x y) 2e+30) (* (/ x y) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t + (x * (z / y));
	} else if ((x / y) <= 2e+30) {
		tmp = (x / y) * z;
	} 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 * ((z - t) / y)
    if ((x / y) <= (-100.0d0)) then
        tmp = t_1
    else if ((x / y) <= 4d-41) then
        tmp = t + (x * (z / y))
    else if ((x / y) <= 2d+30) then
        tmp = (x / y) * z
    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 * ((z - t) / y);
	double tmp;
	if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t + (x * (z / y));
	} else if ((x / y) <= 2e+30) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -100.0:
		tmp = t_1
	elif (x / y) <= 4e-41:
		tmp = t + (x * (z / y))
	elif (x / y) <= 2e+30:
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -100.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-41)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (Float64(x / y) <= 2e+30)
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -100.0)
		tmp = t_1;
	elseif ((x / y) <= 4e-41)
		tmp = t + (x * (z / y));
	elseif ((x / y) <= 2e+30)
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -100.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-41], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+30], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -100 or 2e30 < (/.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 92.1%

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

   4. Taylor expanded in x around -inf 91.0%

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

      1. associate-/l* 93.4%

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

      2. *-commutative 93.4%

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

   6. Applied egg-rr 93.4%

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

   if -100 < (/.f64 x y) < 4.00000000000000002e-41

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 95.8%

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

      1. associate-/l* 96.6%

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

   5. Simplified 96.6%

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

   if 4.00000000000000002e-41 < (/.f64 x y) < 2e30

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.3%

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

   4. Taylor expanded in x around -inf 79.4%

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

   5. Taylor expanded in z around inf 67.5%

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

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

   7. Simplified 73.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -2e-101)
     t_1
     (if (<= (/ x y) 4e-41)
       (* t (- 1.0 (/ x y)))
       (if (<= (/ x y) 2e+30) (* (/ x y) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 2e+30) {
		tmp = (x / y) * z;
	} 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 * ((z - t) / y)
    if ((x / y) <= (-2d-101)) then
        tmp = t_1
    else if ((x / y) <= 4d-41) then
        tmp = t * (1.0d0 - (x / y))
    else if ((x / y) <= 2d+30) then
        tmp = (x / y) * z
    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 * ((z - t) / y);
	double tmp;
	if ((x / y) <= -2e-101) {
		tmp = t_1;
	} else if ((x / y) <= 4e-41) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 2e+30) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -2e-101:
		tmp = t_1
	elif (x / y) <= 4e-41:
		tmp = t * (1.0 - (x / y))
	elif (x / y) <= 2e+30:
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e-101)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-41)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (Float64(x / y) <= 2e+30)
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -2e-101)
		tmp = t_1;
	elseif ((x / y) <= 4e-41)
		tmp = t * (1.0 - (x / y));
	elseif ((x / y) <= 2e+30)
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-101], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-41], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+30], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.0000000000000001e-101 or 2e30 < (/.f64 x y)

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0 91.4%

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

   4. Taylor expanded in x around -inf 89.0%

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

      1. associate-/l* 92.7%

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

      2. *-commutative 92.7%

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

   6. Applied egg-rr 92.7%

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

   if -2.0000000000000001e-101 < (/.f64 x y) < 4.00000000000000002e-41

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

      3. *-rgt-identity 77.8%

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

      4. associate-/l* 79.5%

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

      5. distribute-lft-out-- 79.5%

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

   5. Simplified 79.5%

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

   if 4.00000000000000002e-41 < (/.f64 x y) < 2e30

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.3%

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

   4. Taylor expanded in x around -inf 79.4%

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

   5. Taylor expanded in z around inf 67.5%

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

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

   7. Simplified 73.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+14) (not (<= (/ x y) 2e+30)))
   (* x (/ (- z t) y))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+14) || !((x / y) <= 2e+30)) {
		tmp = x * ((z - t) / 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+14)) .or. (.not. ((x / y) <= 2d+30))) then
        tmp = x * ((z - t) / 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+14) || !((x / y) <= 2e+30)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+14) or not ((x / y) <= 2e+30):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+14) || !(Float64(x / y) <= 2e+30))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+14) || ~(((x / y) <= 2e+30)))
		tmp = x * ((z - t) / 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+14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+30]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e14 or 2e30 < (/.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 91.9%

