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

Percentage Accurate: 96.9% → 96.9%

Time: 10.3s

Alternatives: 14

Speedup: 1.0×

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: 96.9% 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: 96.9% 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]

Derivation

1. Initial program 96.5%

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

3. Final simplification 96.5%

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

Alternative 2: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -1.25e+174)
     t
     (if (<= y -2.2e+128)
       t_1
       (if (<= y -2.8e+37)
         t
         (if (<= y 4.8e+27)
           t_1
           (if (<= y 1.6e+105) (* t (/ (- x y) z)) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -1.25e+174) {
		tmp = t;
	} else if (y <= -2.2e+128) {
		tmp = t_1;
	} else if (y <= -2.8e+37) {
		tmp = t;
	} else if (y <= 4.8e+27) {
		tmp = t_1;
	} else if (y <= 1.6e+105) {
		tmp = t * ((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) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    if (y <= (-1.25d+174)) then
        tmp = t
    else if (y <= (-2.2d+128)) then
        tmp = t_1
    else if (y <= (-2.8d+37)) then
        tmp = t
    else if (y <= 4.8d+27) then
        tmp = t_1
    else if (y <= 1.6d+105) then
        tmp = t * ((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 t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -1.25e+174) {
		tmp = t;
	} else if (y <= -2.2e+128) {
		tmp = t_1;
	} else if (y <= -2.8e+37) {
		tmp = t;
	} else if (y <= 4.8e+27) {
		tmp = t_1;
	} else if (y <= 1.6e+105) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -1.25e+174:
		tmp = t
	elif y <= -2.2e+128:
		tmp = t_1
	elif y <= -2.8e+37:
		tmp = t
	elif y <= 4.8e+27:
		tmp = t_1
	elif y <= 1.6e+105:
		tmp = t * ((x - y) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.25e+174)
		tmp = t;
	elseif (y <= -2.2e+128)
		tmp = t_1;
	elseif (y <= -2.8e+37)
		tmp = t;
	elseif (y <= 4.8e+27)
		tmp = t_1;
	elseif (y <= 1.6e+105)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -1.25e+174)
		tmp = t;
	elseif (y <= -2.2e+128)
		tmp = t_1;
	elseif (y <= -2.8e+37)
		tmp = t;
	elseif (y <= 4.8e+27)
		tmp = t_1;
	elseif (y <= 1.6e+105)
		tmp = t * ((x - y) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+174], t, If[LessEqual[y, -2.2e+128], t$95$1, If[LessEqual[y, -2.8e+37], t, If[LessEqual[y, 4.8e+27], t$95$1, If[LessEqual[y, 1.6e+105], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2499999999999999e174 or -2.20000000000000017e128 < y < -2.7999999999999998e37 or 1.6e105 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.2%

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

      2. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around inf 80.1%

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

   if -1.2499999999999999e174 < y < -2.20000000000000017e128 or -2.7999999999999998e37 < y < 4.79999999999999995e27

