Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.7% → 94.7%

Time: 12.3s

Alternatives: 13

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (+ (/ y z) (/ t (+ z -1.0)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) + (t / (z + -1.0)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) + (t / (z + (-1.0d0))))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) + (t / (z + -1.0)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) + (t / (z + -1.0)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) + Float64(t / Float64(z + -1.0))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) + (t / (z + -1.0)));
end

Wolfram

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

Derivation

1. Initial program 94.5%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Final simplification 94.5%

   \[\leadsto x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \]
4. Add Preprocessing

Alternative 2: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z + -1}\\ \mathbf{if}\;y \leq -34000000000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (+ z -1.0)))))
   (if (<= y -34000000000000.0)
     (* y (/ x z))
     (if (<= y 3e-80)
       t_1
       (if (<= y 9e-61)
         (* x (/ y z))
         (if (<= y 2.6e-25) t_1 (/ (* x y) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z + -1.0));
	double tmp;
	if (y <= -34000000000000.0) {
		tmp = y * (x / z);
	} else if (y <= 3e-80) {
		tmp = t_1;
	} else if (y <= 9e-61) {
		tmp = x * (y / z);
	} else if (y <= 2.6e-25) {
		tmp = t_1;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z + (-1.0d0)))
    if (y <= (-34000000000000.0d0)) then
        tmp = y * (x / z)
    else if (y <= 3d-80) then
        tmp = t_1
    else if (y <= 9d-61) then
        tmp = x * (y / z)
    else if (y <= 2.6d-25) then
        tmp = t_1
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z + -1.0));
	double tmp;
	if (y <= -34000000000000.0) {
		tmp = y * (x / z);
	} else if (y <= 3e-80) {
		tmp = t_1;
	} else if (y <= 9e-61) {
		tmp = x * (y / z);
	} else if (y <= 2.6e-25) {
		tmp = t_1;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z + -1.0))
	tmp = 0
	if y <= -34000000000000.0:
		tmp = y * (x / z)
	elif y <= 3e-80:
		tmp = t_1
	elif y <= 9e-61:
		tmp = x * (y / z)
	elif y <= 2.6e-25:
		tmp = t_1
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (y <= -34000000000000.0)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 3e-80)
		tmp = t_1;
	elseif (y <= 9e-61)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2.6e-25)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z + -1.0));
	tmp = 0.0;
	if (y <= -34000000000000.0)
		tmp = y * (x / z);
	elseif (y <= 3e-80)
		tmp = t_1;
	elseif (y <= 9e-61)
		tmp = x * (y / z);
	elseif (y <= 2.6e-25)
		tmp = t_1;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -34000000000000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-80], t$95$1, If[LessEqual[y, 9e-61], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-25], t$95$1, N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4e13

   1. Initial program 90.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. neg-sub0 86.2%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 86.2%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in t around 0 80.6%

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

   if -3.4e13 < y < 3.00000000000000007e-80 or 9e-61 < y < 2.6e-25

   1. Initial program 96.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/l* 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

      4. distribute-neg-frac2 69.9%

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

      5. neg-sub0 69.9%

         \[\leadsto t \cdot \frac{x}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 69.9%

         \[\leadsto t \cdot \frac{x}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 69.9%

