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

Percentage Accurate: 94.9% → 95.8%

Time: 10.4s

Alternatives: 13

Speedup: 0.5×

• 21.3% 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: 94.9% 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: 95.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 10^{+272}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 1e+272) (* t_1 x) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+272) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 1d+272) then
        tmp = t_1 * x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 1e+272) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 1e+272:
		tmp = t_1 * x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 1e+272)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 1e+272)
		tmp = t_1 * x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+272], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 1.0000000000000001e272

   1. Initial program 96.6%

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

   if 1.0000000000000001e272 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 66.6%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. associate-/l* 70.4%

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

      2. associate-/r/ 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+272}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := t \cdot \frac{x}{z}\\ t_3 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 10^{+241}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))) (t_2 (* t (/ x z))) (t_3 (* t (- x))))
   (if (<= t -7e+258)
     t_2
     (if (<= t -3.7e+205)
       t_3
       (if (<= t -2.4e+134)
         t_2
         (if (<= t -2.15e+85)
           t_1
           (if (<= t -1.9e+45)
             t_2
             (if (<= t -2.25e-98)
               t_1
               (if (<= t 3.6e+71)
                 (* (/ y z) x)
                 (if (<= t 1e+241) t_3 t_2))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = t * (x / z);
	double t_3 = t * -x;
	double tmp;
	if (t <= -7e+258) {
		tmp = t_2;
	} else if (t <= -3.7e+205) {
		tmp = t_3;
	} else if (t <= -2.4e+134) {
		tmp = t_2;
	} else if (t <= -2.15e+85) {
		tmp = t_1;
	} else if (t <= -1.9e+45) {
		tmp = t_2;
	} else if (t <= -2.25e-98) {
		tmp = t_1;
	} else if (t <= 3.6e+71) {
		tmp = (y / z) * x;
	} else if (t <= 1e+241) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = y * (x / z)
    t_2 = t * (x / z)
    t_3 = t * -x
    if (t <= (-7d+258)) then
        tmp = t_2
    else if (t <= (-3.7d+205)) then
        tmp = t_3
    else if (t <= (-2.4d+134)) then
        tmp = t_2
    else if (t <= (-2.15d+85)) then
        tmp = t_1
    else if (t <= (-1.9d+45)) then
        tmp = t_2
    else if (t <= (-2.25d-98)) then
        tmp = t_1
    else if (t <= 3.6d+71) then
        tmp = (y / z) * x
    else if (t <= 1d+241) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = t * (x / z);
	double t_3 = t * -x;
	double tmp;
	if (t <= -7e+258) {
		tmp = t_2;
	} else if (t <= -3.7e+205) {
		tmp = t_3;
	} else if (t <= -2.4e+134) {
		tmp = t_2;
	} else if (t <= -2.15e+85) {
		tmp = t_1;
	} else if (t <= -1.9e+45) {
		tmp = t_2;
	} else if (t <= -2.25e-98) {
		tmp = t_1;
	} else if (t <= 3.6e+71) {
		tmp = (y / z) * x;
	} else if (t <= 1e+241) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	t_2 = t * (x / z)
	t_3 = t * -x
	tmp = 0
	if t <= -7e+258:
		tmp = t_2
	elif t <= -3.7e+205:
		tmp = t_3
	elif t <= -2.4e+134:
		tmp = t_2
	elif t <= -2.15e+85:
		tmp = t_1
	elif t <= -1.9e+45:
		tmp = t_2
	elif t <= -2.25e-98:
		tmp = t_1
	elif t <= 3.6e+71:
		tmp = (y / z) * x
	elif t <= 1e+241:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	t_2 = Float64(t * Float64(x / z))
	t_3 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -7e+258)
		tmp = t_2;
	elseif (t <= -3.7e+205)
		tmp = t_3;
	elseif (t <= -2.4e+134)
		tmp = t_2;
	elseif (t <= -2.15e+85)
		tmp = t_1;
	elseif (t <= -1.9e+45)
		tmp = t_2;
	elseif (t <= -2.25e-98)
		tmp = t_1;
	elseif (t <= 3.6e+71)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 1e+241)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	t_2 = t * (x / z);
	t_3 = t * -x;
	tmp = 0.0;
	if (t <= -7e+258)
		tmp = t_2;
	elseif (t <= -3.7e+205)
		tmp = t_3;
	elseif (t <= -2.4e+134)
		tmp = t_2;
	elseif (t <= -2.15e+85)
		tmp = t_1;
	elseif (t <= -1.9e+45)
		tmp = t_2;
	elseif (t <= -2.25e-98)
		tmp = t_1;
	elseif (t <= 3.6e+71)
		tmp = (y / z) * x;
	elseif (t <= 1e+241)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -7e+258], t$95$2, If[LessEqual[t, -3.7e+205], t$95$3, If[LessEqual[t, -2.4e+134], t$95$2, If[LessEqual[t, -2.15e+85], t$95$1, If[LessEqual[t, -1.9e+45], t$95$2, If[LessEqual[t, -2.25e-98], t$95$1, If[LessEqual[t, 3.6e+71], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1e+241], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.0000000000000002e258 or -3.69999999999999981e205 < t < -2.40000000000000005e134 or -2.15e85 < t < -1.9000000000000001e45 or 1.0000000000000001e241 < t