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 69.1%

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

   if 4.79999999999999995e27 < y < 1.6e105

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 57.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+174}:\\ \;\;\;\;t + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -1.4e+174)
     (+ t (* t (/ z y)))
     (if (<= y -1.52e+128)
       t_1
       (if (<= y -5.8e+34)
         t
         (if (<= y 1.7e+28)
           t_1
           (if (<= y 1.85e+105) (* t (/ (- x y) z)) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -1.4e+174) {
		tmp = t + (t * (z / y));
	} else if (y <= -1.52e+128) {
		tmp = t_1;
	} else if (y <= -5.8e+34) {
		tmp = t;
	} else if (y <= 1.7e+28) {
		tmp = t_1;
	} else if (y <= 1.85e+105) {
		tmp = t * ((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) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    if (y <= (-1.4d+174)) then
        tmp = t + (t * (z / y))
    else if (y <= (-1.52d+128)) then
        tmp = t_1
    else if (y <= (-5.8d+34)) then
        tmp = t
    else if (y <= 1.7d+28) then
        tmp = t_1
    else if (y <= 1.85d+105) then
        tmp = t * ((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 t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -1.4e+174) {
		tmp = t + (t * (z / y));
	} else if (y <= -1.52e+128) {
		tmp = t_1;
	} else if (y <= -5.8e+34) {
		tmp = t;
	} else if (y <= 1.7e+28) {
		tmp = t_1;
	} else if (y <= 1.85e+105) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -1.4e+174:
		tmp = t + (t * (z / y))
	elif y <= -1.52e+128:
		tmp = t_1
	elif y <= -5.8e+34:
		tmp = t
	elif y <= 1.7e+28:
		tmp = t_1
	elif y <= 1.85e+105:
		tmp = t * ((x - y) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.4e+174)
		tmp = Float64(t + Float64(t * Float64(z / y)));
	elseif (y <= -1.52e+128)
		tmp = t_1;
	elseif (y <= -5.8e+34)
		tmp = t;
	elseif (y <= 1.7e+28)
		tmp = t_1;
	elseif (y <= 1.85e+105)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -1.4e+174)
		tmp = t + (t * (z / y));
	elseif (y <= -1.52e+128)
		tmp = t_1;
	elseif (y <= -5.8e+34)
		tmp = t;
	elseif (y <= 1.7e+28)
		tmp = t_1;
	elseif (y <= 1.85e+105)
		tmp = t * ((x - y) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+174], N[(t + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.52e+128], t$95$1, If[LessEqual[y, -5.8e+34], t, If[LessEqual[y, 1.7e+28], t$95$1, If[LessEqual[y, 1.85e+105], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4e174

   1. Initial program 99.9%

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

      1. associate-*l/ 62.1%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

      1. associate-*r/ 62.1%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 95.3%

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

      1. mul-1-neg 95.3%

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

      2. div-sub 95.3%

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

      3. sub-neg 95.3%

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

      4. *-inverses 95.3%

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

      5. metadata-eval 95.3%

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

   9. Simplified 95.3%

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

   10. Taylor expanded in z around 0 65.2%

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

       1. associate-/l* 75.2%

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

   12. Simplified 75.2%

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

   if -1.4e174 < y < -1.51999999999999992e128 or -5.8000000000000003e34 < y < 1.7e28

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 69.1%

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

   if -1.51999999999999992e128 < y < -5.8000000000000003e34 or 1.84999999999999992e105 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.3%

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

      2. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in y around inf 82.5%

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

   if 1.7e28 < y < 1.84999999999999992e105

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 57.9%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+174}:\\ \;\;\;\;t + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.88 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+128} \lor \neg \left(y \leq -1.8 \cdot 10^{+38}\right) \land y \leq 3 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.88e+174)
   t
   (if (or (<= y -2.45e+128) (and (not (<= y -1.8e+38)) (<= y 3e+21)))
     (* t (/ x (- z y)))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.88e+174) {
		tmp = t;
	} else if ((y <= -2.45e+128) || (!(y <= -1.8e+38) && (y <= 3e+21))) {
		tmp = t * (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 (y <= (-1.88d+174)) then
        tmp = t
    else if ((y <= (-2.45d+128)) .or. (.not. (y <= (-1.8d+38))) .and. (y <= 3d+21)) then
        tmp = t * (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 (y <= -1.88e+174) {
		tmp = t;
	} else if ((y <= -2.45e+128) || (!(y <= -1.8e+38) && (y <= 3e+21))) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.88e+174:
		tmp = t
	elif (y <= -2.45e+128) or (not (y <= -1.8e+38) and (y <= 3e+21)):
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.88e+174)
		tmp = t;
	elseif ((y <= -2.45e+128) || (!(y <= -1.8e+38) && (y <= 3e+21)))
		tmp = Float64(t * 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 (y <= -1.88e+174)
		tmp = t;
	elseif ((y <= -2.45e+128) || (~((y <= -1.8e+38)) && (y <= 3e+21)))
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.88e+174], t, If[Or[LessEqual[y, -2.45e+128], And[N[Not[LessEqual[y, -1.8e+38]], $MachinePrecision], LessEqual[y, 3e+21]]], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.88000000000000006e174 or -2.45000000000000009e128 < y < -1.79999999999999985e38 or 3e21 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.4%