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

   5. Simplified 69.9%

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

   if 3.00000000000000007e-80 < y < 9e-61

   1. Initial program 99.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.1%

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

      1. associate-*r/ 87.1%

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

   5. Simplified 87.1%

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

   if 2.6e-25 < y

   1. Initial program 94.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -34000000000000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+90} \lor \neg \left(t \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -5.6e+206)
     t_1
     (if (<= t -1.65e+140)
       (* y (/ x z))
       (if (or (<= t -2.7e+90) (not (<= t 4e+28))) t_1 (* x (/ y z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -5.6e+206) {
		tmp = t_1;
	} else if (t <= -1.65e+140) {
		tmp = y * (x / z);
	} else if ((t <= -2.7e+90) || !(t <= 4e+28)) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-5.6d+206)) then
        tmp = t_1
    else if (t <= (-1.65d+140)) then
        tmp = y * (x / z)
    else if ((t <= (-2.7d+90)) .or. (.not. (t <= 4d+28))) then
        tmp = t_1
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -5.6e+206) {
		tmp = t_1;
	} else if (t <= -1.65e+140) {
		tmp = y * (x / z);
	} else if ((t <= -2.7e+90) || !(t <= 4e+28)) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -5.6e+206:
		tmp = t_1
	elif t <= -1.65e+140:
		tmp = y * (x / z)
	elif (t <= -2.7e+90) or not (t <= 4e+28):
		tmp = t_1
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -5.6e+206)
		tmp = t_1;
	elseif (t <= -1.65e+140)
		tmp = Float64(y * Float64(x / z));
	elseif ((t <= -2.7e+90) || !(t <= 4e+28))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -5.6e+206)
		tmp = t_1;
	elseif (t <= -1.65e+140)
		tmp = y * (x / z);
	elseif ((t <= -2.7e+90) || ~((t <= 4e+28)))
		tmp = t_1;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+206], t$95$1, If[LessEqual[t, -1.65e+140], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.7e+90], N[Not[LessEqual[t, 4e+28]], $MachinePrecision]], t$95$1, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5999999999999996e206 or -1.6500000000000001e140 < t < -2.7e90 or 3.99999999999999983e28 < t

   1. Initial program 94.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-/l* 73.4%

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

      4. distribute-rgt-neg-out 73.4%

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

      5. distribute-neg-frac2 73.4%

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

      6. neg-sub0 73.4%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 73.4%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around inf 60.4%

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

   if -5.5999999999999996e206 < t < -1.6500000000000001e140

   1. Initial program 95.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-neg-frac2 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

      4. neg-sub0 61.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 61.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in t around 0 52.3%

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

   if -2.7e90 < t < 3.99999999999999983e28

   1. Initial program 94.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.6%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+206}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+90} \lor \neg \left(t \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -2.3e+206)
     t_1
     (if (<= t -1.2e+140)
       (* y (/ x z))
       (if (<= t -3.7e+90)
         t_1
         (if (<= t 2e+28) (* x (/ y z)) (/ x (/ z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.3e+206) {
		tmp = t_1;
	} else if (t <= -1.2e+140) {
		tmp = y * (x / z);
	} else if (t <= -3.7e+90) {
		tmp = t_1;
	} else if (t <= 2e+28) {
		tmp = x * (y / z);
	} else {
		tmp = x / (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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-2.3d+206)) then
        tmp = t_1
    else if (t <= (-1.2d+140)) then
        tmp = y * (x / z)
    else if (t <= (-3.7d+90)) then
        tmp = t_1
    else if (t <= 2d+28) then
        tmp = x * (y / z)
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.3e+206) {
		tmp = t_1;
	} else if (t <= -1.2e+140) {
		tmp = y * (x / z);
	} else if (t <= -3.7e+90) {
		tmp = t_1;
	} else if (t <= 2e+28) {
		tmp = x * (y / z);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -2.3e+206:
		tmp = t_1
	elif t <= -1.2e+140:
		tmp = y * (x / z)
	elif t <= -3.7e+90:
		tmp = t_1
	elif t <= 2e+28:
		tmp = x * (y / z)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -2.3e+206)
		tmp = t_1;
	elseif (t <= -1.2e+140)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= -3.7e+90)
		tmp = t_1;
	elseif (t <= 2e+28)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -2.3e+206)
		tmp = t_1;
	elseif (t <= -1.2e+140)
		tmp = y * (x / z);
	elseif (t <= -3.7e+90)
		tmp = t_1;
	elseif (t <= 2e+28)
		tmp = x * (y / z);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+206], t$95$1, If[LessEqual[t, -1.2e+140], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.7e+90], t$95$1, If[LessEqual[t, 2e+28], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.30000000000000016e206 or -1.2e140 < t < -3.7e90