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 69.0%

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

      1. associate-/l* 81.8%

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

      2. cancel-sign-sub-inv 81.8%

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

      3. metadata-eval 81.8%

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

      4. *-lft-identity 81.8%

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

      5. +-commutative 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in t around inf 64.0%

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

      1. associate-*r/ 66.0%

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

   8. Simplified 66.0%

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

   if -7.0000000000000002e258 < t < -3.69999999999999981e205 or 3.6e71 < t < 1.0000000000000001e241

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-*r/ 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*r* 71.8%

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

      5. neg-mul-1 71.8%

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

      6. distribute-rgt-out 71.7%

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

      7. unsub-neg 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in y around 0 54.8%

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

      1. associate-*r* 54.8%

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

      2. mul-1-neg 54.8%

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

   8. Simplified 54.8%

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

   if -2.40000000000000005e134 < t < -2.15e85 or -1.9000000000000001e45 < t < -2.24999999999999998e-98

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 82.1%

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

   5. Simplified 82.1%

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

   if -2.24999999999999998e-98 < t < 3.6e71

   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 inf 83.9%

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

      1. associate-*r/ 89.9%

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

   5. Simplified 89.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+258}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 10^{+241}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := \frac{t}{\frac{z}{x}}\\ t_3 := t \cdot \frac{x}{z}\\ t_4 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+205}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+241}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z)))
        (t_2 (/ t (/ z x)))
        (t_3 (* t (/ x z)))
        (t_4 (* t (- x))))
   (if (<= t -5e+258)
     t_2
     (if (<= t -3.3e+205)
       t_4
       (if (<= t -2.2e+134)
         t_2
         (if (<= t -1.8e+85)
           t_1
           (if (<= t -1.5e+44)
             t_3
             (if (<= t -8.2e-102)
               t_1
               (if (<= t 3.6e+71)
                 (* (/ y z) x)
                 (if (<= t 1.6e+241) t_4 t_3))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = t / (z / x);
	double t_3 = t * (x / z);
	double t_4 = t * -x;
	double tmp;
	if (t <= -5e+258) {
		tmp = t_2;
	} else if (t <= -3.3e+205) {
		tmp = t_4;
	} else if (t <= -2.2e+134) {
		tmp = t_2;
	} else if (t <= -1.8e+85) {
		tmp = t_1;
	} else if (t <= -1.5e+44) {
		tmp = t_3;
	} else if (t <= -8.2e-102) {
		tmp = t_1;
	} else if (t <= 3.6e+71) {
		tmp = (y / z) * x;
	} else if (t <= 1.6e+241) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y * (x / z)
    t_2 = t / (z / x)
    t_3 = t * (x / z)
    t_4 = t * -x
    if (t <= (-5d+258)) then
        tmp = t_2
    else if (t <= (-3.3d+205)) then