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

      2. associate-/l* 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around inf 69.8%

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

   if -1.88000000000000006e174 < y < -2.45000000000000009e128 or -1.79999999999999985e38 < y < 3e21

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 69.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.88 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+128} \lor \neg \left(y \leq -1.8 \cdot 10^{+38}\right) \land y \leq 3 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-75} \lor \neg \left(y \leq 9.2 \cdot 10^{+20}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -2.9e+189)
     t_1
     (if (<= y -9e+164)
       (* t (- 1.0 (/ x y)))
       (if (or (<= y -1.85e-75) (not (<= y 9.2e+20)))
         t_1
         (/ (* x t) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -2.9e+189) {
		tmp = t_1;
	} else if (y <= -9e+164) {
		tmp = t * (1.0 - (x / y));
	} else if ((y <= -1.85e-75) || !(y <= 9.2e+20)) {
		tmp = t_1;
	} else {
		tmp = (x * 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) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-2.9d+189)) then
        tmp = t_1
    else if (y <= (-9d+164)) then
        tmp = t * (1.0d0 - (x / y))
    else if ((y <= (-1.85d-75)) .or. (.not. (y <= 9.2d+20))) then
        tmp = t_1
    else
        tmp = (x * t) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -2.9e+189) {
		tmp = t_1;
	} else if (y <= -9e+164) {
		tmp = t * (1.0 - (x / y));
	} else if ((y <= -1.85e-75) || !(y <= 9.2e+20)) {
		tmp = t_1;
	} else {
		tmp = (x * t) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -2.9e+189:
		tmp = t_1
	elif y <= -9e+164:
		tmp = t * (1.0 - (x / y))
	elif (y <= -1.85e-75) or not (y <= 9.2e+20):
		tmp = t_1
	else:
		tmp = (x * t) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -2.9e+189)
		tmp = t_1;
	elseif (y <= -9e+164)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif ((y <= -1.85e-75) || !(y <= 9.2e+20))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * t) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -2.9e+189)
		tmp = t_1;
	elseif (y <= -9e+164)
		tmp = t * (1.0 - (x / y));
	elseif ((y <= -1.85e-75) || ~((y <= 9.2e+20)))
		tmp = t_1;
	else
		tmp = (x * t) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+189], t$95$1, If[LessEqual[y, -9e+164], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.85e-75], N[Not[LessEqual[y, 9.2e+20]], $MachinePrecision]], t$95$1, N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.90000000000000019e189 or -8.9999999999999995e164 < y < -1.85000000000000012e-75 or 9.2e20 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 86.5%

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

   3. Simplified 86.5%

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

      1. associate-*r/ 80.6%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. div-sub 82.7%

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

      3. sub-neg 82.7%

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

      4. *-inverses 82.7%

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

      5. metadata-eval 82.7%

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

   9. Simplified 82.7%

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

   10. Taylor expanded in t around 0 82.7%

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

   if -2.90000000000000019e189 < y < -8.9999999999999995e164

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if -1.85000000000000012e-75 < y < 9.2e20

