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

Percentage Accurate: 94.6% → 94.6%

Time: 9.8s

Alternatives: 10

Speedup: 1.0×

• 20.7% 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: 94.6% 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: 94.6% 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 96.8%

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

3. Final simplification 96.8%

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

Alternative 2: 42.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -3.85 \cdot 10^{-221}\right) \land \left(z \leq 2.5 \cdot 10^{-291} \lor \neg \left(z \leq 0.0122\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0)
         (and (not (<= z -3.85e-221))
              (or (<= z 2.5e-291) (not (<= z 0.0122)))))
   (* t (/ x z))
   (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || (!(z <= -3.85e-221) && ((z <= 2.5e-291) || !(z <= 0.0122)))) {
		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 <= (-3.85d-221))) .and. (z <= 2.5d-291) .or. (.not. (z <= 0.0122d0))) 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 <= -3.85e-221) && ((z <= 2.5e-291) || !(z <= 0.0122)))) {
		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 <= -3.85e-221) and ((z <= 2.5e-291) or not (z <= 0.0122))):
		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 <= -3.85e-221) && ((z <= 2.5e-291) || !(z <= 0.0122))))
		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 <= -3.85e-221)) && ((z <= 2.5e-291) || ~((z <= 0.0122)))))
		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], And[N[Not[LessEqual[z, -3.85e-221]], $MachinePrecision], Or[LessEqual[z, 2.5e-291], N[Not[LessEqual[z, 0.0122]], $MachinePrecision]]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or -3.84999999999999996e-221 < z < 2.5000000000000002e-291 or 0.0122000000000000008 < z

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-neg-frac2 49.2%

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

      3. neg-sub0 49.2%

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

      4. associate--r- 49.2%

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

      5. metadata-eval 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in z around inf 46.3%

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

      1. associate-/l* 50.8%

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

   8. Simplified 50.8%

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

   if -1 < z < -3.84999999999999996e-221 or 2.5000000000000002e-291 < z < 0.0122000000000000008

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. distribute-neg-frac2 40.9%

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

      3. neg-sub0 40.9%

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

      4. associate--r- 40.9%

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

      5. metadata-eval 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in z around 0 38.3%

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

      1. *-commutative 38.3%

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

      2. neg-mul-1 38.3%

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

      3. distribute-rgt-neg-in 38.3%

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

   8. Simplified 38.3%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -3.85 \cdot 10^{-221}\right) \land \left(z \leq 2.5 \cdot 10^{-291} \lor \neg \left(z \leq 0.0122\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 43.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ t_2 := x \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0122:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))) (t_2 (* x (- t))))
   (if (<= z -1.0)
     t_1
     (if (<= z -1.25e-220)
       t_2
       (if (<= z 2.7e-291) t_1 (if (<= z 0.0122) t_2 (* x (/ t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double t_2 = x * -t;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -1.25e-220) {
		tmp = t_2;
	} else if (z <= 2.7e-291) {
		tmp = t_1;
	} else if (z <= 0.0122) {
		tmp = t_2;
	} else {
		tmp = x * (t / 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) :: t_2
    real(8) :: tmp
    t_1 = t * (x / z)
    t_2 = x * -t
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= (-1.25d-220)) then
        tmp = t_2
    else if (z <= 2.7d-291) then
        tmp = t_1
    else if (z <= 0.0122d0) then
        tmp = t_2
    else
        tmp = x * (t / 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);
	double t_2 = x * -t;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -1.25e-220) {
		tmp = t_2;
	} else if (z <= 2.7e-291) {
		tmp = t_1;
	} else if (z <= 0.0122) {
		tmp = t_2;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	t_2 = x * -t
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= -1.25e-220:
		tmp = t_2
	elif z <= 2.7e-291:
		tmp = t_1
	elif z <= 0.0122:
		tmp = t_2
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	t_2 = Float64(x * Float64(-t))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -1.25e-220)
		tmp = t_2;
	elseif (z <= 2.7e-291)
		tmp = t_1;
	elseif (z <= 0.0122)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	t_2 = x * -t;
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -1.25e-220)
		tmp = t_2;
	elseif (z <= 2.7e-291)
		tmp = t_1;
	elseif (z <= 0.0122)
		tmp = t_2;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-t)), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, -1.25e-220], t$95$2, If[LessEqual[z, 2.7e-291], t$95$1, If[LessEqual[z, 0.0122], t$95$2, N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or -1.25e-220 < z < 2.69999999999999992e-291