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

   4. Taylor expanded in x around -inf 91.9%

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

      1. associate-/l* 95.2%

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

      2. *-commutative 95.2%

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

   6. Applied egg-rr 95.2%

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

   if -2e14 < (/.f64 x y) < 2e30

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 94.4%

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

   4. Taylor expanded in z around inf 91.8%

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

      1. associate-*l/ 95.3%

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

      2. *-commutative 95.3%

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

   6. Simplified 95.3%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 200:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+14)
   (* x (/ (- z t) y))
   (if (<= (/ x y) 200.0) (+ t (* (/ x y) z)) (/ (* x (- z t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+14) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 200.0) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x * (z - 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) :: tmp
    if ((x / y) <= (-2d+14)) then
        tmp = x * ((z - t) / y)
    else if ((x / y) <= 200.0d0) then
        tmp = t + ((x / y) * z)
    else
        tmp = (x * (z - t)) / 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+14) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 200.0) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x * (z - t)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+14:
		tmp = x * ((z - t) / y)
	elif (x / y) <= 200.0:
		tmp = t + ((x / y) * z)
	else:
		tmp = (x * (z - t)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+14)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	elseif (Float64(x / y) <= 200.0)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+14)
		tmp = x * ((z - t) / y);
	elseif ((x / y) <= 200.0)
		tmp = t + ((x / y) * z);
	else
		tmp = (x * (z - t)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+14], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 200.0], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e14

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 90.7%

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

   4. Taylor expanded in x around -inf 90.7%

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

      1. associate-/l* 95.4%

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

      2. *-commutative 95.4%

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

   6. Applied egg-rr 95.4%

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

   if -2e14 < (/.f64 x y) < 200

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 94.1%

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

   4. Taylor expanded in z around inf 93.6%

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

      1. associate-*l/ 97.3%

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

      2. *-commutative 97.3%

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

   6. Simplified 97.3%

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

   if 200 < (/.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 94.0%

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

   4. Taylor expanded in x around -inf 92.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 200:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-101} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-101) (not (<= (/ x y) 4e-41))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-101) || !((x / y) <= 4e-41)) {
		tmp = (x / y) * z;
	} 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) <= (-2d-101)) .or. (.not. ((x / y) <= 4d-41))) then
        tmp = (x / y) * z
    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) <= -2e-101) || !((x / y) <= 4e-41)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-101) or not ((x / y) <= 4e-41):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-101) || !(Float64(x / y) <= 4e-41))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-101) || ~(((x / y) <= 4e-41)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-101], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-41]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0000000000000001e-101 or 4.00000000000000002e-41 < (/.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 91.7%

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

   4. Taylor expanded in x around -inf 87.9%

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

   5. Taylor expanded in z around inf 51.6%

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

      1. associate-*l/ 59.4%

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

      2. *-commutative 59.4%

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

   7. Simplified 57.2%

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

   if -2.0000000000000001e-101 < (/.f64 x y) < 4.00000000000000002e-41

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 79.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-101} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e-101)
   (/ z (/ y x))
   (if (<= (/ x y) 4e-41) t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-101) {
		tmp = z / (y / x);
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else {
		tmp = (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-101)) then
        tmp = z / (y / x)
    else if ((x / y) <= 4d-41) then
        tmp = t
    else
        tmp = (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-101) {
		tmp = z / (y / x);
	} else if ((x / y) <= 4e-41) {
		tmp = t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e-101:
		tmp = z / (y / x)
	elif (x / y) <= 4e-41:
		tmp = t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e-101)
		tmp = Float64(z / Float64(y / x));
	elseif (Float64(x / y) <= 4e-41)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e-101)
		tmp = z / (y / x);
	elseif ((x / y) <= 4e-41)
		tmp = t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e-101], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e-41], t, N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.0000000000000001e-101

