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

Percentage Accurate: 97.0% → 96.7%

Time: 11.1s

Alternatives: 12

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-134} \lor \neg \left(y \leq 1.22 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e-134) (not (<= y 1.22e-32)))
   (* (/ (- x y) (- z y)) t)
   (/ (- x y) (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-134) || !(y <= 1.22e-32)) {
		tmp = ((x - y) / (z - y)) * t;
	} else {
		tmp = (x - y) / ((z - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.1d-134)) .or. (.not. (y <= 1.22d-32))) then
        tmp = ((x - y) / (z - y)) * t
    else
        tmp = (x - y) / ((z - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-134) || !(y <= 1.22e-32)) {
		tmp = ((x - y) / (z - y)) * t;
	} else {
		tmp = (x - y) / ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e-134) or not (y <= 1.22e-32):
		tmp = ((x - y) / (z - y)) * t
	else:
		tmp = (x - y) / ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e-134) || !(y <= 1.22e-32))
		tmp = Float64(Float64(Float64(x - y) / Float64(z - y)) * t);
	else
		tmp = Float64(Float64(x - y) / Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1e-134) || ~((y <= 1.22e-32)))
		tmp = ((x - y) / (z - y)) * t;
	else
		tmp = (x - y) / ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e-134], N[Not[LessEqual[y, 1.22e-32]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000006e-134 or 1.22e-32 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   if -3.10000000000000006e-134 < y < 1.22e-32

   1. Initial program 91.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.5%

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

      2. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 98.9%

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

      2. un-div-inv 99.0%

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

   6. Applied egg-rr 99.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-134} \lor \neg \left(y \leq 1.22 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -14500000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -9.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e+45)
   t
   (if (<= y -14500000000.0)
     (* t (/ x (- y)))
     (if (<= y -9.5) t (if (<= y 2.85e+29) (/ x (/ z t)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+45) {
		tmp = t;
	} else if (y <= -14500000000.0) {
		tmp = t * (x / -y);
	} else if (y <= -9.5) {
		tmp = t;
	} else if (y <= 2.85e+29) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.6d+45)) then
        tmp = t
    else if (y <= (-14500000000.0d0)) then
        tmp = t * (x / -y)
    else if (y <= (-9.5d0)) then
        tmp = t
    else if (y <= 2.85d+29) then
        tmp = x / (z / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+45) {
		tmp = t;
	} else if (y <= -14500000000.0) {
		tmp = t * (x / -y);
	} else if (y <= -9.5) {
		tmp = t;
	} else if (y <= 2.85e+29) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e+45:
		tmp = t
	elif y <= -14500000000.0:
		tmp = t * (x / -y)
	elif y <= -9.5:
		tmp = t
	elif y <= 2.85e+29:
		tmp = x / (z / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e+45)
		tmp = t;
	elseif (y <= -14500000000.0)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (y <= -9.5)
		tmp = t;
	elseif (y <= 2.85e+29)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e+45)
		tmp = t;
	elseif (y <= -14500000000.0)
		tmp = t * (x / -y);
	elseif (y <= -9.5)
		tmp = t;
	elseif (y <= 2.85e+29)
		tmp = x / (z / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e+45], t, If[LessEqual[y, -14500000000.0], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5], t, If[LessEqual[y, 2.85e+29], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5999999999999999e45 or -1.45e10 < y < -9.5 or 2.85e29 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 68.8%

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

      2. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in y around inf 67.6%

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

   if -5.5999999999999999e45 < y < -1.45e10

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 91.4%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around inf 74.1%

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

   6. Taylor expanded in z around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-/l* 63.2%

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

      3. distribute-rgt-neg-in 63.2%

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

   8. Simplified 63.2%

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

   if -9.5 < y < 2.85e29

   1. Initial program 93.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-/l* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in x around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l/ 67.4%

