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

Percentage Accurate: 97.5% → 97.5%

Time: 9.1s

Alternatives: 11

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

3. Final simplification 97.4%

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

Alternative 2: 63.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3000000:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-88}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -3000000.0)
   (/ t (/ y (- x)))
   (if (<= (/ x y) -1e-88)
     (/ (* x z) y)
     (if (<= (/ x y) 5e-62) t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3000000.0) {
		tmp = t / (y / -x);
	} else if ((x / y) <= -1e-88) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 5e-62) {
		tmp = t;
	} else {
		tmp = (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) <= (-3000000.0d0)) then
        tmp = t / (y / -x)
    else if ((x / y) <= (-1d-88)) then
        tmp = (x * z) / y
    else if ((x / y) <= 5d-62) then
        tmp = t
    else
        tmp = (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) <= -3000000.0) {
		tmp = t / (y / -x);
	} else if ((x / y) <= -1e-88) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 5e-62) {
		tmp = t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -3000000.0:
		tmp = t / (y / -x)
	elif (x / y) <= -1e-88:
		tmp = (x * z) / y
	elif (x / y) <= 5e-62:
		tmp = t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -3000000.0)
		tmp = Float64(t / Float64(y / Float64(-x)));
	elseif (Float64(x / y) <= -1e-88)
		tmp = Float64(Float64(x * z) / y);
	elseif (Float64(x / y) <= 5e-62)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -3000000.0)
		tmp = t / (y / -x);
	elseif ((x / y) <= -1e-88)
		tmp = (x * z) / y;
	elseif ((x / y) <= 5e-62)
		tmp = t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -3000000.0], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e-88], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-62], t, N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -3e6

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. *-rgt-identity 62.6%

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

      3. associate-/l* 64.0%

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

      4. distribute-rgt-neg-in 64.0%

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

      5. mul-1-neg 64.0%

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

      6. distribute-lft-in 64.0%

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

      7. mul-1-neg 64.0%

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

      8. unsub-neg 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-frac-neg2 62.7%

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

   8. Simplified 62.7%

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

      1. distribute-frac-neg2 62.7%

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

      2. distribute-rgt-neg-in 62.7%

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

      3. clear-num 62.7%

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

      4. div-inv 62.9%

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

      5. distribute-neg-frac 62.9%

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

   10. Applied egg-rr 62.9%

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

   if -3e6 < (/.f64 x y) < -9.99999999999999934e-89

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.0%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 98.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 98.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 98.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 61.2%

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

   if -9.99999999999999934e-89 < (/.f64 x y) < 5.0000000000000002e-62

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 75.6%

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

   if 5.0000000000000002e-62 < (/.f64 x y)

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.1%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 99.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 66.3%

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

      1. associate-*l/ 74.7%

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

      2. *-commutative 74.7%

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

   7. Simplified 74.7%

      \[\leadsto \color{blue}{z \cdot \frac{x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3000000:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-88}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-88}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -3000000.0)
   (* (/ x y) (- t))
   (if (<= (/ x y) -1e-88)
     (/ (* x z) y)
     (if (<= (/ x y) 5e-62) t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3000000.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= -1e-88) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 5e-62) {
		tmp = t;
	} else {
		tmp = (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) <= (-3000000.0d0)) then
        tmp = (x / y) * -t
    else if ((x / y) <= (-1d-88)) then
        tmp = (x * z) / y
    else if ((x / y) <= 5d-62) then
        tmp = t
    else
        tmp = (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) <= -3000000.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= -1e-88) {
		tmp = (x * z) / y;
	} else if ((x / y) <= 5e-62) {
		tmp = t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -3000000.0:
		tmp = (x / y) * -t
	elif (x / y) <= -1e-88:
		tmp = (x * z) / y
	elif (x / y) <= 5e-62:
		tmp = t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -3000000.0)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= -1e-88)
		tmp = Float64(Float64(x * z) / y);
	elseif (Float64(x / y) <= 5e-62)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -3000000.0)
		tmp = (x / y) * -t;
	elseif ((x / y) <= -1e-88)
		tmp = (x * z) / y;
	elseif ((x / y) <= 5e-62)
		tmp = t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -3000000.0], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e-88], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-62], t, N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -3e6

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. *-rgt-identity 62.6%

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

      3. associate-/l* 64.0%

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

      4. distribute-rgt-neg-in 64.0%

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

      5. mul-1-neg 64.0%

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

      6. distribute-lft-in 64.0%

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

      7. mul-1-neg 64.0%

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

      8. unsub-neg 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-frac-neg2 62.7%

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

   8. Simplified 62.7%

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

   if -3e6 < (/.f64 x y) < -9.99999999999999934e-89

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.0%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 98.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 98.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 98.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 61.2%

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

   if -9.99999999999999934e-89 < (/.f64 x y) < 5.0000000000000002e-62

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 75.6%

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

   if 5.0000000000000002e-62 < (/.f64 x y)