   1. Initial program 92.3%

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

      1. associate-*l/ 89.9%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 76.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+189}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-75} \lor \neg \left(y \leq 9.2 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -8.2e+186)
     t_1
     (if (<= y -7.5e+163)
       (* t (- 1.0 (/ x y)))
       (if (<= y -1.85e-75)
         (* t (/ y (- y z)))
         (if (<= y 3.8e+21) (/ (* x t) (- z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -8.2e+186) {
		tmp = t_1;
	} else if (y <= -7.5e+163) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -1.85e-75) {
		tmp = t * (y / (y - z));
	} else if (y <= 3.8e+21) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-8.2d+186)) then
        tmp = t_1
    else if (y <= (-7.5d+163)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-1.85d-75)) then
        tmp = t * (y / (y - z))
    else if (y <= 3.8d+21) then
        tmp = (x * t) / (z - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -8.2e+186) {
		tmp = t_1;
	} else if (y <= -7.5e+163) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -1.85e-75) {
		tmp = t * (y / (y - z));
	} else if (y <= 3.8e+21) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -8.2e+186:
		tmp = t_1
	elif y <= -7.5e+163:
		tmp = t * (1.0 - (x / y))
	elif y <= -1.85e-75:
		tmp = t * (y / (y - z))
	elif y <= 3.8e+21:
		tmp = (x * t) / (z - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -8.2e+186)
		tmp = t_1;
	elseif (y <= -7.5e+163)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -1.85e-75)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 3.8e+21)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -8.2e+186)
		tmp = t_1;
	elseif (y <= -7.5e+163)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -1.85e-75)
		tmp = t * (y / (y - z));
	elseif (y <= 3.8e+21)
		tmp = (x * t) / (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+186], t$95$1, If[LessEqual[y, -7.5e+163], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-75], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+21], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.2e186 or 3.8e21 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.9%

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

      2. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

      1. associate-*r/ 70.9%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. div-sub 89.5%

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

      3. sub-neg 89.5%

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

      4. *-inverses 89.5%

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

      5. metadata-eval 89.5%

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

   9. Simplified 89.5%

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

   10. Taylor expanded in t around 0 89.5%

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

   if -8.2e186 < y < -7.50000000000000001e163

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if -7.50000000000000001e163 < y < -1.85000000000000012e-75

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.8%

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

      1. neg-mul-1 72.8%

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

      2. distribute-neg-frac2 72.8%

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

   5. Simplified 72.8%

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

   if -1.85000000000000012e-75 < y < 3.8e21

   1. Initial program 92.3%

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

      1. associate-*l/ 89.9%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 76.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+186}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-91}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.8e+32)
   t
   (if (<= y -4.2e-71)
     (* (/ t z) (- y))
     (if (<= y -1.55e-91)
       (/ (* x t) (- y))
       (if (<= y 9.2e+20) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.8e+32) {
		tmp = t;
	} else if (y <= -4.2e-71) {
		tmp = (t / z) * -y;
	} else if (y <= -1.55e-91) {
		tmp = (x * t) / -y;
	} else if (y <= 9.2e+20) {
		tmp = t * (x / 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 <= (-8.8d+32)) then
        tmp = t
    else if (y <= (-4.2d-71)) then
        tmp = (t / z) * -y
    else if (y <= (-1.55d-91)) then
        tmp = (x * t) / -y
    else if (y <= 9.2d+20) then
        tmp = t * (x / 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 <= -8.8e+32) {
		tmp = t;
	} else if (y <= -4.2e-71) {
		tmp = (t / z) * -y;
	} else if (y <= -1.55e-91) {
		tmp = (x * t) / -y;
	} else if (y <= 9.2e+20) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.8e+32:
		tmp = t
	elif y <= -4.2e-71:
		tmp = (t / z) * -y
	elif y <= -1.55e-91:
		tmp = (x * t) / -y
	elif y <= 9.2e+20:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.8e+32)
		tmp = t;
	elseif (y <= -4.2e-71)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= -1.55e-91)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (y <= 9.2e+20)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.8e+32)
		tmp = t;
	elseif (y <= -4.2e-71)
		tmp = (t / z) * -y;
	elseif (y <= -1.55e-91)
		tmp = (x * t) / -y;
	elseif (y <= 9.2e+20)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.8e+32], t, If[LessEqual[y, -4.2e-71], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, -1.55e-91], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 9.2e+20], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.80000000000000004e32 or 9.2e20 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 75.9%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in y around inf 64.1%