   1. Initial program 99.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. *-commutative 71.2%

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

      3. associate-/l* 78.3%

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

      4. distribute-rgt-neg-out 78.3%

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

      5. distribute-neg-frac2 78.3%

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

      6. neg-sub0 78.3%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 78.3%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in z around inf 67.4%

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

   if -2.30000000000000016e206 < t < -1.2e140

   1. Initial program 95.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-neg-frac2 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

      4. neg-sub0 61.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(0 - \left(1 - z\right)\right)}} + \frac{x}{z}\right) \]

      5. associate--r- 61.5%

         \[\leadsto y \cdot \left(\frac{t \cdot x}{y \cdot \color{blue}{\left(\left(0 - 1\right) + z\right)}} + \frac{x}{z}\right) \]

      6. metadata-eval 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in t around 0 52.3%

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

   if -3.7e90 < t < 1.99999999999999992e28

   1. Initial program 94.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.6%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

   if 1.99999999999999992e28 < t

   1. Initial program 91.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 62.9%

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

      1. mul-1-neg 62.9%

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

      2. *-commutative 62.9%

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

      3. associate-/l* 71.1%

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

      4. distribute-rgt-neg-out 71.1%

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

      5. distribute-neg-frac2 71.1%

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

      6. neg-sub0 71.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 71.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around inf 57.1%

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

      1. clear-num 57.1%

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

      2. un-div-inv 57.1%

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

   8. Applied egg-rr 57.1%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+206}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+50} \lor \neg \left(t \leq 3.8 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e+50) (not (<= t 3.8e+28)))
   (* x (/ t (+ z -1.0)))
   (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e+50) || !(t <= 3.8e+28)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.2d+50)) .or. (.not. (t <= 3.8d+28))) then
        tmp = x * (t / (z + (-1.0d0)))
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e+50) || !(t <= 3.8e+28)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.2e+50) or not (t <= 3.8e+28):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e+50) || !(t <= 3.8e+28))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.2e+50) || ~((t <= 3.8e+28)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e+50], N[Not[LessEqual[t, 3.8e+28]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000017e50 or 3.7999999999999999e28 < t

   1. Initial program 94.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. *-commutative 63.5%

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

      3. associate-/l* 70.3%

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

      4. distribute-rgt-neg-out 70.3%

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

      5. distribute-neg-frac2 70.3%

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

      6. neg-sub0 70.3%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 70.3%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 70.3%

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

   5. Simplified 70.3%

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

   if -2.20000000000000017e50 < t < 3.7999999999999999e28

   1. Initial program 94.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 82.3%

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

      1. associate-*r/ 85.3%

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

   5. Simplified 85.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+50} \lor \neg \left(t \leq 3.8 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05) (not (<= z 1.0)))
   (* (+ y t) (/ x z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.05d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y + t) * (x / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05) or not (z <= 1.0):
		tmp = (y + t) * (x / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05) || !(z <= 1.0))
		tmp = Float64(Float64(y + t) * Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05) || ~((z <= 1.0)))
		tmp = (y + t) * (x / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 1 < z

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-/l* 82.8%

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

      3. cancel-sign-sub-inv 82.8%

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

      4. metadata-eval 82.8%

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

      5. *-lft-identity 82.8%

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

      6. +-commutative 82.8%

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

   5. Simplified 82.8%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 92.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.6e+128)
   (* x (/ y z))
   (if (<= z 1.6e+19) (* x (- (/ y z) t)) (/ x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+128) {
		tmp = x * (y / z);
	} else if (z <= 1.6e+19) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (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 <= (-2.6d+128)) then
        tmp = x * (y / z)
    else if (z <= 1.6d+19) then
        tmp = x * ((y / z) - t)
    else
        tmp = x / (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 <= -2.6e+128) {
		tmp = x * (y / z);
	} else if (z <= 1.6e+19) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.6e+128:
		tmp = x * (y / z)
	elif z <= 1.6e+19:
		tmp = x * ((y / z) - t)
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.6e+128)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 1.6e+19)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.6e+128)
		tmp = x * (y / z);
	elseif (z <= 1.6e+19)
		tmp = x * ((y / z) - t);
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.6e+128], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+19], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e128

