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

Percentage Accurate: 97.9% → 97.9%

Time: 8.2s

Alternatives: 12

Speedup: 1.0×

• 24.1% 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: 97.9% 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: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{x}{y}\right), t\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{y}{x}}\right), t\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{y}{x}}\right), t\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{y}{x}\right)\right), t\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{y}{x}\right)\right), t\right) \]

   6. /-lowering-/.f64 97.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, x\right)\right), t\right) \]

4. Applied egg-rr 97.9%

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

5. Final simplification 97.9%

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

Alternative 2: 95.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-13}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -100.0)
   (/ (* (- z t) x) y)
   (if (<= (/ x y) 5e-13) (+ t (* z (/ x y))) (/ (- z t) (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -100.0) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 5e-13) {
		tmp = t + (z * (x / y));
	} else {
		tmp = (z - t) / (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) <= (-100.0d0)) then
        tmp = ((z - t) * x) / y
    else if ((x / y) <= 5d-13) then
        tmp = t + (z * (x / y))
    else
        tmp = (z - t) / (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) <= -100.0) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 5e-13) {
		tmp = t + (z * (x / y));
	} else {
		tmp = (z - t) / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -100.0:
		tmp = ((z - t) * x) / y
	elif (x / y) <= 5e-13:
		tmp = t + (z * (x / y))
	else:
		tmp = (z - t) / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -100.0)
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	elseif (Float64(x / y) <= 5e-13)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(Float64(z - t) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -100.0)
		tmp = ((z - t) * x) / y;
	elseif ((x / y) <= 5e-13)
		tmp = t + (z * (x / y));
	else
		tmp = (z - t) / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -100.0], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-13], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 94.5%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.8%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 94.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 94.7%

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

   if -100 < (/.f64 x y) < 4.9999999999999999e-13

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 97.0%

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

   if 4.9999999999999999e-13 < (/.f64 x y)

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 93.0%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 93.0%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z - t\right), \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{\color{blue}{y}}{x}\right)\right) \]

      6. /-lowering-/.f64 99.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 99.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-13}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -100.0)
   (/ (* (- z t) x) y)
   (if (<= (/ x y) 2e-10) (+ t (* z (/ x y))) (/ x (/ y (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -100.0) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z * (x / y));
	} 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) <= (-100.0d0)) then
        tmp = ((z - t) * x) / y
    else if ((x / y) <= 2d-10) then
        tmp = t + (z * (x / y))
    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) <= -100.0) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z * (x / y));
	} else {
		tmp = x / (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -100.0:
		tmp = ((z - t) * x) / y
	elif (x / y) <= 2e-10:
		tmp = t + (z * (x / y))
	else:
		tmp = x / (y / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -100.0)
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	elseif (Float64(x / y) <= 2e-10)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(x / Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -100.0)
		tmp = ((z - t) * x) / y;
	elseif ((x / y) <= 2e-10)
		tmp = t + (z * (x / y));
	else
		tmp = x / (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -100.0], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-10], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 94.5%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.8%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 94.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 94.7%

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

   if -100 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 97.0%

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

   if 2.00000000000000007e-10 < (/.f64 x y)

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.9%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 92.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 92.9%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      5. --lowering--.f64 93.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   9. Applied egg-rr 93.3%

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

4. Final simplification 95.4%

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

Alternative 4: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+23)
   (* x (/ (- z t) y))
   (if (<= (/ x y) 2e-10) (+ t (* z (/ x y))) (/ x (/ y (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z * (x / y));
	} 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) <= (-5d+23)) then
        tmp = x * ((z - t) / y)
    else if ((x / y) <= 2d-10) then
        tmp = t + (z * (x / y))
    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) <= -5e+23) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z * (x / y));
	} else {
		tmp = x / (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+23:
		tmp = x * ((z - t) / y)
	elif (x / y) <= 2e-10:
		tmp = t + (z * (x / y))
	else:
		tmp = x / (y / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+23)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	elseif (Float64(x / y) <= 2e-10)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(x / Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+23)
		tmp = x * ((z - t) / y);
	elseif ((x / y) <= 2e-10)
		tmp = t + (z * (x / y));
	else
		tmp = x / (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+23], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-10], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999999e23