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.1%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 99.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 66.3%

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

      1. associate-*l/ 74.7%

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

      2. *-commutative 74.7%

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

   7. Simplified 74.7%

      \[\leadsto \color{blue}{z \cdot \frac{x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-88}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000 \lor \neg \left(\frac{x}{y} \leq 10^{+43}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2000000.0) (not (<= (/ x y) 1e+43)))
   (/ (* x (- z t)) y)
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2000000.0) || !((x / y) <= 1e+43)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2000000.0d0)) .or. (.not. ((x / y) <= 1d+43))) then
        tmp = (x * (z - t)) / y
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2000000.0) || !((x / y) <= 1e+43)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2000000.0) or not ((x / y) <= 1e+43):
		tmp = (x * (z - t)) / y
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2000000.0) || !(Float64(x / y) <= 1e+43))
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2000000.0) || ~(((x / y) <= 1e+43)))
		tmp = (x * (z - t)) / y;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+43]], $MachinePrecision]], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e6 or 1.00000000000000001e43 < (/.f64 x y)

   1. Initial program 96.8%

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

      1. add-cube-cbrt 96.0%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 96.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 96.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 96.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 96.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in x around inf 87.0%

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

      1. div-sub 90.4%

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

      2. associate-/l* 94.5%

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

   7. Simplified 94.5%

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

   if -2e6 < (/.f64 x y) < 1.00000000000000001e43

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 94.6%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000 \lor \neg \left(\frac{x}{y} \leq 10^{+43}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-88} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-88) (not (<= (/ x y) 5e-62))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-88) || !((x / y) <= 5e-62)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d-88)) .or. (.not. ((x / y) <= 5d-62))) then
        tmp = (x / y) * z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-88) || !((x / y) <= 5e-62)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-88) or not ((x / y) <= 5e-62):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-88) || !(Float64(x / y) <= 5e-62))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-88) || ~(((x / y) <= 5e-62)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-88], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-62]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999934e-89 or 5.0000000000000002e-62 < (/.f64 x y)

   1. Initial program 97.5%

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

      1. add-cube-cbrt 96.6%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 96.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 96.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 96.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 51.8%

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

      1. associate-*l/ 58.2%

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

      2. *-commutative 58.2%

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

   7. Simplified 58.2%

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

   if -9.99999999999999934e-89 < (/.f64 x y) < 5.0000000000000002e-62

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 75.6%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-88} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+43} \lor \neg \left(z \leq 6 \cdot 10^{-89}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e+43) (not (<= z 6e-89)))
   (+ t (* (/ x y) z))
   (- t (/ t (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+43) || !(z <= 6e-89)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - (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 ((z <= (-7.5d+43)) .or. (.not. (z <= 6d-89))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t - (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 ((z <= -7.5e+43) || !(z <= 6e-89)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e+43) or not (z <= 6e-89):
		tmp = t + ((x / y) * z)
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e+43) || !(z <= 6e-89))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e+43) || ~((z <= 6e-89)))
		tmp = t + ((x / y) * z);
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e+43], N[Not[LessEqual[z, 6e-89]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999967e43 or 5.9999999999999999e-89 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 89.3%

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

   if -7.49999999999999967e43 < z < 5.9999999999999999e-89

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. *-rgt-identity 81.0%

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

      3. associate-/l* 83.8%

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

      4. distribute-rgt-neg-in 83.8%

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

      5. mul-1-neg 83.8%

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

      6. distribute-lft-in 83.8%

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

      7. mul-1-neg 83.8%

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

      8. unsub-neg 83.8%

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

   5. Simplified 83.8%

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

      1. distribute-rgt-out-- 83.8%

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

      2. *-un-lft-identity 83.8%

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

      3. *-commutative 83.8%

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

      4. clear-num 83.7%

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

      5. un-div-inv 83.9%

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

   7. Applied egg-rr 83.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+43} \lor \neg \left(z \leq 6 \cdot 10^{-89}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+42} \lor \neg \left(z \leq 1.95 \cdot 10^{-90}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.3e+42) (not (<= z 1.95e-90)))
   (+ t (* (/ x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e+42) || !(z <= 1.95e-90)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.3d+42)) .or. (.not. (z <= 1.95d-90))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e+42) || !(z <= 1.95e-90)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3e+42) or not (z <= 1.95e-90):
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3e+42) || !(z <= 1.95e-90))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.3e+42) || ~((z <= 1.95e-90)))
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.3e+42], N[Not[LessEqual[z, 1.95e-90]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e42 or 1.95000000000000002e-90 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 89.3%

