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

Percentage Accurate: 94.3% → 94.3%

Time: 8.3s

Alternatives: 10

Speedup: 1.0×

• 21.2% 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: 94.3% 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: 94.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. clear-num 94.6%

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

   2. associate-/r/ 94.7%

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

3. Applied egg-rr 94.7%

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

4. Final simplification 94.7%

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

Alternative 2: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= z -8.2e+74)
     t_1
     (if (<= z 7.5e+41)
       (* x (- (/ y z) t))
       (if (<= z 1.1e+116)
         (/ x (/ z t))
         (if (<= z 3.2e+149)
           t_1
           (if (<= z 7.6e+156) (* t (/ x z)) (/ x (/ z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -8.2e+74) {
		tmp = t_1;
	} else if (z <= 7.5e+41) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.1e+116) {
		tmp = x / (z / t);
	} else if (z <= 3.2e+149) {
		tmp = t_1;
	} else if (z <= 7.6e+156) {
		tmp = t * (x / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (z <= (-8.2d+74)) then
        tmp = t_1
    else if (z <= 7.5d+41) then
        tmp = x * ((y / z) - t)
    else if (z <= 1.1d+116) then
        tmp = x / (z / t)
    else if (z <= 3.2d+149) then
        tmp = t_1
    else if (z <= 7.6d+156) then
        tmp = t * (x / z)
    else
        tmp = x / (z / y)
    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 <= -8.2e+74) {
		tmp = t_1;
	} else if (z <= 7.5e+41) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.1e+116) {
		tmp = x / (z / t);
	} else if (z <= 3.2e+149) {
		tmp = t_1;
	} else if (z <= 7.6e+156) {
		tmp = t * (x / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	tmp = 0
	if z <= -8.2e+74:
		tmp = t_1
	elif z <= 7.5e+41:
		tmp = x * ((y / z) - t)
	elif z <= 1.1e+116:
		tmp = x / (z / t)
	elif z <= 3.2e+149:
		tmp = t_1
	elif z <= 7.6e+156:
		tmp = t * (x / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -8.2e+74)
		tmp = t_1;
	elseif (z <= 7.5e+41)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 1.1e+116)
		tmp = Float64(x / Float64(z / t));
	elseif (z <= 3.2e+149)
		tmp = t_1;
	elseif (z <= 7.6e+156)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -8.2e+74)
		tmp = t_1;
	elseif (z <= 7.5e+41)
		tmp = x * ((y / z) - t);
	elseif (z <= 1.1e+116)
		tmp = x / (z / t);
	elseif (z <= 3.2e+149)
		tmp = t_1;
	elseif (z <= 7.6e+156)
		tmp = t * (x / z);
	else
		tmp = x / (z / y);
	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, -8.2e+74], t$95$1, If[LessEqual[z, 7.5e+41], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+116], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+149], t$95$1, If[LessEqual[z, 7.6e+156], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.2000000000000001e74 or 1.1e116 < z < 3.2000000000000002e149

   1. Initial program 98.1%

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

   2. Taylor expanded in y around inf 66.1%

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

      1. associate-*r/ 74.9%

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

   4. Simplified 74.9%

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

   if -8.2000000000000001e74 < z < 7.50000000000000072e41

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*r/ 86.5%

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

      3. *-commutative 86.5%

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

      4. associate-*r* 86.5%

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

      5. neg-mul-1 86.5%

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

      6. distribute-rgt-out 88.4%

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

      7. unsub-neg 88.4%

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

   4. Simplified 88.4%

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

   if 7.50000000000000072e41 < z < 1.1e116

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 65.0%

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

      1. associate-*r/ 65.0%

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

      2. mul-1-neg 65.0%

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

      3. *-commutative 65.0%

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

      4. distribute-rgt-neg-in 65.0%

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

      5. associate-*r/ 65.1%

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

      6. neg-mul-1 65.1%

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

      7. *-commutative 65.1%

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

      8. associate-*r/ 65.1%

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

      9. metadata-eval 65.1%

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

      10. associate-/r* 65.1%

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

      11. neg-mul-1 65.1%

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

      12. associate-*r/ 65.1%

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

      13. *-rgt-identity 65.1%

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

      14. neg-sub0 65.1%

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

      15. associate--r- 65.1%

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

      16. metadata-eval 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. *-commutative 65.0%

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

      2. associate-/l* 65.1%

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

   7. Simplified 65.1%

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

   if 3.2000000000000002e149 < z < 7.60000000000000048e156

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 99.2%

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

      1. associate-*r/ 99.2%

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

      2. mul-1-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. associate-*r/ 99.2%

