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

Percentage Accurate: 97.6% → 98.5%

Time: 7.7s

Alternatives: 12

Speedup: 0.4×

• 24.5% 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: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ t (* (/ x y) (- z t))) 5e+307)
   (+ t (/ (- z t) (/ y x)))
   (/ (* x (- z t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t + ((x / y) * (z - t))) <= 5e+307) {
		tmp = t + ((z - t) / (y / x));
	} 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 ((t + ((x / y) * (z - t))) <= 5d+307) then
        tmp = t + ((z - t) / (y / x))
    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 ((t + ((x / y) * (z - t))) <= 5e+307) {
		tmp = t + ((z - t) / (y / x));
	} else {
		tmp = (x * (z - t)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t + ((x / y) * (z - t))) <= 5e+307:
		tmp = t + ((z - t) / (y / x))
	else:
		tmp = (x * (z - t)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(t + Float64(Float64(x / y) * Float64(z - t))) <= 5e+307)
		tmp = Float64(t + Float64(Float64(z - t) / Float64(y / x)));
	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 ((t + ((x / y) * (z - t))) <= 5e+307)
		tmp = t + ((z - t) / (y / x));
	else
		tmp = (x * (z - t)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+307], N[(t + N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 5e307

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 93.9%

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

      1. associate-*r/ 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-/r/ 98.5%

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

   5. Simplified 98.5%

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

   if 5e307 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 81.8%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in x around -inf 100.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) (- z t)))))
   (if (<= t_1 5e+307) t_1 (/ (* x (- z t)) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+307) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / y) * (z - t))
    if (t_1 <= 5d+307) then
        tmp = t_1
    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 t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+307) {
		tmp = t_1;
	} else {
		tmp = (x * (z - t)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * (z - t))
	tmp = 0
	if t_1 <= 5e+307:
		tmp = t_1
	else:
		tmp = (x * (z - t)) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * Float64(z - t)))
	tmp = 0.0
	if (t_1 <= 5e+307)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * (z - t));
	tmp = 0.0;
	if (t_1 <= 5e+307)
		tmp = t_1;
	else
		tmp = (x * (z - t)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+307], t$95$1, N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 5e307

   1. Initial program 98.4%

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

   if 5e307 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 81.8%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in x around -inf 100.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+26} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+26) (not (<= (/ x y) 2e-8)))
   (* (/ x y) (- z t))
   (+ t (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+26) || !((x / y) <= 2e-8)) {
		tmp = (x / y) * (z - t);
	} 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+26)) .or. (.not. ((x / y) <= 2d-8))) then
        tmp = (x / y) * (z - t)
    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+26) || !((x / y) <= 2e-8)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t + ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+26) or not ((x / y) <= 2e-8):
		tmp = (x / y) * (z - t)
	else:
		tmp = t + ((x * z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+26) || !(Float64(x / y) <= 2e-8))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	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+26) || ~(((x / y) <= 2e-8)))
		tmp = (x / y) * (z - t);
	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+26], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000001e26 or 2e-8 < (/.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 92.8%

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

   4. Taylor expanded in x around -inf 92.4%

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

   5. Taylor expanded in z around 0 83.1%

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

      1. fma-define 83.1%

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

      2. associate-*l/ 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r/ 79.1%

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

      5. fma-define 79.1%

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

      6. neg-mul-1 79.1%

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

      7. +-commutative 79.1%

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

      8. distribute-rgt-neg-in 79.1%

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

      9. mul-1-neg 79.1%

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

      10. distribute-lft-in 85.0%

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

      11. mul-1-neg 85.0%

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

      12. sub-neg 85.0%

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

      13. div-sub 89.2%

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

      14. *-commutative 89.2%

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

      15. associate-*l/ 92.4%

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

      16. associate-/l* 92.4%

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

   7. Simplified 92.4%

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

   if -5.0000000000000001e26 < (/.f64 x y) < 2e-8

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 98.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+26} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+28) (not (<= (/ x y) 2e-8)))
   (* (/ x y) (- z t))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+28) || !((x / y) <= 2e-8)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+28)) .or. (.not. ((x / y) <= 2d-8))) then
        tmp = (x / y) * (z - t)
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+28) || !((x / y) <= 2e-8)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+28) or not ((x / y) <= 2e-8):
		tmp = (x / y) * (z - t)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+28) || !(Float64(x / y) <= 2e-8))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+28) || ~(((x / y) <= 2e-8)))
		tmp = (x / y) * (z - t);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+28], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999992e28 or 2e-8 < (/.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in x around -inf 93.1%