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

      3. associate-/r/ 70.4%

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

   10. Simplified 70.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -14500000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -9.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -23500000000:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -10.6:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.46e+51)
   t
   (if (<= y -23500000000.0)
     (* x (/ t (- y)))
     (if (<= y -10.6) t (if (<= y 6.2e+29) (/ x (/ z t)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.46e+51) {
		tmp = t;
	} else if (y <= -23500000000.0) {
		tmp = x * (t / -y);
	} else if (y <= -10.6) {
		tmp = t;
	} else if (y <= 6.2e+29) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.46d+51)) then
        tmp = t
    else if (y <= (-23500000000.0d0)) then
        tmp = x * (t / -y)
    else if (y <= (-10.6d0)) then
        tmp = t
    else if (y <= 6.2d+29) then
        tmp = x / (z / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.46e+51) {
		tmp = t;
	} else if (y <= -23500000000.0) {
		tmp = x * (t / -y);
	} else if (y <= -10.6) {
		tmp = t;
	} else if (y <= 6.2e+29) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.46e+51:
		tmp = t
	elif y <= -23500000000.0:
		tmp = x * (t / -y)
	elif y <= -10.6:
		tmp = t
	elif y <= 6.2e+29:
		tmp = x / (z / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.46e+51)
		tmp = t;
	elseif (y <= -23500000000.0)
		tmp = Float64(x * Float64(t / Float64(-y)));
	elseif (y <= -10.6)
		tmp = t;
	elseif (y <= 6.2e+29)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.46e+51)
		tmp = t;
	elseif (y <= -23500000000.0)
		tmp = x * (t / -y);
	elseif (y <= -10.6)
		tmp = t;
	elseif (y <= 6.2e+29)
		tmp = x / (z / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.46e+51], t, If[LessEqual[y, -23500000000.0], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -10.6], t, If[LessEqual[y, 6.2e+29], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4600000000000001e51 or -2.35e10 < y < -10.5999999999999996 or 6.1999999999999998e29 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 68.5%

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

      2. associate-/l* 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in y around inf 68.1%

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

   if -1.4600000000000001e51 < y < -2.35e10

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.2%

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

      2. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 76.5%

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

   6. Taylor expanded in z around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. associate-/l* 57.8%

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

      3. distribute-rgt-neg-in 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in t around 0 50.0%

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

       1. associate-*r/ 50.0%

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

       2. associate-*r* 50.0%

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

       3. neg-mul-1 50.0%

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

       4. *-commutative 50.0%

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

       5. associate-/l* 66.6%

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

   11. Simplified 66.6%

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

   if -10.5999999999999996 < y < 6.1999999999999998e29

   1. Initial program 93.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-/l* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in x around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l/ 67.4%

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

      3. associate-/r/ 70.4%

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

   10. Simplified 70.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -23500000000:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -10.6:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+170} \lor \neg \left(y \leq 2.7 \cdot 10^{+119}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.7e+170) (not (<= y 2.7e+119)))
   (* t (/ y (- y z)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.7e+170) || !(y <= 2.7e+119)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.7d+170)) .or. (.not. (y <= 2.7d+119))) then
        tmp = t * (y / (y - z))
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.7e+170) || !(y <= 2.7e+119)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.7e+170) or not (y <= 2.7e+119):
		tmp = t * (y / (y - z))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.7e+170) || !(y <= 2.7e+119))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.7e+170) || ~((y <= 2.7e+119)))
		tmp = t * (y / (y - z));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.7e+170], N[Not[LessEqual[y, 2.7e+119]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000002e170 or 2.6999999999999998e119 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.8%