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

      6. neg-mul-1 99.2%

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

      7. *-commutative 99.2%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate-/r* 100.0%

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

      11. neg-mul-1 100.0%

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

      12. associate-*r/ 99.2%

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

      13. *-rgt-identity 99.2%

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

      14. neg-sub0 99.2%

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

      15. associate--r- 99.2%

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

      16. metadata-eval 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in z around inf 99.2%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   if 7.60000000000000048e156 < z

   1. Initial program 86.8%

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

   2. Taylor expanded in y around inf 57.8%

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

      1. associate-*r/ 67.4%

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

   4. Simplified 67.4%

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

      1. associate-*r/ 57.8%

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

      2. associate-/l* 67.6%

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

   6. Applied egg-rr 67.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 3: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52000000 \lor \neg \left(z \leq 0.021\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + t \cdot \left(-1 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -52000000.0) (not (<= z 0.021)))
   (/ x (/ z (+ y t)))
   (* x (+ (/ y z) (* t (- -1.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -52000000.0) || !(z <= 0.021)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) + (t * (-1.0 - 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 <= (-52000000.0d0)) .or. (.not. (z <= 0.021d0))) then
        tmp = x / (z / (y + t))
    else
        tmp = x * ((y / z) + (t * ((-1.0d0) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -52000000.0) || !(z <= 0.021)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) + (t * (-1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -52000000.0) or not (z <= 0.021):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) + (t * (-1.0 - z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -52000000.0) || !(z <= 0.021))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	else
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t * Float64(-1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -52000000.0) || ~((z <= 0.021)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) + (t * (-1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -52000000.0], N[Not[LessEqual[z, 0.021]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t * N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e7 or 0.0210000000000000013 < z

   1. Initial program 96.0%

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

   2. Taylor expanded in z around inf 87.9%

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

      1. associate-/l* 95.5%

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

      2. cancel-sign-sub-inv 95.5%

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

      3. metadata-eval 95.5%

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

      4. *-lft-identity 95.5%

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

      5. +-commutative 95.5%

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

   4. Simplified 95.5%

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

   if -5.2e7 < z < 0.0210000000000000013

   1. Initial program 93.3%

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

      1. clear-num 93.3%

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

      2. associate-/r/ 93.3%

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

   3. Applied egg-rr 93.3%

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

   4. Taylor expanded in z around 0 93.1%

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

      1. +-commutative 93.1%

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

   6. Simplified 93.1%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52000000 \lor \neg \left(z \leq 0.021\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + t \cdot \left(-1 - z\right)\right)\\ \end{array} \]

Alternative 4: 42.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-6} \lor \neg \left(z \leq -9 \cdot 10^{-260} \lor \neg \left(z \leq 2.3 \cdot 10^{-300}\right) \land z \leq 0.021\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-6)
         (not (or (<= z -9e-260) (and (not (<= z 2.3e-300)) (<= z 0.021)))))
   (* t (/ x z))
   (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-6) || !((z <= -9e-260) || (!(z <= 2.3e-300) && (z <= 0.021)))) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-6)) .or. (.not. (z <= (-9d-260)) .or. (.not. (z <= 2.3d-300)) .and. (z <= 0.021d0))) then
        tmp = t * (x / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-6) || !((z <= -9e-260) || (!(z <= 2.3e-300) && (z <= 0.021)))) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-6) or not ((z <= -9e-260) or (not (z <= 2.3e-300) and (z <= 0.021))):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-6) || !((z <= -9e-260) || (!(z <= 2.3e-300) && (z <= 0.021))))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-6) || ~(((z <= -9e-260) || (~((z <= 2.3e-300)) && (z <= 0.021)))))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-6], N[Not[Or[LessEqual[z, -9e-260], And[N[Not[LessEqual[z, 2.3e-300]], $MachinePrecision], LessEqual[z, 0.021]]]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5999999999999999e-6 or -8.9999999999999995e-260 < z < 2.30000000000000001e-300 or 0.0210000000000000013 < z