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. distribute-neg-frac2 45.2%

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

      3. neg-sub0 45.2%

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

      4. associate--r- 45.2%

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

      5. metadata-eval 45.2%

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

   5. Simplified 45.2%

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

   6. Taylor expanded in z around inf 46.2%

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

      1. associate-/l* 52.0%

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

   8. Simplified 52.0%

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

   if -1 < z < -1.25e-220 or 2.69999999999999992e-291 < z < 0.0122000000000000008

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. distribute-neg-frac2 40.9%

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

      3. neg-sub0 40.9%

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

      4. associate--r- 40.9%

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

      5. metadata-eval 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in z around 0 38.3%

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

      1. *-commutative 38.3%

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

      2. neg-mul-1 38.3%

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

      3. distribute-rgt-neg-in 38.3%

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

   8. Simplified 38.3%

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

   if 0.0122000000000000008 < z

   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 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. distribute-neg-frac2 54.8%

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

      3. neg-sub0 54.8%

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

      4. associate--r- 54.8%

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

      5. metadata-eval 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in z around inf 46.4%

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

      1. *-commutative 46.4%

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

      2. *-lft-identity 46.4%

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

      3. times-frac 53.7%

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

      4. /-rgt-identity 53.7%

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

   8. Simplified 53.7%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.0122:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 0.0122:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= z -5.5e+163)
     t_1
     (if (<= z -3.6e+51)
       (* x (/ t z))
       (if (<= z 0.0122) (* x (- (/ y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -5.5e+163) {
		tmp = t_1;
	} else if (z <= -3.6e+51) {
		tmp = x * (t / z);
	} else if (z <= 0.0122) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (z <= (-5.5d+163)) then
        tmp = t_1
    else if (z <= (-3.6d+51)) then
        tmp = x * (t / z)
    else if (z <= 0.0122d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -5.5e+163) {
		tmp = t_1;
	} else if (z <= -3.6e+51) {
		tmp = x * (t / z);
	} else if (z <= 0.0122) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	tmp = 0
	if z <= -5.5e+163:
		tmp = t_1
	elif z <= -3.6e+51:
		tmp = x * (t / z)
	elif z <= 0.0122:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -5.5e+163)
		tmp = t_1;
	elseif (z <= -3.6e+51)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= 0.0122)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -5.5e+163)
		tmp = t_1;
	elseif (z <= -3.6e+51)
		tmp = x * (t / z);
	elseif (z <= 0.0122)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+163], t$95$1, If[LessEqual[z, -3.6e+51], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0122], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000014e163 or 0.0122000000000000008 < z

   1. Initial program 97.7%

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

   3. Taylor expanded in y around inf 61.8%

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

      1. associate-*r/ 68.6%

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

   5. Simplified 68.6%

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

   if -5.50000000000000014e163 < z < -3.60000000000000011e51

   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 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-neg-frac2 73.4%

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

      3. neg-sub0 73.4%

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

      4. associate--r- 73.4%

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

      5. metadata-eval 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. *-lft-identity 65.1%

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

      3. times-frac 73.4%

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

      4. /-rgt-identity 73.4%

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

   8. Simplified 73.4%

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

   if -3.60000000000000011e51 < z < 0.0122000000000000008

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 91.9%

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

      1. mul-1-neg 91.9%

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

      2. unsub-neg 91.9%

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

      3. div-sub 91.9%

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

      4. associate-/l* 91.9%

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

      5. *-inverses 91.9%

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

      6. *-rgt-identity 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 0.0122:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+92} \lor \neg \left(t \leq 2.7 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9e+92) (not (<= t 2.7e+71)))
   (* t (/ x (+ z -1.0)))
   (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+92) || !(t <= 2.7e+71)) {
		tmp = t * (x / (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 <= (-9d+92)) .or. (.not. (t <= 2.7d+71))) then
        tmp = t * (x / (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 <= -9e+92) || !(t <= 2.7e+71)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9e+92) or not (t <= 2.7e+71):
		tmp = t * (x / (z + -1.0))
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9e+92) || !(t <= 2.7e+71))
		tmp = Float64(t * Float64(x / 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 <= -9e+92) || ~((t <= 2.7e+71)))
		tmp = t * (x / (z + -1.0));
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9e+92], N[Not[LessEqual[t, 2.7e+71]], $MachinePrecision]], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.9999999999999998e92 or 2.69999999999999997e71 < t