   1. Initial program 97.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 49.1%

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

      1. associate-*r/ 61.8%

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

   5. Simplified 61.8%

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

   if -2.6e128 < z < 1.6e19

   1. Initial program 93.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.3%

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

   if 1.6e19 < z

   1. Initial program 94.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-/l* 65.4%

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

      4. distribute-rgt-neg-out 65.4%

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

      5. distribute-neg-frac2 65.4%

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

      6. neg-sub0 65.4%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 65.4%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in z around inf 65.4%

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

      1. clear-num 65.4%

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

      2. un-div-inv 65.5%

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

   8. Applied egg-rr 65.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.88)
   (/ (* x (+ y t)) z)
   (if (<= z 1.0) (* x (- (/ y z) t)) (* (+ y t) (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.88) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (y + t) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.88d0)) then
        tmp = (x * (y + t)) / z
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = (y + t) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.88) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (y + t) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.88:
		tmp = (x * (y + t)) / z
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = (y + t) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.88)
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(y + t) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.88)
		tmp = (x * (y + t)) / z;
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = (y + t) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.88], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.880000000000000004

   1. Initial program 98.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 97.9%

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

      2. frac-sub 57.9%

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

      3. *-un-lft-identity 57.9%

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

   4. Applied egg-rr 57.9%

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

      1. div-sub 57.9%

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

      2. times-frac 64.6%

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

      3. *-inverses 86.7%

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

      4. *-lft-identity 86.7%

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

      5. remove-double-neg 86.7%

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

      6. distribute-frac-neg 86.7%

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

      7. *-rgt-identity 86.7%

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

      8. distribute-lft-neg-in 86.7%

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

      9. cancel-sign-sub 86.7%

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

      10. *-commutative 86.7%

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

      11. associate-/r* 97.9%

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

      12. *-inverses 97.9%

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

      13. *-rgt-identity 97.9%

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

      14. distribute-frac-neg 97.9%

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

      15. distribute-neg-frac2 97.9%

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

      16. neg-sub0 97.9%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{0 - \left(1 - z\right)}}\right) \]

      17. associate--r- 97.9%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{\left(0 - 1\right) + z}}\right) \]

      18. metadata-eval 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in z around inf 83.5%

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

   if -0.880000000000000004 < z < 1

   1. Initial program 92.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.5%

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

   if 1 < z

   1. Initial program 95.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.4%

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

      1. *-commutative 88.4%

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

      2. associate-/l* 89.3%

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

      3. cancel-sign-sub-inv 89.3%

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

      4. metadata-eval 89.3%

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

      5. *-lft-identity 89.3%

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

      6. +-commutative 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.06)
   (/ 1.0 (/ z (* x (+ y t))))
   (if (<= z 1.0) (* x (- (/ y z) t)) (* (+ y t) (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.06) {
		tmp = 1.0 / (z / (x * (y + t)));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (y + t) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.06d0)) then
        tmp = 1.0d0 / (z / (x * (y + t)))
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = (y + t) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.06) {
		tmp = 1.0 / (z / (x * (y + t)));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (y + t) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.06:
		tmp = 1.0 / (z / (x * (y + t)))
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = (y + t) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.06)
		tmp = Float64(1.0 / Float64(z / Float64(x * Float64(y + t))));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(y + t) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.06)
		tmp = 1.0 / (z / (x * (y + t)));
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = (y + t) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.06], N[(1.0 / N[(z / N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(y + t), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0600000000000001

