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

Percentage Accurate: 97.6% → 97.6%

Time: 4.8s

Alternatives: 9

Speedup: 1.0×

• 25.7% 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: 97.6% 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: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Final simplification 97.0%

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

Alternative 2: 61.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-170}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- t) y))))
   (if (<= (/ x y) -4e+14)
     t_1
     (if (<= (/ x y) -5e-170)
       (/ z (/ y x))
       (if (<= (/ x y) 1e-43)
         t
         (if (<= (/ x y) 5e+92)
           (/ (* x z) y)
           (if (<= (/ x y) 1e+284) t_1 (* x (/ z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-t / y);
	double tmp;
	if ((x / y) <= -4e+14) {
		tmp = t_1;
	} else if ((x / y) <= -5e-170) {
		tmp = z / (y / x);
	} else if ((x / y) <= 1e-43) {
		tmp = t;
	} else if ((x / y) <= 5e+92) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 1e+284) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x * (-t / y)
    if ((x / y) <= (-4d+14)) then
        tmp = t_1
    else if ((x / y) <= (-5d-170)) then
        tmp = z / (y / x)
    else if ((x / y) <= 1d-43) then
        tmp = t
    else if ((x / y) <= 5d+92) then
        tmp = (x * z) / y
    else if ((x / y) <= 1d+284) then
        tmp = t_1
    else
        tmp = x * (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (-t / y);
	double tmp;
	if ((x / y) <= -4e+14) {
		tmp = t_1;
	} else if ((x / y) <= -5e-170) {
		tmp = z / (y / x);
	} else if ((x / y) <= 1e-43) {
		tmp = t;
	} else if ((x / y) <= 5e+92) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 1e+284) {
		tmp = t_1;
	} else {
		tmp = x * (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-t / y)
	tmp = 0
	if (x / y) <= -4e+14:
		tmp = t_1
	elif (x / y) <= -5e-170:
		tmp = z / (y / x)
	elif (x / y) <= 1e-43:
		tmp = t
	elif (x / y) <= 5e+92:
		tmp = (x * z) / y
	elif (x / y) <= 1e+284:
		tmp = t_1
	else:
		tmp = x * (z / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -4e+14)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e-170)
		tmp = Float64(z / Float64(y / x));
	elseif (Float64(x / y) <= 1e-43)
		tmp = t;
	elseif (Float64(x / y) <= 5e+92)
		tmp = Float64(Float64(x * z) / y);
	elseif (Float64(x / y) <= 1e+284)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-t / y);
	tmp = 0.0;
	if ((x / y) <= -4e+14)
		tmp = t_1;
	elseif ((x / y) <= -5e-170)
		tmp = z / (y / x);
	elseif ((x / y) <= 1e-43)
		tmp = t;
	elseif ((x / y) <= 5e+92)
		tmp = (x * z) / y;
	elseif ((x / y) <= 1e+284)
		tmp = t_1;
	else
		tmp = x * (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4e+14], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e-170], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-43], t, If[LessEqual[N[(x / y), $MachinePrecision], 5e+92], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e+284], t$95$1, N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -4e14 or 5.00000000000000022e92 < (/.f64 x y) < 1.00000000000000008e284

   1. Initial program 97.6%

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

   2. Taylor expanded in x around inf 91.5%

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

   3. Taylor expanded in z around 0 58.0%

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

      1. mul-1-neg 58.0%

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

      2. distribute-frac-neg 58.0%

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

   5. Simplified 58.0%

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

   if -4e14 < (/.f64 x y) < -5.0000000000000001e-170

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 89.1%

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

   3. Taylor expanded in z around inf 58.4%

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

      1. associate-/l* 65.8%

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

   5. Simplified 65.8%

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

   if -5.0000000000000001e-170 < (/.f64 x y) < 1.00000000000000008e-43

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 81.4%

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

   if 1.00000000000000008e-43 < (/.f64 x y) < 5.00000000000000022e92

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 67.7%

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

   3. Taylor expanded in z around inf 57.9%

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

   if 1.00000000000000008e284 < (/.f64 x y)

   1. Initial program 91.8%

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

   2. Taylor expanded in z around inf 78.2%

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

   3. Taylor expanded in z around inf 78.2%

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

      1. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

      1. associate-/r/ 78.2%

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

   7. Applied egg-rr 78.2%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-170}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+284}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \]

Alternative 3: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-170) (not (<= (/ x y) 2e-5))) (* x (/ (- z t) y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-170) || !((x / y) <= 2e-5)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d-170)) .or. (.not. ((x / y) <= 2d-5))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-170) || !((x / y) <= 2e-5)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-170) or not ((x / y) <= 2e-5):
		tmp = x * ((z - t) / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-170) || !(Float64(x / y) <= 2e-5))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-170) || ~(((x / y) <= 2e-5)))
		tmp = x * ((z - t) / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-170], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-5]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000001e-170 or 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 85.0%