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. associate-/l* 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

      4. distribute-neg-frac2 73.0%

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

      5. neg-sub0 73.0%

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

      6. associate--r- 73.0%

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

      7. metadata-eval 73.0%

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

   5. Simplified 73.0%

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

   if -8.9999999999999998e92 < t < 2.69999999999999997e71

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. associate-*r/ 79.3%

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

   5. Simplified 79.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+92} \lor \neg \left(t \leq 2.7 \cdot 10^{+71}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0122\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.0122)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.0122)) {
		tmp = x * ((y + t) / 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 <= (-1.0d0)) .or. (.not. (z <= 0.0122d0))) then
        tmp = x * ((y + t) / 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 <= -1.0) || !(z <= 0.0122)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.0122):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.0122))
		tmp = Float64(x * Float64(Float64(y + t) / 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 <= -1.0) || ~((z <= 0.0122)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.0122]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.0122000000000000008 < z

   1. Initial program 98.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. remove-double-neg 86.1%

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

      3. cancel-sign-sub-inv 86.1%

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

      4. metadata-eval 86.1%

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

      5. *-lft-identity 86.1%

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

      6. distribute-neg-out 86.1%

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

      7. neg-mul-1 86.1%

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

      8. sub-neg 86.1%

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

      9. distribute-lft-neg-in 86.1%

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

      10. *-commutative 86.1%

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

      11. distribute-neg-frac 86.1%

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

      12. associate-/l* 97.2%

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

      13. distribute-rgt-neg-in 97.2%

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

      14. distribute-neg-frac 97.2%

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

   5. Simplified 97.2%

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

   if -1 < z < 0.0122000000000000008

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

      3. div-sub 93.4%

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

      4. associate-/l* 93.4%

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

      5. *-inverses 93.4%

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

      6. *-rgt-identity 93.4%

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

   5. Simplified 93.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0122\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 0.0122:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* x (+ (/ y z) (/ t z)))
   (if (<= z 0.0122) (* x (- (/ y z) t)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 0.0122) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / 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 <= (-1.0d0)) then
        tmp = x * ((y / z) + (t / z))
    else if (z <= 0.0122d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 0.0122) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * ((y / z) + (t / z))
	elif z <= 0.0122:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	elseif (z <= 0.0122)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * ((y / z) + (t / z));
	elseif (z <= 0.0122)
		tmp = x * ((y / z) - t);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0122], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 96.0%

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

      1. associate-*r/ 96.0%

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

      2. neg-mul-1 96.0%

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

   5. Simplified 96.0%

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

      1. sub-neg 96.0%

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

      2. distribute-frac-neg 96.0%

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

      3. remove-double-neg 96.0%

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

   7. Applied egg-rr 96.0%

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

   if -1 < z < 0.0122000000000000008

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

      3. div-sub 93.4%

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

      4. associate-/l* 93.4%

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

      5. *-inverses 93.4%

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

      6. *-rgt-identity 93.4%

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

   5. Simplified 93.4%

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

   if 0.0122000000000000008 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 86.8%