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

      1. neg-mul-1 93.8%

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

      2. distribute-neg-frac 93.8%

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

   5. Simplified 93.8%

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

      1. frac-2neg 93.8%

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

      2. div-inv 93.7%

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

      3. remove-double-neg 93.7%

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

      4. sub-neg 93.7%

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

      5. distribute-neg-in 93.7%

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

      6. remove-double-neg 93.7%

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

   7. Applied egg-rr 93.7%

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

      1. associate-*r/ 93.8%

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

      2. *-rgt-identity 93.8%

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

      3. +-commutative 93.8%

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

      4. unsub-neg 93.8%

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

   9. Simplified 93.8%

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

   if -2.7000000000000002e170 < y < 2.6999999999999998e119

   1. Initial program 94.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+170} \lor \neg \left(y \leq 2.7 \cdot 10^{+119}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-138} \lor \neg \left(y \leq 4.4 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e-138) (not (<= y 4.4e-33)))
   (* (/ (- x y) (- z y)) t)
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-138) || !(y <= 4.4e-33)) {
		tmp = ((x - y) / (z - y)) * t;
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.4d-138)) .or. (.not. (y <= 4.4d-33))) then
        tmp = ((x - y) / (z - y)) * t
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-138) || !(y <= 4.4e-33)) {
		tmp = ((x - y) / (z - y)) * t;
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e-138) or not (y <= 4.4e-33):
		tmp = ((x - y) / (z - y)) * t
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e-138) || !(y <= 4.4e-33))
		tmp = Float64(Float64(Float64(x - y) / Float64(z - y)) * t);
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.4e-138) || ~((y <= 4.4e-33)))
		tmp = ((x - y) / (z - y)) * t;
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e-138], N[Not[LessEqual[y, 4.4e-33]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4000000000000001e-138 or 4.40000000000000011e-33 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   if -3.4000000000000001e-138 < y < 4.40000000000000011e-33

   1. Initial program 91.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.3%

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

      2. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-138} \lor \neg \left(y \leq 4.4 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+98} \lor \neg \left(x \leq 2.4 \cdot 10^{-12}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.4e+98) (not (<= x 2.4e-12)))
   (* t (/ x (- z y)))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.4e+98) || !(x <= 2.4e-12)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (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 <= (-8.4d+98)) .or. (.not. (x <= 2.4d-12))) then
        tmp = t * (x / (z - y))
    else
        tmp = t * (y / (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 <= -8.4e+98) || !(x <= 2.4e-12)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.4e+98) or not (x <= 2.4e-12):
		tmp = t * (x / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.4e+98) || !(x <= 2.4e-12))
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.4e+98) || ~((x <= 2.4e-12)))
		tmp = t * (x / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.4e+98], N[Not[LessEqual[x, 2.4e-12]], $MachinePrecision]], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.40000000000000016e98 or 2.39999999999999987e-12 < x

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.8%

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

   if -8.40000000000000016e98 < x < 2.39999999999999987e-12

   1. Initial program 97.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.5%

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

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac 83.5%

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

   5. Simplified 83.5%

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

      1. frac-2neg 83.5%

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

      2. div-inv 83.4%

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

      3. remove-double-neg 83.4%

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

      4. sub-neg 83.4%

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

      5. distribute-neg-in 83.4%

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

      6. remove-double-neg 83.4%

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

   7. Applied egg-rr 83.4%

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

      1. associate-*r/ 83.5%

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

      2. *-rgt-identity 83.5%

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

      3. +-commutative 83.5%

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

      4. unsub-neg 83.5%

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

   9. Simplified 83.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+98} \lor \neg \left(x \leq 2.4 \cdot 10^{-12}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-16} \lor \neg \left(z \leq 2.6 \cdot 10^{-12}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e-16) (not (<= z 2.6e-12)))
   (* t (/ (- x y) z))
   (- t (* t (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-16) || !(z <= 2.6e-12)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t - (t * (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 <= (-7.8d-16)) .or. (.not. (z <= 2.6d-12))) then
        tmp = t * ((x - y) / z)
    else
        tmp = t - (t * (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 <= -7.8e-16) || !(z <= 2.6e-12)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e-16) or not (z <= 2.6e-12):
		tmp = t * ((x - y) / z)
	else:
		tmp = t - (t * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e-16) || !(z <= 2.6e-12))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e-16) || ~((z <= 2.6e-12)))
		tmp = t * ((x - y) / z);
	else
		tmp = t - (t * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e-16], N[Not[LessEqual[z, 2.6e-12]], $MachinePrecision]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.79999999999999954e-16 or 2.59999999999999983e-12 < z

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.8%

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

   if -7.79999999999999954e-16 < z < 2.59999999999999983e-12

   1. Initial program 95.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 87.4%

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

      2. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. associate-/l* 83.2%

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

   10. Simplified 83.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-16} \lor \neg \left(z \leq 2.6 \cdot 10^{-12}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e+51) t (if (<= y 1.7e+35) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+51) {
		tmp = t;
	} else if (y <= 1.7e+35) {
		tmp = x * (t / (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 (y <= (-8.2d+51)) then
        tmp = t
    else if (y <= 1.7d+35) then
        tmp = x * (t / (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 (y <= -8.2e+51) {
		tmp = t;
	} else if (y <= 1.7e+35) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e+51:
		tmp = t
	elif y <= 1.7e+35:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e+51)
		tmp = t;
	elseif (y <= 1.7e+35)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e+51)
		tmp = t;
	elseif (y <= 1.7e+35)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e+51], t, If[LessEqual[y, 1.7e+35], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.20000000000000021e51 or 1.7000000000000001e35 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 67.3%