        tmp = t_4
    else if (t <= (-2.2d+134)) then
        tmp = t_2
    else if (t <= (-1.8d+85)) then
        tmp = t_1
    else if (t <= (-1.5d+44)) then
        tmp = t_3
    else if (t <= (-8.2d-102)) then
        tmp = t_1
    else if (t <= 3.6d+71) then
        tmp = (y / z) * x
    else if (t <= 1.6d+241) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = t / (z / x);
	double t_3 = t * (x / z);
	double t_4 = t * -x;
	double tmp;
	if (t <= -5e+258) {
		tmp = t_2;
	} else if (t <= -3.3e+205) {
		tmp = t_4;
	} else if (t <= -2.2e+134) {
		tmp = t_2;
	} else if (t <= -1.8e+85) {
		tmp = t_1;
	} else if (t <= -1.5e+44) {
		tmp = t_3;
	} else if (t <= -8.2e-102) {
		tmp = t_1;
	} else if (t <= 3.6e+71) {
		tmp = (y / z) * x;
	} else if (t <= 1.6e+241) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	t_2 = t / (z / x)
	t_3 = t * (x / z)
	t_4 = t * -x
	tmp = 0
	if t <= -5e+258:
		tmp = t_2
	elif t <= -3.3e+205:
		tmp = t_4
	elif t <= -2.2e+134:
		tmp = t_2
	elif t <= -1.8e+85:
		tmp = t_1
	elif t <= -1.5e+44:
		tmp = t_3
	elif t <= -8.2e-102:
		tmp = t_1
	elif t <= 3.6e+71:
		tmp = (y / z) * x
	elif t <= 1.6e+241:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	t_2 = Float64(t / Float64(z / x))
	t_3 = Float64(t * Float64(x / z))
	t_4 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -5e+258)
		tmp = t_2;
	elseif (t <= -3.3e+205)
		tmp = t_4;
	elseif (t <= -2.2e+134)
		tmp = t_2;
	elseif (t <= -1.8e+85)
		tmp = t_1;
	elseif (t <= -1.5e+44)
		tmp = t_3;
	elseif (t <= -8.2e-102)
		tmp = t_1;
	elseif (t <= 3.6e+71)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 1.6e+241)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	t_2 = t / (z / x);
	t_3 = t * (x / z);
	t_4 = t * -x;
	tmp = 0.0;
	if (t <= -5e+258)
		tmp = t_2;
	elseif (t <= -3.3e+205)
		tmp = t_4;
	elseif (t <= -2.2e+134)
		tmp = t_2;
	elseif (t <= -1.8e+85)
		tmp = t_1;
	elseif (t <= -1.5e+44)
		tmp = t_3;
	elseif (t <= -8.2e-102)
		tmp = t_1;
	elseif (t <= 3.6e+71)
		tmp = (y / z) * x;
	elseif (t <= 1.6e+241)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -5e+258], t$95$2, If[LessEqual[t, -3.3e+205], t$95$4, If[LessEqual[t, -2.2e+134], t$95$2, If[LessEqual[t, -1.8e+85], t$95$1, If[LessEqual[t, -1.5e+44], t$95$3, If[LessEqual[t, -8.2e-102], t$95$1, If[LessEqual[t, 3.6e+71], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.6e+241], t$95$4, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5e258 or -3.3000000000000002e205 < t < -2.2e134

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 58.3%

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

      1. associate-/l* 80.7%

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

      2. cancel-sign-sub-inv 80.7%

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

      3. metadata-eval 80.7%

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

      4. *-lft-identity 80.7%

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

      5. +-commutative 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in t around inf 54.0%

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

      1. associate-*r/ 65.4%

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

   8. Simplified 65.4%

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

      1. associate-*r/ 54.0%

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

      2. associate-/l* 65.7%

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

   10. Applied egg-rr 65.7%

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

   if -5e258 < t < -3.3000000000000002e205 or 3.6e71 < t < 1.60000000000000002e241

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-*r/ 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*r* 71.8%