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

   3. Taylor expanded in z around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-frac-neg 85.0%

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

      3. +-commutative 85.0%

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

      4. distribute-frac-neg 85.0%

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

      5. sub-neg 85.0%

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

      6. div-sub 88.3%

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

   5. Simplified 88.3%

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

   if -5.0000000000000001e-170 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 77.7%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100.0) (not (<= (/ x y) 2e-5)))
   (* x (/ (- z t) y))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100.0) || !((x / y) <= 2e-5)) {
		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) <= (-100.0d0)) .or. (.not. ((x / y) <= 2d-5))) 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) <= -100.0) || !((x / y) <= 2e-5)) {
		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) <= -100.0) or not ((x / y) <= 2e-5):
		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) <= -100.0) || !(Float64(x / y) <= 2e-5))
		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) <= -100.0) || ~(((x / y) <= 2e-5)))
		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], -100.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-5]], $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) < -100 or 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 91.6%

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

   3. Taylor expanded in z around 0 91.6%

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

      1. mul-1-neg 91.6%

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

      2. distribute-frac-neg 91.6%

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

      3. +-commutative 91.6%

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

      4. distribute-frac-neg 91.6%

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

      5. sub-neg 91.6%

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

      6. div-sub 95.6%

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

   5. Simplified 95.6%

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

   if -100 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 96.4%

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

      1. associate-*r/ 95.9%

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

   4. Simplified 95.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 5: 93.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d-5)) .or. (.not. ((x / y) <= 2d-5))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + ((x * z) / y)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000024e-5 or 2.00000000000000016e-5 < (/.f64 x y)

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 91.6%

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

   3. Taylor expanded in z around 0 91.6%

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

      1. mul-1-neg 91.6%

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

      2. distribute-frac-neg 91.6%

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

      3. +-commutative 91.6%

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

      4. distribute-frac-neg 91.6%

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

      5. sub-neg 91.6%

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

      6. div-sub 95.6%

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

   5. Simplified 95.6%

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

   if -5.00000000000000024e-5 < (/.f64 x y) < 2.00000000000000016e-5

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 97.0%

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

4. Final simplification 96.3%

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

Alternative 6: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170} \lor \neg \left(\frac{x}{y} \leq 10^{-43}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-170) (not (<= (/ x y) 1e-43))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-170) || !((x / y) <= 1e-43)) {
		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) <= (-5d-170)) .or. (.not. ((x / y) <= 1d-43))) 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) <= -5e-170) || !((x / y) <= 1e-43)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-170) or not ((x / y) <= 1e-43):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-170) || !(Float64(x / y) <= 1e-43))
		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) <= -5e-170) || ~(((x / y) <= 1e-43)))
		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], -5e-170], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-43]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000001e-170 or 1.00000000000000008e-43 < (/.f64 x y)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 62.6%

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

   3. Taylor expanded in z around inf 55.2%

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

      1. associate-*r/ 54.7%

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

   5. Simplified 54.7%

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

   if -5.0000000000000001e-170 < (/.f64 x y) < 1.00000000000000008e-43

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 81.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170} \lor \neg \left(\frac{x}{y} \leq 10^{-43}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-43}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-170)
   (* (/ x y) z)
   (if (<= (/ x y) 1e-43) t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-170) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 1e-43) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d-170)) then
        tmp = (x / y) * z
    else if ((x / y) <= 1d-43) then
        tmp = t
    else
        tmp = z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-170) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 1e-43) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-170:
		tmp = (x / y) * z
	elif (x / y) <= 1e-43:
		tmp = t
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-170)
		tmp = Float64(Float64(x / y) * z);
	elseif (Float64(x / y) <= 1e-43)
		tmp = t;
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-170)
		tmp = (x / y) * z;
	elseif ((x / y) <= 1e-43)
		tmp = t;
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-170], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-43], t, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000001e-170

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 63.8%

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

   3. Taylor expanded in z around inf 51.8%

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

      1. associate-*r/ 53.2%

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

   5. Simplified 53.2%

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

   if -5.0000000000000001e-170 < (/.f64 x y) < 1.00000000000000008e-43

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 81.4%

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

   if 1.00000000000000008e-43 < (/.f64 x y)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 61.3%

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

   3. Taylor expanded in z around inf 58.6%

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

      1. associate-/l* 56.2%

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

   5. Simplified 56.2%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-43}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-43}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-170)
   (* (/ x y) z)
   (if (<= (/ x y) 1e-43) t (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-170) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 1e-43) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d-170)) then
        tmp = (x / y) * z
    else if ((x / y) <= 1d-43) then
        tmp = t
    else
        tmp = (x * z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-170) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 1e-43) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-170:
		tmp = (x / y) * z
	elif (x / y) <= 1e-43:
		tmp = t
	else:
		tmp = (x * z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-170)
		tmp = Float64(Float64(x / y) * z);
	elseif (Float64(x / y) <= 1e-43)
		tmp = t;
	else
		tmp = Float64(Float64(x * z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-170)
		tmp = (x / y) * z;
	elseif ((x / y) <= 1e-43)
		tmp = t;
	else
		tmp = (x * z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-170], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-43], t, N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000001e-170

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 63.8%

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

   3. Taylor expanded in z around inf 51.8%

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

      1. associate-*r/ 53.2%

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

   5. Simplified 53.2%

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

   if -5.0000000000000001e-170 < (/.f64 x y) < 1.00000000000000008e-43

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 81.4%

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

   if 1.00000000000000008e-43 < (/.f64 x y)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 61.3%

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

   3. Taylor expanded in z around inf 58.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-43}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]

Alternative 9: 37.6% 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 97.0%

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

2. Taylor expanded in x around 0 36.8%

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

3. Final simplification 36.8%

   \[\leadsto t \]

Developer target: 97.3% 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 2023192 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (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))