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

   5. Taylor expanded in z around 0 83.7%

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

      1. fma-define 83.7%

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

      2. associate-*l/ 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-*r/ 78.9%

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

      5. fma-define 78.9%

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

      6. neg-mul-1 78.9%

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

      7. +-commutative 78.9%

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

      8. distribute-rgt-neg-in 78.9%

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

      9. mul-1-neg 78.9%

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

      10. distribute-lft-in 84.9%

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

      11. mul-1-neg 84.9%

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

      12. sub-neg 84.9%

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

      13. div-sub 89.1%

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

      14. *-commutative 89.1%

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

      15. associate-*l/ 93.1%

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

      16. associate-/l* 92.3%

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

   7. Simplified 92.3%

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

   if -1.99999999999999992e28 < (/.f64 x y) < 2e-8

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 97.8%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+28) (not (<= (/ x y) 2e-8)))
   (* (/ x y) (- z t))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+28) || !((x / y) <= 2e-8)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+28)) .or. (.not. ((x / y) <= 2d-8))) then
        tmp = (x / y) * (z - t)
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+28) || !((x / y) <= 2e-8)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+28) or not ((x / y) <= 2e-8):
		tmp = (x / y) * (z - t)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+28) || !(Float64(x / y) <= 2e-8))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+28) || ~(((x / y) <= 2e-8)))
		tmp = (x / y) * (z - t);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+28], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999992e28 or 2e-8 < (/.f64 x y)

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in x around -inf 93.1%

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

   5. Taylor expanded in z around 0 83.7%

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

      1. fma-define 83.7%

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

      2. associate-*l/ 78.9%

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

      3. *-commutative 78.9%

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

      4. associate-*r/ 78.9%

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

      5. fma-define 78.9%

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

      6. neg-mul-1 78.9%

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

      7. +-commutative 78.9%

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

      8. distribute-rgt-neg-in 78.9%

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

      9. mul-1-neg 78.9%

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

      10. distribute-lft-in 84.9%

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

      11. mul-1-neg 84.9%

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

      12. sub-neg 84.9%

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

      13. div-sub 89.1%

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

      14. *-commutative 89.1%

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

      15. associate-*l/ 93.1%

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

      16. associate-/l* 92.3%

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

   7. Simplified 92.3%

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

   if -1.99999999999999992e28 < (/.f64 x y) < 2e-8

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 97.4%

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

      1. associate-/l* 93.1%

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

   5. Simplified 93.1%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-50} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-50) (not (<= (/ x y) 2e-26))) (* (/ x y) (- z t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-50) || !((x / y) <= 2e-26)) {
		tmp = (x / y) * (z - t);
	} 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-50)) .or. (.not. ((x / y) <= 2d-26))) then
        tmp = (x / y) * (z - t)
    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-50) || !((x / y) <= 2e-26)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-50) or not ((x / y) <= 2e-26):
		tmp = (x / y) * (z - t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-50) || !(Float64(x / y) <= 2e-26))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-50) || ~(((x / y) <= 2e-26)))
		tmp = (x / y) * (z - t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-50], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-26]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999968e-50 or 2.0000000000000001e-26 < (/.f64 x y)

