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

Percentage Accurate: 97.8% → 96.6%

Time: 9.0s

Alternatives: 10

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-233}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 5e-233) (+ t (/ (- z t) (/ y x))) (+ t (/ x (/ y (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5e-233) {
		tmp = t + ((z - t) / (y / x));
	} else {
		tmp = t + (x / (y / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 5d-233) then
        tmp = t + ((z - t) / (y / x))
    else
        tmp = t + (x / (y / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5e-233) {
		tmp = t + ((z - t) / (y / x));
	} else {
		tmp = t + (x / (y / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 5e-233:
		tmp = t + ((z - t) / (y / x))
	else:
		tmp = t + (x / (y / (z - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 5e-233)
		tmp = Float64(t + Float64(Float64(z - t) / Float64(y / x)));
	else
		tmp = Float64(t + Float64(x / Float64(y / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 5e-233)
		tmp = t + ((z - t) / (y / x));
	else
		tmp = t + (x / (y / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 5e-233], N[(t + N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.00000000000000012e-233

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. clear-num 98.2%

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

      3. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   if 5.00000000000000012e-233 < x

   1. Initial program 92.4%

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

      1. div-inv 92.3%

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

      2. associate-*l* 94.2%

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

      3. associate-/r/ 94.2%

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

      4. un-div-inv 97.5%

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

   4. Applied egg-rr 97.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-233}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-27} \lor \neg \left(z \leq 1.1 \cdot 10^{-44}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-27) (not (<= z 1.1e-44)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-27) || !(z <= 1.1e-44)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.2d-27)) .or. (.not. (z <= 1.1d-44))) then
        tmp = t + (x * (z / y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-27) || !(z <= 1.1e-44)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e-27) or not (z <= 1.1e-44):
		tmp = t + (x * (z / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-27) || !(z <= 1.1e-44))
		tmp = Float64(t + Float64(x * Float64(z / y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.2e-27) || ~((z <= 1.1e-44)))
		tmp = t + (x * (z / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-27], N[Not[LessEqual[z, 1.1e-44]], $MachinePrecision]], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000031e-27 or 1.10000000000000006e-44 < z

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 87.4%

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

      1. associate-/l* 88.5%

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

   5. Simplified 88.5%

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

   if -4.20000000000000031e-27 < z < 1.10000000000000006e-44

   1. Initial program 96.1%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 93.8%

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

      3. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. *-lft-identity 84.4%

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

      3. associate-/l* 87.4%

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

      4. distribute-rgt-neg-in 87.4%

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

      5. mul-1-neg 87.4%

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

      6. *-commutative 87.4%

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

      7. distribute-rgt-in 87.4%

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

      8. mul-1-neg 87.4%

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

      9. unsub-neg 87.4%

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

   7. Simplified 87.4%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-27} \lor \neg \left(z \leq 1.1 \cdot 10^{-44}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-33}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 10^{-44}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.2e-33)
   (+ t (* z (/ x y)))
   (if (<= z 1e-44) (- t (/ t (/ y x))) (+ t (/ x (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e-33) {
		tmp = t + (z * (x / y));
	} else if (z <= 1e-44) {
		tmp = t - (t / (y / x));
	} 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 (z <= (-6.2d-33)) then
        tmp = t + (z * (x / y))
    else if (z <= 1d-44) then
        tmp = t - (t / (y / x))
    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 (z <= -6.2e-33) {
		tmp = t + (z * (x / y));
	} else if (z <= 1e-44) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e-33:
		tmp = t + (z * (x / y))
	elif z <= 1e-44:
		tmp = t - (t / (y / x))
	else:
		tmp = t + (x / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e-33)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	elseif (z <= 1e-44)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.2e-33)
		tmp = t + (z * (x / y));
	elseif (z <= 1e-44)
		tmp = t - (t / (y / x));
	else
		tmp = t + (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.2e-33], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-44], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.19999999999999994e-33

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 92.0%

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

   if -6.19999999999999994e-33 < z < 9.99999999999999953e-45

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

      2. clear-num 96.1%

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

      3. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around 0 87.5%

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

      1. neg-mul-1 87.5%

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

   7. Simplified 87.5%

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

   if 9.99999999999999953e-45 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 90.3%

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

      1. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

      1. clear-num 92.3%

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

      2. un-div-inv 95.8%

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

   7. Applied egg-rr 95.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-33}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 10^{-44}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 10^{-44}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e-26)
   (+ t (* z (/ x y)))
   (if (<= z 1e-44) (* t (- 1.0 (/ x y))) (+ t (/ x (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-26) {
		tmp = t + (z * (x / y));
	} else if (z <= 1e-44) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.3d-26)) then
        tmp = t + (z * (x / y))
    else if (z <= 1d-44) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-26) {
		tmp = t + (z * (x / y));
	} else if (z <= 1e-44) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e-26:
		tmp = t + (z * (x / y))
	elif z <= 1e-44:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e-26)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	elseif (z <= 1e-44)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e-26)
		tmp = t + (z * (x / y));
	elseif (z <= 1e-44)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e-26], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-44], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000009e-26