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0 90.1%

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

   4. Taylor expanded in x around -inf 86.0%

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

   5. Taylor expanded in z around inf 53.2%

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

      1. associate-*l/ 66.3%

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

      2. *-commutative 66.3%

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

   7. Simplified 62.8%

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

      1. clear-num 62.8%

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

      2. un-div-inv 62.8%

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

   9. Applied egg-rr 62.8%

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

   if -2.0000000000000001e-101 < (/.f64 x y) < 4.00000000000000002e-41

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 79.5%

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

   if 4.00000000000000002e-41 < (/.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.4%

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

   4. Taylor expanded in x around -inf 89.8%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. associate-*l/ 52.0%

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

      2. *-commutative 52.0%

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

   7. Simplified 51.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.08e+92)
   (* (/ x y) z)
   (if (<= z 6.1e+88) (* t (- 1.0 (/ x y))) (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e+92) {
		tmp = (x / y) * z;
	} else if (z <= 6.1e+88) {
		tmp = t * (1.0 - (x / y));
	} 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) :: tmp
    if (z <= (-1.08d+92)) then
        tmp = (x / y) * z
    else if (z <= 6.1d+88) then
        tmp = t * (1.0d0 - (x / y))
    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 tmp;
	if (z <= -1.08e+92) {
		tmp = (x / y) * z;
	} else if (z <= 6.1e+88) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.08e+92:
		tmp = (x / y) * z
	elif z <= 6.1e+88:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.08e+92)
		tmp = Float64(Float64(x / y) * z);
	elseif (z <= 6.1e+88)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.08e+92)
		tmp = (x / y) * z;
	elseif (z <= 6.1e+88)
		tmp = t * (1.0 - (x / y));
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.08e+92], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 6.1e+88], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.08e92

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 92.5%

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

   4. Taylor expanded in x around -inf 73.9%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. associate-*l/ 90.2%

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

      2. *-commutative 90.2%

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

   7. Simplified 71.6%

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

   if -1.08e92 < z < 6.0999999999999998e88

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. *-rgt-identity 74.4%

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

      4. associate-/l* 76.6%

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

      5. distribute-lft-out-- 76.6%

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

   5. Simplified 76.6%

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

   if 6.0999999999999998e88 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in x around -inf 67.0%

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

   5. Taylor expanded in z around inf 62.5%

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

      1. associate-*l/ 95.3%

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

      2. *-commutative 95.3%

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

   7. Simplified 76.0%

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

      1. clear-num 76.0%

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

      2. un-div-inv 76.1%

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

   9. Applied egg-rr 76.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -math.inf:
		tmp = x * ((z - t) / y)
	else:
		tmp = t + ((x / y) * (z - t))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -inf.0

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in x around -inf 99.9%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -inf.0 < (/.f64 x y)

   1. Initial program 99.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 13: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-100} \lor \neg \left(z \leq 3.25 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-100) (not (<= z 3.25e+19))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-100) || !(z <= 3.25e+19)) {
		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 ((z <= (-7.2d-100)) .or. (.not. (z <= 3.25d+19))) 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 ((z <= -7.2e-100) || !(z <= 3.25e+19)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-100) or not (z <= 3.25e+19):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-100) || !(z <= 3.25e+19))
		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 ((z <= -7.2e-100) || ~((z <= 3.25e+19)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-100], N[Not[LessEqual[z, 3.25e+19]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999997e-100 or 3.25e19 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0 91.2%

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

   4. Taylor expanded in x around -inf 67.6%

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

   5. Taylor expanded in z around inf 56.2%

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

      1. associate-*r/ 53.9%

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

   7. Simplified 53.9%

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

   if -7.1999999999999997e-100 < z < 3.25e19

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 48.1%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-100} \lor \neg \left(z \leq 3.25 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.3% 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 97.7%

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

3. Taylor expanded in x around 0 35.3%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Developer target: 97.5% 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 2024100 
(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))