   1. Initial program 98.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/l* 75.3%

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

      3. cancel-sign-sub-inv 75.3%

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

      4. metadata-eval 75.3%

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

      5. *-lft-identity 75.3%

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

      6. +-commutative 75.3%

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

   5. Simplified 75.3%

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

      1. associate-*r/ 83.5%

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

      2. clear-num 83.5%

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

      3. *-commutative 83.5%

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

      4. +-commutative 83.5%

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

   7. Applied egg-rr 83.5%

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

   if -1.0600000000000001 < z < 1

   1. Initial program 92.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.5%

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

   if 1 < z

   1. Initial program 95.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.4%

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

      1. *-commutative 88.4%

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

      2. associate-/l* 89.3%

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

      3. cancel-sign-sub-inv 89.3%

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

      4. metadata-eval 89.3%

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

      5. *-lft-identity 89.3%

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

      6. +-commutative 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(y + t\right)}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.5% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. *-commutative 53.6%

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

      3. associate-/l* 57.8%

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

      4. distribute-rgt-neg-out 57.8%

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

      5. distribute-neg-frac2 57.8%

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

      6. neg-sub0 57.8%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 57.8%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate-/l* 49.3%

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

   8. Simplified 49.3%

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

   if -1 < z < 1

   1. Initial program 92.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 33.5%

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

      1. mul-1-neg 33.5%

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

      2. *-commutative 33.5%

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

      3. associate-/l* 33.5%

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

      4. distribute-rgt-neg-out 33.5%

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

      5. distribute-neg-frac2 33.5%

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

      6. neg-sub0 33.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 33.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in z around 0 32.4%

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

      1. neg-mul-1 32.4%

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

   8. Simplified 32.4%

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

4. Final simplification 40.7%

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

Alternative 11: 44.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* x (/ t z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * (t / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 96.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. *-commutative 53.6%

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

      3. associate-/l* 57.8%

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

      4. distribute-rgt-neg-out 57.8%

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

      5. distribute-neg-frac2 57.8%

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

      6. neg-sub0 57.8%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 57.8%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in z around inf 57.0%

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

   if -1 < z < 1

   1. Initial program 92.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 33.5%

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

      1. mul-1-neg 33.5%

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

      2. *-commutative 33.5%

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

      3. associate-/l* 33.5%

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

      4. distribute-rgt-neg-out 33.5%

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

      5. distribute-neg-frac2 33.5%

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

      6. neg-sub0 33.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 33.5%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in z around 0 32.4%

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

      1. neg-mul-1 32.4%

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

   8. Simplified 32.4%

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

4. Final simplification 44.5%

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

Alternative 12: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+89} \lor \neg \left(t \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.2e+89) (not (<= t 1.5e+28))) (* x (/ t z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.2e+89) || !(t <= 1.5e+28)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-7.2d+89)) .or. (.not. (t <= 1.5d+28))) then
        tmp = x * (t / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.2e+89) || !(t <= 1.5e+28)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.2e+89) or not (t <= 1.5e+28):
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.2e+89) || !(t <= 1.5e+28))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.2e+89) || ~((t <= 1.5e+28)))
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.2e+89], N[Not[LessEqual[t, 1.5e+28]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2e89 or 1.5e28 < t

   1. Initial program 94.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-/l* 71.1%

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

      4. distribute-rgt-neg-out 71.1%

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

      5. distribute-neg-frac2 71.1%

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

      6. neg-sub0 71.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      7. associate--r- 71.1%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      8. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around inf 54.7%

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

   if -7.2e89 < t < 1.5e28

   1. Initial program 94.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.6%

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

      1. associate-*r/ 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+89} \lor \neg \left(t \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 23.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 43.4%

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

   1. mul-1-neg 43.4%

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

   2. *-commutative 43.4%

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

   3. associate-/l* 45.5%

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

   4. distribute-rgt-neg-out 45.5%

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

   5. distribute-neg-frac2 45.5%

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

   6. neg-sub0 45.5%

      \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

   7. associate--r- 45.5%

      \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

   8. metadata-eval 45.5%

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

5. Simplified 45.5%

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

6. Taylor expanded in z around 0 21.9%

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

   1. neg-mul-1 21.9%

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

8. Simplified 21.9%

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

9. Final simplification 21.9%

   \[\leadsto x \cdot \left(-t\right) \]
10. Add Preprocessing

Developer target: 95.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))