   1. Initial program 94.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 98.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 98.4%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 98.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 98.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - t}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), y\right), x\right) \]

      5. --lowering--.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), y\right), x\right) \]

   9. Applied egg-rr 95.6%

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

   if -4.9999999999999999e23 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 95.1%

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

   if 2.00000000000000007e-10 < (/.f64 x y)

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.9%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 92.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 92.9%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      5. --lowering--.f64 93.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   9. Applied egg-rr 93.3%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -5e+23)
     t_1
     (if (<= (/ x y) 2e-10) (+ t (* z (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - t) / y)
    if ((x / y) <= (-5d+23)) then
        tmp = t_1
    else if ((x / y) <= 2d-10) then
        tmp = t + (z * (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -5e+23) {
		tmp = t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -5e+23:
		tmp = t_1
	elif (x / y) <= 2e-10:
		tmp = t + (z * (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e+23)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-10)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -5e+23)
		tmp = t_1;
	elseif ((x / y) <= 2e-10)
		tmp = t + (z * (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+23], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-10], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e23 or 2.00000000000000007e-10 < (/.f64 x y)

   1. Initial program 97.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.5%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 95.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 95.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - t}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), y\right), x\right) \]

      5. --lowering--.f64 94.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), y\right), x\right) \]

   9. Applied egg-rr 94.1%

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

   if -4.9999999999999999e23 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 95.1%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -5e-48) t_1 (if (<= (/ x y) 2e-30) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -5e-48) {
		tmp = t_1;
	} else if ((x / y) <= 2e-30) {
		tmp = 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 * ((z - t) / y)
    if ((x / y) <= (-5d-48)) then
        tmp = t_1
    else if ((x / y) <= 2d-30) then
        tmp = 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 * ((z - t) / y);
	double tmp;
	if ((x / y) <= -5e-48) {
		tmp = t_1;
	} else if ((x / y) <= 2e-30) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -5e-48:
		tmp = t_1
	elif (x / y) <= 2e-30:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e-48)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-30)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -5e-48)
		tmp = t_1;
	elseif ((x / y) <= 2e-30)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-48], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-30], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e-48 or 2e-30 < (/.f64 x y)

   1. Initial program 97.3%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.5%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 93.5%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 91.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 91.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z - t}{y}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), y\right), x\right) \]

      5. --lowering--.f64 89.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), y\right), x\right) \]

   9. Applied egg-rr 89.8%

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

   if -4.9999999999999999e-48 < (/.f64 x y) < 2e-30

   1. Initial program 98.2%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 96.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 96.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   6. Step-by-step derivation

   7. Simplified 79.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-48)
   (/ z (/ y x))
   (if (<= (/ x y) 5e-79) t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-48) {
		tmp = z / (y / x);
	} else if ((x / y) <= 5e-79) {
		tmp = t;
	} else {
		tmp = z * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d-48)) then
        tmp = z / (y / x)
    else if ((x / y) <= 5d-79) then
        tmp = t
    else
        tmp = z * (x / 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-48) {
		tmp = z / (y / x);
	} else if ((x / y) <= 5e-79) {
		tmp = t;
	} else {
		tmp = z * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-48:
		tmp = z / (y / x)
	elif (x / y) <= 5e-79:
		tmp = t
	else:
		tmp = z * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-48)
		tmp = Float64(z / Float64(y / x));
	elseif (Float64(x / y) <= 5e-79)
		tmp = t;
	else
		tmp = Float64(z * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-48)
		tmp = z / (y / x);
	elseif ((x / y) <= 5e-79)
		tmp = t;
	else
		tmp = z * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-48], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-79], t, N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999999e-48