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 92.0%

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

   if -2.30000000000000009e-26 < z < 9.99999999999999953e-45

   1. Initial program 96.1%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 93.8%

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

      3. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. *-lft-identity 84.4%

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

      3. associate-/l* 87.4%

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

      4. distribute-rgt-neg-in 87.4%

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

      5. mul-1-neg 87.4%

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

      6. *-commutative 87.4%

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

      7. distribute-rgt-in 87.4%

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

      8. mul-1-neg 87.4%

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

      9. unsub-neg 87.4%

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

   7. Simplified 87.4%

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

   if 9.99999999999999953e-45 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 90.3%

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

      1. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

      1. clear-num 92.3%

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

      2. un-div-inv 95.8%

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

   7. Applied egg-rr 95.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-26}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 10^{-44}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-31}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e-31)
   (+ t (* z (/ x y)))
   (if (<= z 1.35e-44) (* t (- 1.0 (/ x y))) (+ t (* x (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-31) {
		tmp = t + (z * (x / y));
	} else if (z <= 1.35e-44) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.7d-31)) then
        tmp = t + (z * (x / y))
    else if (z <= 1.35d-44) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-31) {
		tmp = t + (z * (x / y));
	} else if (z <= 1.35e-44) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e-31:
		tmp = t + (z * (x / y))
	elif z <= 1.35e-44:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e-31)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	elseif (z <= 1.35e-44)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e-31)
		tmp = t + (z * (x / y));
	elseif (z <= 1.35e-44)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e-31], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-44], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000014e-31

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 92.0%

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

   if -2.70000000000000014e-31 < z < 1.35e-44

   1. Initial program 96.1%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 93.8%

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

      3. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. *-lft-identity 84.4%

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

      3. associate-/l* 87.4%

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

      4. distribute-rgt-neg-in 87.4%

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

      5. mul-1-neg 87.4%

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

      6. *-commutative 87.4%

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

      7. distribute-rgt-in 87.4%

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

      8. mul-1-neg 87.4%

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

      9. unsub-neg 87.4%

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

   7. Simplified 87.4%

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

   if 1.35e-44 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 90.3%

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

      1. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-31}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-233}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 5e-233) (+ t (* (- z t) (/ x y))) (+ t (/ x (/ y (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5e-233) {
		tmp = t + ((z - t) * (x / y));
	} else {
		tmp = t + (x / (y / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 5d-233) then
        tmp = t + ((z - t) * (x / y))
    else
        tmp = t + (x / (y / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5e-233) {
		tmp = t + ((z - t) * (x / y));
	} else {
		tmp = t + (x / (y / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 5e-233:
		tmp = t + ((z - t) * (x / y))
	else:
		tmp = t + (x / (y / (z - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 5e-233)
		tmp = Float64(t + Float64(Float64(z - t) * Float64(x / y)));
	else
		tmp = Float64(t + Float64(x / Float64(y / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 5e-233)
		tmp = t + ((z - t) * (x / y));
	else
		tmp = t + (x / (y / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 5e-233], N[(t + N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.00000000000000012e-233

   1. Initial program 98.2%

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

   if 5.00000000000000012e-233 < x

   1. Initial program 92.4%

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

      1. div-inv 92.3%

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

      2. associate-*l* 94.2%

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

      3. associate-/r/ 94.2%

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

      4. un-div-inv 97.5%

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

   4. Applied egg-rr 97.5%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-233}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

3. Final simplification 95.9%

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

Alternative 8: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

3. Taylor expanded in x around 0 92.4%

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

   1. associate-/l* 92.4%

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

5. Simplified 92.4%

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

6. Final simplification 92.4%

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

Alternative 9: 64.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

   1. associate-*l/ 92.4%

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

   2. associate-/l* 92.4%

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

   3. fma-define 92.4%

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

3. Simplified 92.4%

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

5. Taylor expanded in z around 0 61.0%

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

   1. mul-1-neg 61.0%

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

   2. *-lft-identity 61.0%

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

   3. associate-/l* 64.3%

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

   4. distribute-rgt-neg-in 64.3%

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

   5. mul-1-neg 64.3%

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

   6. *-commutative 64.3%

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

   7. distribute-rgt-in 64.3%

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

   8. mul-1-neg 64.3%

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

   9. unsub-neg 64.3%

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

7. Simplified 64.3%

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

Alternative 10: 38.1% 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 95.9%

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

   1. associate-*l/ 92.4%

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

   2. associate-/l* 92.4%

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

   3. fma-define 92.4%

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

3. Simplified 92.4%

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

5. Taylor expanded in x around 0 37.4%

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

Developer target: 97.4% 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 2024111 
(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))