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 40.1%

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

      1. associate-*r/ 40.1%

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

      2. mul-1-neg 40.1%

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

      3. *-commutative 40.1%

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

      4. distribute-rgt-neg-in 40.1%

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

      5. associate-*r/ 41.5%

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

      6. neg-mul-1 41.5%

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

      7. *-commutative 41.5%

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

      8. associate-*r/ 41.5%

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

      9. metadata-eval 41.5%

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

      10. associate-/r* 41.5%

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

      11. neg-mul-1 41.5%

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

      12. associate-*r/ 41.5%

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

      13. *-rgt-identity 41.5%

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

      14. neg-sub0 41.5%

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

      15. associate--r- 41.5%

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

      16. metadata-eval 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in z around inf 42.3%

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

      1. associate-*r/ 45.1%

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

   7. Simplified 45.1%

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

   if -1.5999999999999999e-6 < z < -8.9999999999999995e-260 or 2.30000000000000001e-300 < z < 0.0210000000000000013

   1. Initial program 92.0%

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

   2. Taylor expanded in y around 0 37.5%

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

      1. associate-*r/ 37.5%

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

      2. mul-1-neg 37.5%

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

      3. *-commutative 37.5%

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

      4. distribute-rgt-neg-in 37.5%

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

      5. associate-*r/ 37.5%

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

      6. neg-mul-1 37.5%

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

      7. *-commutative 37.5%

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

      8. associate-*r/ 37.5%

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

      9. metadata-eval 37.5%

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

      10. associate-/r* 37.5%

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

      11. neg-mul-1 37.5%

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

      12. associate-*r/ 37.5%

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

      13. *-rgt-identity 37.5%

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

      14. neg-sub0 37.5%

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

      15. associate--r- 37.5%

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

      16. metadata-eval 37.5%

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

   4. Simplified 37.5%

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

   5. Taylor expanded in z around 0 36.6%

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

      1. associate-*r* 36.6%

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

      2. *-commutative 36.6%

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

      3. neg-mul-1 36.6%

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

   7. Simplified 36.6%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-6} \lor \neg \left(z \leq -9 \cdot 10^{-260} \lor \neg \left(z \leq 2.3 \cdot 10^{-300}\right) \land z \leq 0.021\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+15} \lor \neg \left(z \leq 1.15\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.1e+15) (not (<= z 1.15)))
   (* (+ y t) (/ x z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.1e+15) || !(z <= 1.15)) {
		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 <= (-7.1d+15)) .or. (.not. (z <= 1.15d0))) 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 <= -7.1e+15) || !(z <= 1.15)) {
		tmp = (y + t) * (x / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.1e+15) or not (z <= 1.15):
		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 <= -7.1e+15) || !(z <= 1.15))
		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 <= -7.1e+15) || ~((z <= 1.15)))
		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, -7.1e+15], N[Not[LessEqual[z, 1.15]], $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 < -7.1e15 or 1.1499999999999999 < z

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 87.6%

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

      1. associate-/l* 95.4%

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

      2. associate-/r/ 88.8%

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

      3. cancel-sign-sub-inv 88.8%

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

      4. metadata-eval 88.8%

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

      5. *-lft-identity 88.8%

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

      6. +-commutative 88.8%

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

   4. Simplified 88.8%

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

   if -7.1e15 < z < 1.1499999999999999

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-*r/ 91.2%

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

      3. *-commutative 91.2%

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

      4. associate-*r* 91.2%

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

      5. neg-mul-1 91.2%

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

      6. distribute-rgt-out 92.7%

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

      7. unsub-neg 92.7%

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

   4. Simplified 92.7%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+15} \lor \neg \left(z \leq 1.15\right):\\ \;\;\;\;\left(y + t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 6: 93.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+15} \lor \neg \left(z \leq 0.021\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.1e+15) (not (<= z 0.021)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.1e+15) || !(z <= 0.021)) {
		tmp = x / (z / (y + t));
	} 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 <= (-7.1d+15)) .or. (.not. (z <= 0.021d0))) then
        tmp = x / (z / (y + t))
    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 <= -7.1e+15) || !(z <= 0.021)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.1e+15) or not (z <= 0.021):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.1e+15) || !(z <= 0.021))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	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 <= -7.1e+15) || ~((z <= 0.021)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.1e+15], N[Not[LessEqual[z, 0.021]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1e15 or 0.0210000000000000013 < z

   1. Initial program 96.0%

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

   2. Taylor expanded in z around inf 87.8%

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

      1. associate-/l* 95.4%

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

      2. cancel-sign-sub-inv 95.4%

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

      3. metadata-eval 95.4%

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

      4. *-lft-identity 95.4%

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

      5. +-commutative 95.4%

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

   4. Simplified 95.4%

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

   if -7.1e15 < z < 0.0210000000000000013

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-*r/ 91.1%

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

      3. *-commutative 91.1%

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

      4. associate-*r* 91.1%

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

      5. neg-mul-1 91.1%

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

      6. distribute-rgt-out 92.6%

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

      7. unsub-neg 92.6%

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

   4. Simplified 92.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+15} \lor \neg \left(z \leq 0.021\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 7: 94.3% 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]