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

      2. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in y around inf 66.9%

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

   if -8.20000000000000021e51 < y < 1.7000000000000001e35

   1. Initial program 93.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.7%

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

      2. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-/l* 78.6%

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

   7. Applied egg-rr 78.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-12}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e-15)
   (* t (/ (- x y) z))
   (if (<= z 2.1e-12) (- t (* t (/ x y))) (/ (- x y) (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e-15) {
		tmp = t * ((x - y) / z);
	} else if (z <= 2.1e-12) {
		tmp = t - (t * (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 (z <= (-4.5d-15)) then
        tmp = t * ((x - y) / z)
    else if (z <= 2.1d-12) then
        tmp = t - (t * (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 (z <= -4.5e-15) {
		tmp = t * ((x - y) / z);
	} else if (z <= 2.1e-12) {
		tmp = t - (t * (x / y));
	} else {
		tmp = (x - y) / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e-15:
		tmp = t * ((x - y) / z)
	elif z <= 2.1e-12:
		tmp = t - (t * (x / y))
	else:
		tmp = (x - y) / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e-15)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (z <= 2.1e-12)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e-15)
		tmp = t * ((x - y) / z);
	elseif (z <= 2.1e-12)
		tmp = t - (t * (x / y));
	else
		tmp = (x - y) / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e-15], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-12], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4999999999999998e-15

   1. Initial program 96.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.3%

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

   if -4.4999999999999998e-15 < z < 2.09999999999999994e-12

   1. Initial program 95.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 87.4%

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

      2. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. associate-*r/ 65.5%

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

      2. neg-mul-1 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. associate-/l* 83.2%

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

   10. Simplified 83.2%

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

   if 2.09999999999999994e-12 < z

   1. Initial program 97.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.6%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 94.6%

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

      2. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in z around inf 86.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-12}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45) t (if (<= y 2.2e+30) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45) {
		tmp = t;
	} else if (y <= 2.2e+30) {
		tmp = x * (t / 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 (y <= (-1.45d0)) then
        tmp = t
    else if (y <= 2.2d+30) then
        tmp = x * (t / 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 (y <= -1.45) {
		tmp = t;
	} else if (y <= 2.2e+30) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45:
		tmp = t
	elif y <= 2.2e+30:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45)
		tmp = t;
	elseif (y <= 2.2e+30)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45)
		tmp = t;
	elseif (y <= 2.2e+30)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45], t, If[LessEqual[y, 2.2e+30], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999996 or 2.2e30 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.8%

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

      2. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in y around inf 62.3%

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

   if -1.44999999999999996 < y < 2.2e30

   1. Initial program 93.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-/l* 70.3%

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

   7. Simplified 70.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8) t (if (<= y 9.6e+29) (/ x (/ z t)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8) {
		tmp = t;
	} else if (y <= 9.6e+29) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.8d0)) then
        tmp = t
    else if (y <= 9.6d+29) then
        tmp = x / (z / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8) {
		tmp = t;
	} else if (y <= 9.6e+29) {
		tmp = x / (z / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8:
		tmp = t
	elif y <= 9.6e+29:
		tmp = x / (z / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8)
		tmp = t;
	elseif (y <= 9.6e+29)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8)
		tmp = t;
	elseif (y <= 9.6e+29)
		tmp = x / (z / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8], t, If[LessEqual[y, 9.6e+29], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998 or 9.6000000000000003e29 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.8%

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

      2. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in y around inf 62.3%

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

   if -3.7999999999999998 < y < 9.6000000000000003e29

   1. Initial program 93.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-/l* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in x around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l/ 67.4%

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

      3. associate-/r/ 70.4%

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

   10. Simplified 70.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.2%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 84.5%

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

   2. associate-/l* 85.8%

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

3. Simplified 85.8%

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

5. Taylor expanded in y around inf 34.8%

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

6. Final simplification 34.8%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024062 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))