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 93.4%

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

   4. Taylor expanded in x around -inf 88.8%

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

   5. Taylor expanded in z around 0 80.4%

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

      1. fma-define 80.4%

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

      2. associate-*l/ 76.1%

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

      3. *-commutative 76.1%

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

      4. associate-*r/ 76.0%

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

      5. fma-define 76.0%

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

      6. neg-mul-1 76.0%

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

      7. +-commutative 76.0%

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

      8. distribute-rgt-neg-in 76.0%

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

      9. mul-1-neg 76.0%

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

      10. distribute-lft-in 81.3%

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

      11. mul-1-neg 81.3%

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

      12. sub-neg 81.3%

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

      13. div-sub 85.2%

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

      14. *-commutative 85.2%

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

      15. associate-*l/ 88.8%

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

      16. associate-/l* 88.9%

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

   7. Simplified 88.9%

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

   if -4.99999999999999968e-50 < (/.f64 x y) < 2.0000000000000001e-26

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 82.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-50} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+28)
   (/ (* x (- z t)) y)
   (if (<= (/ x y) 2e-8) (+ t (* (/ x y) z)) (* (/ x y) (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+28) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 2e-8) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (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 / y) <= (-2d+28)) then
        tmp = (x * (z - t)) / y
    else if ((x / y) <= 2d-8) then
        tmp = t + ((x / y) * z)
    else
        tmp = (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 / y) <= -2e+28) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 2e-8) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x / y) * (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+28:
		tmp = (x * (z - t)) / y
	elif (x / y) <= 2e-8:
		tmp = t + ((x / y) * z)
	else:
		tmp = (x / y) * (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+28)
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	elseif (Float64(x / y) <= 2e-8)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(Float64(x / y) * Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+28)
		tmp = (x * (z - t)) / y;
	elseif ((x / y) <= 2e-8)
		tmp = t + ((x / y) * z);
	else
		tmp = (x / y) * (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+28], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-8], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999992e28

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0 95.9%

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

   4. Taylor expanded in x around -inf 95.9%

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

   if -1.99999999999999992e28 < (/.f64 x y) < 2e-8

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 97.8%

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

   if 2e-8 < (/.f64 x y)

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 92.1%

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

   4. Taylor expanded in x around -inf 91.3%

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

   5. Taylor expanded in z around 0 82.9%

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

      1. fma-define 82.9%

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

      2. associate-*l/ 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-*r/ 77.6%

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

      5. fma-define 77.6%

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

      6. neg-mul-1 77.6%

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

      7. +-commutative 77.6%

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

      8. distribute-rgt-neg-in 77.6%

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

      9. mul-1-neg 77.6%

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

      10. distribute-lft-in 83.2%

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

      11. mul-1-neg 83.2%

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

      12. sub-neg 83.2%

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

      13. div-sub 87.4%

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

      14. *-commutative 87.4%

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

      15. associate-*l/ 91.3%

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

      16. associate-/l* 95.2%

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

   7. Simplified 95.2%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-193} \lor \neg \left(t \leq 10^{-127}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.95e-193) (not (<= t 1e-127)))
   (* t (- 1.0 (/ x y)))
   (/ (* x z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.95e-193) || !(t <= 1e-127)) {
		tmp = t * (1.0 - (x / y));
	} 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 ((t <= (-1.95d-193)) .or. (.not. (t <= 1d-127))) then
        tmp = t * (1.0d0 - (x / y))
    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 ((t <= -1.95e-193) || !(t <= 1e-127)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.95e-193) or not (t <= 1e-127):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x * z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.95e-193) || !(t <= 1e-127))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x * z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.95e-193) || ~((t <= 1e-127)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x * z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.95e-193], N[Not[LessEqual[t, 1e-127]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9499999999999999e-193 or 1e-127 < t

