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

Percentage Accurate: 97.8% → 98.3%

Time: 8.3s

Alternatives: 9

Speedup: 0.6×

• 25.4% 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: 98.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) (- INFINITY))
   (/ (fma (- t) x (* x z)) 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 = fma(-t, x, (x * z)) / 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(fma(Float64(-t), x, Float64(x * z)) / 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[(N[((-t) * x + N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $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 70.3%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 100.0%

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

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

   1. Initial program 99.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 99.1

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

   4. Applied rewrites 99.1%

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

Alternative 2: 93.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5000:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -0.0005)
   (* x (/ (- z t) y))
   (if (<= (/ x y) 5000.0) (+ t (/ (* x z) y)) (/ (* x (- z t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.0005) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 5000.0) {
		tmp = t + ((x * z) / y);
	} 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) <= (-0.0005d0)) then
        tmp = x * ((z - t) / y)
    else if ((x / y) <= 5000.0d0) then
        tmp = t + ((x * z) / y)
    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) <= -0.0005) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 5000.0) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = (x * (z - t)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -0.0005:
		tmp = x * ((z - t) / y)
	elif (x / y) <= 5000.0:
		tmp = t + ((x * z) / y)
	else:
		tmp = (x * (z - t)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -0.0005)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	elseif (Float64(x / y) <= 5000.0)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	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) <= -0.0005)
		tmp = x * ((z - t) / y);
	elseif ((x / y) <= 5000.0)
		tmp = t + ((x * z) / y);
	else
		tmp = (x * (z - t)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -0.0005], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5000.0], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000001e-4

   1. Initial program 92.2%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 91.9

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

   5. Applied rewrites 91.9%

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

   7. Applied rewrites 95.3%

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

   if -5.0000000000000001e-4 < (/.f64 x y) < 5e3

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if 5e3 < (/.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

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 95.2

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

   5. Applied rewrites 95.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5000:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5000000000.0)
   (* x (/ (- z t) y))
   (if (<= (/ x y) 4e+30) (fma (/ z y) x t) (/ (* x (- z t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5000000000.0) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 4e+30) {
		tmp = fma((z / y), x, t);
	} else {
		tmp = (x * (z - t)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5000000000.0)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	elseif (Float64(x / y) <= 4e+30)
		tmp = fma(Float64(z / y), x, t);
	else
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5000000000.0], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e+30], N[(N[(z / y), $MachinePrecision] * x + t), $MachinePrecision], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e9

   1. Initial program 91.8%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   7. Applied rewrites 97.6%

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

   if -5e9 < (/.f64 x y) < 4.0000000000000001e30

   1. Initial program 99.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.4

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

   4. Applied rewrites 89.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 90.2

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

   7. Applied rewrites 90.2%

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

   if 4.0000000000000001e30 < (/.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

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 98.2

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

   5. Applied rewrites 98.2%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.002:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -5000000000.0)
     t_1
     (if (<= (/ x y) 0.002) (fma (/ z y) x t) 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) <= -5000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.002) {
		tmp = fma((z / y), x, t);
	} 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) <= -5000000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.002)
		tmp = fma(Float64(z / y), x, t);
	else
		tmp = t_1;
	end
	return 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], -5000000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.002], N[(N[(z / y), $MachinePrecision] * x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e9 or 2e-3 < (/.f64 x y)

   1. Initial program 94.8%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 93.9

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

   5. Applied rewrites 93.9%

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

   7. Applied rewrites 95.7%

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

   if -5e9 < (/.f64 x y) < 2e-3

   1. Initial program 99.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.1

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

   4. Applied rewrites 89.1%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 91.4

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

   7. Applied rewrites 91.4%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.002:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+129)
   (* x (/ (- t) y))
   (if (<= (/ x y) 5e+63) (fma (/ z y) x t) (* (/ x y) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+129) {
		tmp = x * (-t / y);
	} else if ((x / y) <= 5e+63) {
		tmp = fma((z / y), x, t);
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+129)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (Float64(x / y) <= 5e+63)
		tmp = fma(Float64(z / y), x, t);
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+129], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+63], N[(N[(z / y), $MachinePrecision] * x + t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e129

   1. Initial program 88.0%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 60.6%

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

   10. Applied rewrites 60.6%

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

   if -2e129 < (/.f64 x y) < 5.00000000000000011e63

   1. Initial program 99.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 89.7

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

   4. Applied rewrites 89.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 82.9

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

   7. Applied rewrites 82.9%

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

   if 5.00000000000000011e63 < (/.f64 x y)

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 62.5%

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

   10. Applied rewrites 64.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.6× speedup

Math

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

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(Float64(x * 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[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $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 70.3%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

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

   1. Initial program 99.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 99.1

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

   4. Applied rewrites 99.1%

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

Alternative 7: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) 5e+63) (fma (/ z y) x t) (* (/ x y) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 5e+63) {
		tmp = fma((z / y), x, t);
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 5e+63)
		tmp = fma(Float64(z / y), x, t);
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 5e+63], N[(N[(z / y), $MachinePrecision] * x + t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 5.00000000000000011e63

   1. Initial program 96.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 92.0

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

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 75.7

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

   7. Applied rewrites 75.7%

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

   if 5.00000000000000011e63 < (/.f64 x y)

   1. Initial program 97.9%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 62.5%

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

   10. Applied rewrites 64.3%

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

Alternative 8: 73.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{z}{y}, x, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. associate-*l/ N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 92.8

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

4. Applied rewrites 92.8%

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

5. Taylor expanded in z around inf

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

   1. lower-/.f64 70.7

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

7. Applied rewrites 70.7%

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

Alternative 9: 41.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in z around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 36.9

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

5. Applied rewrites 36.9%

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

7. Applied rewrites 37.8%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot z} \]
8. Add Preprocessing

Developer Target 1: 97.6% accurate, 0.7× 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 2024221 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

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