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

   if -8.80000000000000004e32 < y < -4.2000000000000002e-71

   1. Initial program 99.8%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in x around 0 52.2%

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

      1. associate-*r/ 52.2%

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

      2. mul-1-neg 52.2%

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

      3. distribute-rgt-neg-out 52.2%

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

      4. associate-*l/ 52.4%

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

   10. Simplified 52.4%

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

   if -4.2000000000000002e-71 < y < -1.5499999999999999e-91

   1. Initial program 87.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 64.3%

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

   6. Taylor expanded in z around 0 64.3%

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

      1. associate-*r/ 64.3%

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

      2. mul-1-neg 64.3%

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

      3. distribute-rgt-neg-out 64.3%

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

   8. Simplified 64.3%

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

   if -1.5499999999999999e-91 < y < 9.2e20

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 65.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-91}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+103}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.35e+187)
     t_1
     (if (<= y -7.5e+163)
       (* t (- 1.0 (/ x y)))
       (if (<= y 1.65e+103) (* (- x y) (/ t (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.35e+187) {
		tmp = t_1;
	} else if (y <= -7.5e+163) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 1.65e+103) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-1.35d+187)) then
        tmp = t_1
    else if (y <= (-7.5d+163)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 1.65d+103) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.35e+187) {
		tmp = t_1;
	} else if (y <= -7.5e+163) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 1.65e+103) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.35e+187:
		tmp = t_1
	elif y <= -7.5e+163:
		tmp = t * (1.0 - (x / y))
	elif y <= 1.65e+103:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.35e+187)
		tmp = t_1;
	elseif (y <= -7.5e+163)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 1.65e+103)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.35e+187)
		tmp = t_1;
	elseif (y <= -7.5e+163)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 1.65e+103)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+187], t$95$1, If[LessEqual[y, -7.5e+163], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+103], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35000000000000004e187 or 1.65000000000000004e103 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 64.6%

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

      2. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

      1. associate-*r/ 64.6%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 97.1%

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

      1. mul-1-neg 97.1%

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

      2. div-sub 97.2%

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

      3. sub-neg 97.2%

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

      4. *-inverses 97.2%

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

      5. metadata-eval 97.2%

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

   9. Simplified 97.2%

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

   10. Taylor expanded in t around 0 97.2%

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

   if -1.35000000000000004e187 < y < -7.50000000000000001e163

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if -7.50000000000000001e163 < y < 1.65000000000000004e103

   1. Initial program 95.3%

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

      1. associate-*l/ 90.9%

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

      2. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+187}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+103}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-75} \lor \neg \left(y \leq 2.6 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e-75) (not (<= y 2.6e+20)))
   (/ t (- 1.0 (/ z y)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-75) || !(y <= 2.6e+20)) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.85d-75)) .or. (.not. (y <= 2.6d+20))) then
        tmp = t / (1.0d0 - (z / y))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-75) || !(y <= 2.6e+20)) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.85e-75) or not (y <= 2.6e+20):
		tmp = t / (1.0 - (z / y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.85e-75) || !(y <= 2.6e+20))
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.85e-75) || ~((y <= 2.6e+20)))
		tmp = t / (1.0 - (z / y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.85e-75], N[Not[LessEqual[y, 2.6e+20]], $MachinePrecision]], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000012e-75 or 2.6e20 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 81.0%

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

      2. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

      1. associate-*r/ 81.0%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. div-sub 80.2%

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

      3. sub-neg 80.2%

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

      4. *-inverses 80.2%

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

      5. metadata-eval 80.2%

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

   9. Simplified 80.2%

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

   10. Taylor expanded in t around 0 80.2%

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

   if -1.85000000000000012e-75 < y < 2.6e20

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 75.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-75} \lor \neg \left(y \leq 2.6 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-75} \lor \neg \left(y \leq 3.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e-75) (not (<= y 3.8e+20)))
   (/ t (- 1.0 (/ z y)))
   (/ (* x t) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-75) || !(y <= 3.8e+20)) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = (x * 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 <= (-1.85d-75)) .or. (.not. (y <= 3.8d+20))) then
        tmp = t / (1.0d0 - (z / y))
    else
        tmp = (x * 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 <= -1.85e-75) || !(y <= 3.8e+20)) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = (x * t) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.85e-75) or not (y <= 3.8e+20):
		tmp = t / (1.0 - (z / y))
	else:
		tmp = (x * t) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.85e-75) || !(y <= 3.8e+20))
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(Float64(x * t) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.85e-75) || ~((y <= 3.8e+20)))
		tmp = t / (1.0 - (z / y));
	else
		tmp = (x * t) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.85e-75], N[Not[LessEqual[y, 3.8e+20]], $MachinePrecision]], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000012e-75 or 3.8e20 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 81.0%