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 76.8%

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

      1. *-rgt-identity 76.8%

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

      2. mul-1-neg 76.8%

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

      3. associate-/l* 78.9%

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

      4. distribute-rgt-neg-in 78.9%

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

      5. mul-1-neg 78.9%

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

      6. distribute-lft-in 78.8%

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

      7. mul-1-neg 78.8%

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

      8. unsub-neg 78.8%

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

   5. Simplified 78.8%

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

   if -1.9499999999999999e-193 < t < 1e-127

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 98.0%

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

   4. Taylor expanded in x around -inf 77.5%

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

   5. Taylor expanded in z around inf 66.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-193} \lor \neg \left(t \leq 10^{-127}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;-\frac{x \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.8e+122) (* x (/ z y)) (if (<= x 6.5e+30) t (- (/ (* x t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.8e+122) {
		tmp = x * (z / y);
	} else if (x <= 6.5e+30) {
		tmp = t;
	} else {
		tmp = -((x * t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-8.8d+122)) then
        tmp = x * (z / y)
    else if (x <= 6.5d+30) then
        tmp = t
    else
        tmp = -((x * t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.8e+122) {
		tmp = x * (z / y);
	} else if (x <= 6.5e+30) {
		tmp = t;
	} else {
		tmp = -((x * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.8e+122:
		tmp = x * (z / y)
	elif x <= 6.5e+30:
		tmp = t
	else:
		tmp = -((x * t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.8e+122)
		tmp = Float64(x * Float64(z / y));
	elseif (x <= 6.5e+30)
		tmp = t;
	else
		tmp = Float64(-Float64(Float64(x * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.8e+122)
		tmp = x * (z / y);
	elseif (x <= 6.5e+30)
		tmp = t;
	else
		tmp = -((x * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.8e+122], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+30], t, (-N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if x < -8.7999999999999997e122

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in x around -inf 81.8%

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

   5. Taylor expanded in z around inf 54.3%

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

      1. associate-*r/ 55.7%

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

   7. Simplified 55.7%

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

   if -8.7999999999999997e122 < x < 6.5e30

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 63.4%

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

   if 6.5e30 < x

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0 92.5%

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

   4. Taylor expanded in x around -inf 90.8%

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

   5. Taylor expanded in z around 0 66.4%

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

      1. neg-mul-1 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;-\frac{x \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.2e+122) (* x (/ z y)) (if (<= x 1.45e+27) t (* (/ x y) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.2e+122) {
		tmp = x * (z / y);
	} else if (x <= 1.45e+27) {
		tmp = t;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-8.2d+122)) then
        tmp = x * (z / y)
    else if (x <= 1.45d+27) then
        tmp = t
    else
        tmp = (x / y) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.2e+122) {
		tmp = x * (z / y);
	} else if (x <= 1.45e+27) {
		tmp = t;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.2e+122:
		tmp = x * (z / y)
	elif x <= 1.45e+27:
		tmp = t
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.2e+122)
		tmp = Float64(x * Float64(z / y));
	elseif (x <= 1.45e+27)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.2e+122)
		tmp = x * (z / y);
	elseif (x <= 1.45e+27)
		tmp = t;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.2e+122], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+27], t, N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2000000000000004e122

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in x around -inf 81.8%

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

   5. Taylor expanded in z around inf 54.3%

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

      1. associate-*r/ 55.7%

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

   7. Simplified 55.7%

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

   if -8.2000000000000004e122 < x < 1.4500000000000001e27

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 63.4%

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

   if 1.4500000000000001e27 < x

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0 92.5%

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

   4. Taylor expanded in x around -inf 90.8%

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

   5. Taylor expanded in z around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. associate-*r/ 63.1%

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

      3. distribute-rgt-neg-out 63.1%

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

      4. distribute-neg-frac2 63.1%

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

   7. Simplified 63.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+123} \lor \neg \left(x \leq 4.8 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.18e+123) (not (<= x 4.8e+22))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.18e+123) || !(x <= 4.8e+22)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.18d+123)) .or. (.not. (x <= 4.8d+22))) then
        tmp = x * (z / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.18e+123) || !(x <= 4.8e+22)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.18e+123) or not (x <= 4.8e+22):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.18e+123) || !(x <= 4.8e+22))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.18e+123) || ~((x <= 4.8e+22)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.18e+123], N[Not[LessEqual[x, 4.8e+22]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -1.18000000000000006e123 or 4.8e22 < x

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 89.9%

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

   4. Taylor expanded in x around -inf 87.0%

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

   5. Taylor expanded in z around inf 46.8%

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

      1. associate-*r/ 49.4%

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

   7. Simplified 49.4%

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

   if -1.18000000000000006e123 < x < 4.8e22

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 64.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+123} \lor \neg \left(x \leq 4.8 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 96.1%

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

3. Taylor expanded in x around 0 43.4%

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

Developer Target 1: 97.3% 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 2024176 
(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))