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

   if -3.2999999999999999e42 < z < 1.95000000000000002e-90

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. *-rgt-identity 81.0%

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

      3. associate-/l* 83.8%

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

      4. distribute-rgt-neg-in 83.8%

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

      5. mul-1-neg 83.8%

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

      6. distribute-lft-in 83.8%

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

      7. mul-1-neg 83.8%

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

      8. unsub-neg 83.8%

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

   5. Simplified 83.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+42} \lor \neg \left(z \leq 1.95 \cdot 10^{-90}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+43} \lor \neg \left(z \leq 0.0035\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.82e+43) (not (<= z 0.0035)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.82e+43) || !(z <= 0.0035)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.82d+43)) .or. (.not. (z <= 0.0035d0))) then
        tmp = t + (x * (z / y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.82e+43) || !(z <= 0.0035)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.82e+43) or not (z <= 0.0035):
		tmp = t + (x * (z / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.82e+43) || !(z <= 0.0035))
		tmp = Float64(t + Float64(x * Float64(z / y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.82e+43) || ~((z <= 0.0035)))
		tmp = t + (x * (z / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.82e+43], N[Not[LessEqual[z, 0.0035]], $MachinePrecision]], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8199999999999999e43 or 0.00350000000000000007 < z

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 85.1%

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

      1. associate-/l* 89.4%

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

   5. Simplified 89.4%

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

   if -1.8199999999999999e43 < z < 0.00350000000000000007

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. *-rgt-identity 80.4%

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

      3. associate-/l* 82.7%

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

      4. distribute-rgt-neg-in 82.7%

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

      5. mul-1-neg 82.7%

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

      6. distribute-lft-in 82.7%

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

      7. mul-1-neg 82.7%

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

      8. unsub-neg 82.7%

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

   5. Simplified 82.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+43} \lor \neg \left(z \leq 0.0035\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+93)
   (/ x (/ y z))
   (if (<= z 1.65e+80) (* t (- 1.0 (/ x y))) (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+93) {
		tmp = x / (y / z);
	} else if (z <= 1.65e+80) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.5d+93)) then
        tmp = x / (y / z)
    else if (z <= 1.65d+80) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x / y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+93) {
		tmp = x / (y / z);
	} else if (z <= 1.65e+80) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+93:
		tmp = x / (y / z)
	elif z <= 1.65e+80:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+93)
		tmp = Float64(x / Float64(y / z));
	elseif (z <= 1.65e+80)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+93)
		tmp = x / (y / z);
	elseif (z <= 1.65e+80)
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+93], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+80], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999989e93

   1. Initial program 96.4%

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

      1. add-cube-cbrt 95.7%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 95.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 95.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 95.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 66.9%

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

      1. associate-*r/ 75.2%

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

   7. Simplified 75.2%

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

      1. clear-num 75.2%

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

      2. un-div-inv 75.3%

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

   9. Applied egg-rr 75.3%

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

   if -1.49999999999999989e93 < z < 1.64999999999999995e80

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. *-rgt-identity 76.2%

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

      3. associate-/l* 78.1%

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

      4. distribute-rgt-neg-in 78.1%

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

      5. mul-1-neg 78.1%

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

      6. distribute-lft-in 78.1%

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

      7. mul-1-neg 78.1%

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

      8. unsub-neg 78.1%

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

   5. Simplified 78.1%

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

   if 1.64999999999999995e80 < z

   1. Initial program 98.1%

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

      1. add-cube-cbrt 97.2%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 97.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 97.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 97.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 97.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 69.4%

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

      1. associate-*l/ 77.7%

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

      2. *-commutative 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.4e+37) t (if (<= t 3.4e-24) (* x (/ z y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.4e+37) {
		tmp = t;
	} else if (t <= 3.4e-24) {
		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 (t <= (-6.4d+37)) then
        tmp = t
    else if (t <= 3.4d-24) 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 (t <= -6.4e+37) {
		tmp = t;
	} else if (t <= 3.4e-24) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.4e+37:
		tmp = t
	elif t <= 3.4e-24:
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.4e+37)
		tmp = t;
	elseif (t <= 3.4e-24)
		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 (t <= -6.4e+37)
		tmp = t;
	elseif (t <= 3.4e-24)
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.4e+37], t, If[LessEqual[t, 3.4e-24], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -6.40000000000000027e37 or 3.39999999999999992e-24 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 47.5%

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

   if -6.40000000000000027e37 < t < 3.39999999999999992e-24

   1. Initial program 95.2%

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

      1. add-cube-cbrt 94.3%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t \]

      2. associate-*l* 94.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t \]

      3. fma-define 94.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

      4. pow2 94.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right) \]

   4. Applied egg-rr 94.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2}, \sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right), t\right)} \]

   5. Taylor expanded in z around inf 60.8%

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

      1. associate-*r/ 62.9%

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

   7. Simplified 62.9%

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

Alternative 11: 37.9% 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 97.4%

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

3. Taylor expanded in x around 0 33.3%

   \[\leadsto \color{blue}{t} \]
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 2024139 
(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))