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

      1. *-commutative 86.8%

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

      2. remove-double-neg 86.8%

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

      3. cancel-sign-sub-inv 86.8%

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

      4. metadata-eval 86.8%

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

      5. *-lft-identity 86.8%

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

      6. distribute-neg-out 86.8%

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

      7. neg-mul-1 86.8%

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

      8. sub-neg 86.8%

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

      9. distribute-lft-neg-in 86.8%

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

      10. *-commutative 86.8%

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

      11. distribute-neg-frac 86.8%

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

      12. associate-/l* 98.4%

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

      13. distribute-rgt-neg-in 98.4%

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

      14. distribute-neg-frac 98.4%

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

   5. Simplified 98.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 0.0122:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+96} \lor \neg \left(t \leq 2.4 \cdot 10^{+159}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e+96) (not (<= t 2.4e+159))) (* x (/ t z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e+96) || !(t <= 2.4e+159)) {
		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 <= (-1.65d+96)) .or. (.not. (t <= 2.4d+159))) 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 <= -1.65e+96) || !(t <= 2.4e+159)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e+96) or not (t <= 2.4e+159):
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e+96) || !(t <= 2.4e+159))
		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 <= -1.65e+96) || ~((t <= 2.4e+159)))
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e+96], N[Not[LessEqual[t, 2.4e+159]], $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 < -1.64999999999999992e96 or 2.4e159 < t

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-neg-frac2 83.1%

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

      3. neg-sub0 83.1%

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

      4. associate--r- 83.1%

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

      5. metadata-eval 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in z around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. *-lft-identity 48.9%

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

      3. times-frac 58.7%

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

      4. /-rgt-identity 58.7%

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

   8. Simplified 58.7%

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

   if -1.64999999999999992e96 < t < 2.4e159

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. associate-*r/ 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+96} \lor \neg \left(t \leq 2.4 \cdot 10^{+159}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e+92)
   (/ x (/ z t))
   (if (<= t 3.25e+156) (* x (/ y z)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e+92) {
		tmp = x / (z / t);
	} else if (t <= 3.25e+156) {
		tmp = x * (y / z);
	} else {
		tmp = x * (t / 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 <= (-4d+92)) then
        tmp = x / (z / t)
    else if (t <= 3.25d+156) then
        tmp = x * (y / z)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e+92) {
		tmp = x / (z / t);
	} else if (t <= 3.25e+156) {
		tmp = x * (y / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4e+92:
		tmp = x / (z / t)
	elif t <= 3.25e+156:
		tmp = x * (y / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e+92)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 3.25e+156)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4e+92)
		tmp = x / (z / t);
	elseif (t <= 3.25e+156)
		tmp = x * (y / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4e+92], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.25e+156], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000002e92

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. distribute-neg-frac2 81.1%

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

      3. neg-sub0 81.1%

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

      4. associate--r- 81.1%

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

      5. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in z around inf 46.1%

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

      1. *-commutative 46.1%

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

      2. *-lft-identity 46.1%

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

      3. times-frac 54.8%

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

      4. /-rgt-identity 54.8%

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

   8. Simplified 54.8%

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

      1. associate-*r/ 46.1%

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

      2. clear-num 46.0%

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

   10. Applied egg-rr 46.0%

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

       1. associate-/r/ 46.1%

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

       2. associate-*r* 47.1%

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

       3. associate-*l/ 47.1%

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

       4. *-lft-identity 47.1%

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

       5. associate-/r/ 54.9%

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

   12. Simplified 54.9%

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

   if -4.0000000000000002e92 < t < 3.25000000000000014e156

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. associate-*r/ 77.7%

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

   5. Simplified 77.7%

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

   if 3.25000000000000014e156 < t

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 86.8%

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

      1. mul-1-neg 86.8%

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

      2. distribute-neg-frac2 86.8%

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

      3. neg-sub0 86.8%

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

      4. associate--r- 86.8%

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

      5. metadata-eval 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. *-lft-identity 54.0%

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

      3. times-frac 65.8%

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

      4. /-rgt-identity 65.8%

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

   8. Simplified 65.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 22.7% 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 96.8%

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

3. Taylor expanded in y around 0 45.8%

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

   1. mul-1-neg 45.8%

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

   2. distribute-neg-frac2 45.8%

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

   3. neg-sub0 45.8%

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

   4. associate--r- 45.8%

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

   5. metadata-eval 45.8%

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

5. Simplified 45.8%

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

6. Taylor expanded in z around 0 22.5%

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

   1. *-commutative 22.5%

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

   2. neg-mul-1 22.5%

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

   3. distribute-rgt-neg-in 22.5%

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

8. Simplified 22.5%

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

9. Final simplification 22.5%

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

Developer target: 94.9% 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 2024112 
(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)))))