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

      2. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

      1. associate-*r/ 81.0%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. div-sub 80.2%

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

      3. sub-neg 80.2%

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

      4. *-inverses 80.2%

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

      5. metadata-eval 80.2%

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

   9. Simplified 80.2%

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

   10. Taylor expanded in t around 0 80.2%

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

   if -1.85000000000000012e-75 < y < 3.8e20

   1. Initial program 92.3%

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

      1. associate-*l/ 89.9%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 76.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-75} \lor \neg \left(y \leq 3.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+103}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+37) t (if (<= y 9.5e+103) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+37) {
		tmp = t;
	} else if (y <= 9.5e+103) {
		tmp = (x - y) * (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 <= (-1.85d+37)) then
        tmp = t
    else if (y <= 9.5d+103) then
        tmp = (x - y) * (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 <= -1.85e+37) {
		tmp = t;
	} else if (y <= 9.5e+103) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+37:
		tmp = t
	elif y <= 9.5e+103:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+37)
		tmp = t;
	elseif (y <= 9.5e+103)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.85e+37)
		tmp = t;
	elseif (y <= 9.5e+103)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+37], t, If[LessEqual[y, 9.5e+103], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e37 or 9.49999999999999922e103 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.8%

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

      2. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in y around inf 71.3%

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

   if -1.85e37 < y < 9.49999999999999922e103

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+103}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e+31) t (if (<= y 3.8e+20) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e+31) {
		tmp = t;
	} else if (y <= 3.8e+20) {
		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 <= (-8.5d+31)) then
        tmp = t
    else if (y <= 3.8d+20) 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 <= -8.5e+31) {
		tmp = t;
	} else if (y <= 3.8e+20) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e+31:
		tmp = t
	elif y <= 3.8e+20:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e+31)
		tmp = t;
	elseif (y <= 3.8e+20)
		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 <= -8.5e+31)
		tmp = t;
	elseif (y <= 3.8e+20)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e+31], t, If[LessEqual[y, 3.8e+20], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999947e31 or 3.8e20 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 75.9%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in y around inf 64.1%

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

   if -8.49999999999999947e31 < y < 3.8e20

   1. Initial program 93.9%

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

      1. associate-*l/ 92.0%

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

      2. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

      2. associate-/l* 55.9%

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

   7. Simplified 55.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e+36) t (if (<= y 6.5e+20) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+36) {
		tmp = t;
	} else if (y <= 6.5e+20) {
		tmp = t * (x / 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 <= (-4.8d+36)) then
        tmp = t
    else if (y <= 6.5d+20) then
        tmp = t * (x / 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 <= -4.8e+36) {
		tmp = t;
	} else if (y <= 6.5e+20) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e+36:
		tmp = t
	elif y <= 6.5e+20:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e+36)
		tmp = t;
	elseif (y <= 6.5e+20)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e+36)
		tmp = t;
	elseif (y <= 6.5e+20)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e+36], t, If[LessEqual[y, 6.5e+20], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999985e36 or 6.5e20 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 75.9%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in y around inf 64.1%

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

   if -4.79999999999999985e36 < y < 6.5e20

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0 58.7%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.0% 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 96.5%

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

   1. associate-*l/ 85.1%

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

   2. associate-/l* 87.7%

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

3. Simplified 87.7%

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

5. Taylor expanded in y around inf 37.1%

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

6. Final simplification 37.1%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 96.9% 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 2024059 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

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