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

      5. neg-mul-1 71.8%

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

      6. distribute-rgt-out 71.7%

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

      7. unsub-neg 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in y around 0 54.8%

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

      1. associate-*r* 54.8%

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

      2. mul-1-neg 54.8%

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

   8. Simplified 54.8%

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

   if -2.2e134 < t < -1.7999999999999999e85 or -1.49999999999999993e44 < t < -8.2000000000000005e-102

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 82.1%

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

   5. Simplified 82.1%

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

   if -1.7999999999999999e85 < t < -1.49999999999999993e44 or 1.60000000000000002e241 < t

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 79.3%

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

      1. associate-/l* 82.9%

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

      2. cancel-sign-sub-inv 82.9%

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

      3. metadata-eval 82.9%

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

      4. *-lft-identity 82.9%

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

      5. +-commutative 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in t around inf 73.7%

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

      1. associate-*r/ 66.6%

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

   8. Simplified 66.6%

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

   if -8.2000000000000005e-102 < t < 3.6e71

   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 inf 83.9%

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

      1. associate-*r/ 89.9%

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

   5. Simplified 89.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+258}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+134}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+241}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot x\\ t_2 := t \cdot \frac{x}{z}\\ t_3 := t \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{+256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+203}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+241}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) x)) (t_2 (* t (/ x z))) (t_3 (* t (- x))))
   (if (<= t -9.8e+256)
     t_2
     (if (<= t -6.8e+203)
       t_3
       (if (<= t -9e+133)
         t_2
         (if (<= t -6.3e+84)
           t_1
           (if (<= t -4.4e+27)
             t_2
             (if (<= t 3.6e+71) t_1 (if (<= t 1.25e+241) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * x;
	double t_2 = t * (x / z);
	double t_3 = t * -x;
	double tmp;
	if (t <= -9.8e+256) {
		tmp = t_2;
	} else if (t <= -6.8e+203) {
		tmp = t_3;
	} else if (t <= -9e+133) {
		tmp = t_2;
	} else if (t <= -6.3e+84) {
		tmp = t_1;
	} else if (t <= -4.4e+27) {
		tmp = t_2;
	} else if (t <= 3.6e+71) {
		tmp = t_1;
	} else if (t <= 1.25e+241) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (y / z) * x
    t_2 = t * (x / z)
    t_3 = t * -x
    if (t <= (-9.8d+256)) then
        tmp = t_2
    else if (t <= (-6.8d+203)) then
        tmp = t_3
    else if (t <= (-9d+133)) then
        tmp = t_2
    else if (t <= (-6.3d+84)) then
        tmp = t_1
    else if (t <= (-4.4d+27)) then
        tmp = t_2
    else if (t <= 3.6d+71) then
        tmp = t_1
    else if (t <= 1.25d+241) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * x;
	double t_2 = t * (x / z);
	double t_3 = t * -x;
	double tmp;
	if (t <= -9.8e+256) {
		tmp = t_2;
	} else if (t <= -6.8e+203) {
		tmp = t_3;
	} else if (t <= -9e+133) {
		tmp = t_2;
	} else if (t <= -6.3e+84) {
		tmp = t_1;
	} else if (t <= -4.4e+27) {
		tmp = t_2;
	} else if (t <= 3.6e+71) {
		tmp = t_1;
	} else if (t <= 1.25e+241) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * x
	t_2 = t * (x / z)
	t_3 = t * -x
	tmp = 0
	if t <= -9.8e+256:
		tmp = t_2
	elif t <= -6.8e+203:
		tmp = t_3
	elif t <= -9e+133:
		tmp = t_2
	elif t <= -6.3e+84:
		tmp = t_1
	elif t <= -4.4e+27:
		tmp = t_2
	elif t <= 3.6e+71:
		tmp = t_1
	elif t <= 1.25e+241:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * x)
	t_2 = Float64(t * Float64(x / z))
	t_3 = Float64(t * Float64(-x))
	tmp = 0.0
	if (t <= -9.8e+256)
		tmp = t_2;
	elseif (t <= -6.8e+203)
		tmp = t_3;
	elseif (t <= -9e+133)
		tmp = t_2;
	elseif (t <= -6.3e+84)
		tmp = t_1;
	elseif (t <= -4.4e+27)
		tmp = t_2;
	elseif (t <= 3.6e+71)
		tmp = t_1;
	elseif (t <= 1.25e+241)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * x;
	t_2 = t * (x / z);
	t_3 = t * -x;
	tmp = 0.0;
	if (t <= -9.8e+256)
		tmp = t_2;
	elseif (t <= -6.8e+203)
		tmp = t_3;
	elseif (t <= -9e+133)
		tmp = t_2;
	elseif (t <= -6.3e+84)
		tmp = t_1;
	elseif (t <= -4.4e+27)
		tmp = t_2;
	elseif (t <= 3.6e+71)
		tmp = t_1;
	elseif (t <= 1.25e+241)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[t, -9.8e+256], t$95$2, If[LessEqual[t, -6.8e+203], t$95$3, If[LessEqual[t, -9e+133], t$95$2, If[LessEqual[t, -6.3e+84], t$95$1, If[LessEqual[t, -4.4e+27], t$95$2, If[LessEqual[t, 3.6e+71], t$95$1, If[LessEqual[t, 1.25e+241], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.8000000000000004e256 or -6.8000000000000002e203 < t < -8.9999999999999997e133 or -6.30000000000000013e84 < t < -4.3999999999999997e27 or 1.25000000000000006e241 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 69.6%