Derivation

1. Initial program 94.6%

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

2. Final simplification 94.6%

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

Alternative 8: 63.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8e+161) (* t (/ x z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e+161) {
		tmp = t * (x / 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 <= (-8d+161)) then
        tmp = t * (x / 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 <= -8e+161) {
		tmp = t * (x / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8e+161:
		tmp = t * (x / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8e+161)
		tmp = Float64(t * Float64(x / 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 <= -8e+161)
		tmp = t * (x / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8e+161], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.0000000000000003e161

   1. Initial program 87.0%

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

   2. Taylor expanded in y around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. mul-1-neg 57.7%

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

      3. *-commutative 57.7%

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

      4. distribute-rgt-neg-in 57.7%

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

      5. associate-*r/ 67.2%

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

      6. neg-mul-1 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-*r/ 67.1%

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

      9. metadata-eval 67.1%

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

      10. associate-/r* 67.1%

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

      11. neg-mul-1 67.1%

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

      12. associate-*r/ 67.2%

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

      13. *-rgt-identity 67.2%

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

      14. neg-sub0 67.2%

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

      15. associate--r- 67.2%

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

      16. metadata-eval 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in z around inf 47.2%

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

      1. associate-*r/ 50.1%

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

   7. Simplified 50.1%

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

   if -8.0000000000000003e161 < t

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 71.3%

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

   4. Simplified 71.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9: 63.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.75e+48) (/ x (/ z t)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.75e+48) {
		tmp = x / (z / t);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.75d+48)) then
        tmp = x / (z / t)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.75e+48) {
		tmp = x / (z / t);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.75e+48:
		tmp = x / (z / t)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.75e+48)
		tmp = Float64(x / Float64(z / t));
	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 <= -2.75e+48)
		tmp = x / (z / t);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.75e+48], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7500000000000001e48

   1. Initial program 92.0%

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

   2. Taylor expanded in y around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. mul-1-neg 58.4%

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

      3. *-commutative 58.4%

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

      4. distribute-rgt-neg-in 58.4%

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

      5. associate-*r/ 64.1%

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

      6. neg-mul-1 64.1%

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

      7. *-commutative 64.1%

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

      8. associate-*r/ 64.1%

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

      9. metadata-eval 64.1%

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

      10. associate-/r* 64.1%

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

      11. neg-mul-1 64.1%

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

      12. associate-*r/ 64.1%

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

      13. *-rgt-identity 64.1%

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

      14. neg-sub0 64.1%

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

      15. associate--r- 64.1%

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

      16. metadata-eval 64.1%

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

   4. Simplified 64.1%

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

   5. Taylor expanded in z around inf 46.2%

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

      1. *-commutative 46.2%

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

      2. associate-/l* 52.0%

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

   7. Simplified 52.0%

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

   if -2.7500000000000001e48 < t

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 69.7%

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

      1. associate-*r/ 73.7%

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

   4. Simplified 73.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 10: 22.8% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

2. Taylor expanded in y around 0 39.0%

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

   1. associate-*r/ 39.0%

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

   2. mul-1-neg 39.0%

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

   3. *-commutative 39.0%

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

   4. distribute-rgt-neg-in 39.0%

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

   5. associate-*r/ 39.8%

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

   6. neg-mul-1 39.8%

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

   7. *-commutative 39.8%

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

   8. associate-*r/ 39.8%

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

   9. metadata-eval 39.8%

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

   10. associate-/r* 39.8%

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

   11. neg-mul-1 39.8%

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

   12. associate-*r/ 39.8%

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

   13. *-rgt-identity 39.8%

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

   14. neg-sub0 39.8%

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

   15. associate--r- 39.8%

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

   16. metadata-eval 39.8%

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

4. Simplified 39.8%

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

5. Taylor expanded in z around 0 22.7%

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

   1. associate-*r* 22.7%

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

   2. *-commutative 22.7%

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

   3. neg-mul-1 22.7%

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

7. Simplified 22.7%

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

8. Final simplification 22.7%

   \[\leadsto t \cdot \left(-x\right) \]

Developer target: 94.8% accurate, 0.3× 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 2023314 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (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)))))