   1. Initial program 95.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.0%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 50.8%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      5. /-lowering-/.f64 53.0%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 53.0%

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

   if -4.9999999999999999e-48 < (/.f64 x y) < 4.99999999999999999e-79

   1. Initial program 98.1%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 96.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 96.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   6. Step-by-step derivation

   7. Simplified 82.5%

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

   if 4.99999999999999999e-79 < (/.f64 x y)

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.9%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.9%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 49.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 49.9%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 55.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right) \]

   9. Applied egg-rr 55.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -5e-48) t_1 (if (<= (/ x y) 5e-79) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -5e-48) {
		tmp = t_1;
	} else if ((x / y) <= 5e-79) {
		tmp = 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 = z * (x / y)
    if ((x / y) <= (-5d-48)) then
        tmp = t_1
    else if ((x / y) <= 5d-79) then
        tmp = 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 = z * (x / y);
	double tmp;
	if ((x / y) <= -5e-48) {
		tmp = t_1;
	} else if ((x / y) <= 5e-79) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -5e-48:
		tmp = t_1
	elif (x / y) <= 5e-79:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e-48)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-79)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -5e-48)
		tmp = t_1;
	elseif ((x / y) <= 5e-79)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-48], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-79], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e-48 or 4.99999999999999999e-79 < (/.f64 x y)

   1. Initial program 97.5%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.9%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 93.9%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 50.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 50.3%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 53.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right) \]

   9. Applied egg-rr 53.9%

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

   if -4.9999999999999999e-48 < (/.f64 x y) < 4.99999999999999999e-79

   1. Initial program 98.1%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 96.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 96.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   6. Step-by-step derivation

   7. Simplified 82.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-109}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -5.6e-166) t_1 (if (<= t 2.6e-109) (/ (* z x) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -5.6e-166) {
		tmp = t_1;
	} else if (t <= 2.6e-109) {
		tmp = (z * x) / y;
	} 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 = t * (1.0d0 - (x / y))
    if (t <= (-5.6d-166)) then
        tmp = t_1
    else if (t <= 2.6d-109) then
        tmp = (z * x) / y
    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 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -5.6e-166) {
		tmp = t_1;
	} else if (t <= 2.6e-109) {
		tmp = (z * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -5.6e-166:
		tmp = t_1
	elif t <= 2.6e-109:
		tmp = (z * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -5.6e-166)
		tmp = t_1;
	elseif (t <= 2.6e-109)
		tmp = Float64(Float64(z * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -5.6e-166)
		tmp = t_1;
	elseif (t <= 2.6e-109)
		tmp = (z * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e-166], t$95$1, If[LessEqual[t, 2.6e-109], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999999e-166 or 2.5999999999999998e-109 < t

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 93.3%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 81.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 81.5%

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

   if -5.5999999999999999e-166 < t < 2.5999999999999998e-109

   1. Initial program 92.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 98.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 98.3%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 78.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 78.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-109}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;t + \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.2e+119) (+ t (/ (* (- z t) x) y)) (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e+119) {
		tmp = t + (((z - t) * x) / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.2d+119) then
        tmp = t + (((z - t) * x) / y)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e+119) {
		tmp = t + (((z - t) * x) / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.2e+119:
		tmp = t + (((z - t) * x) / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.2e+119)
		tmp = Float64(t + Float64(Float64(Float64(z - t) * x) / y));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.2e+119)
		tmp = t + (((z - t) * x) / y);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.2e+119], N[(t + N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.2e119

   1. Initial program 97.3%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 96.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 96.4%

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

   if 1.2e119 < t

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 84.1%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 84.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 100.0%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;t + \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Final simplification 97.7%

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

Alternative 12: 40.1% 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 97.7%

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

   3. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

   6. --lowering--.f64 94.7%

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

3. Simplified 94.7%

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

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t} \]
6. Step-by-step derivation

7. Simplified 36.1%

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

Developer Target 1: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024155 
(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))