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

      1. associate-/l* 82.2%

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

      2. cancel-sign-sub-inv 82.2%

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

      3. metadata-eval 82.2%

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

      4. *-lft-identity 82.2%

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

      5. +-commutative 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in t around inf 64.7%

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

      1. associate-*r/ 66.7%

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

   8. Simplified 66.7%

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

   if -9.8000000000000004e256 < t < -6.8000000000000002e203 or 3.6e71 < t < 1.25000000000000006e241

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-*r/ 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-*r* 71.8%

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

      5. neg-mul-1 71.8%

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

      6. distribute-rgt-out 71.7%

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

      7. unsub-neg 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in y around 0 54.8%

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

      1. associate-*r* 54.8%

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

      2. mul-1-neg 54.8%

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

   8. Simplified 54.8%

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

   if -8.9999999999999997e133 < t < -6.30000000000000013e84 or -4.3999999999999997e27 < t < 3.6e71

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 83.1%

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

      1. associate-*r/ 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+256}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+133}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+241}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ t_2 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{+244}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))) (t_2 (/ x (/ z t))))
   (if (<= t -2.65e+244)
     t_2
     (if (<= t -1.16e+206)
       (* t (- x))
       (if (<= t -2.3e+133)
         t_2
         (if (<= t -6.1e+85)
           t_1
           (if (<= t -1.9e+45)
             (* t (/ x z))
             (if (<= t -5.5e-103)
               t_1
               (if (<= t 3.4e+71) (* (/ y z) x) t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = x / (z / t);
	double tmp;
	if (t <= -2.65e+244) {
		tmp = t_2;
	} else if (t <= -1.16e+206) {
		tmp = t * -x;
	} else if (t <= -2.3e+133) {
		tmp = t_2;
	} else if (t <= -6.1e+85) {
		tmp = t_1;
	} else if (t <= -1.9e+45) {
		tmp = t * (x / z);
	} else if (t <= -5.5e-103) {
		tmp = t_1;
	} else if (t <= 3.4e+71) {
		tmp = (y / z) * x;
	} else {
		tmp = t_2;
	}
	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 = y * (x / z)
    t_2 = x / (z / t)
    if (t <= (-2.65d+244)) then
        tmp = t_2
    else if (t <= (-1.16d+206)) then
        tmp = t * -x
    else if (t <= (-2.3d+133)) then
        tmp = t_2
    else if (t <= (-6.1d+85)) then
        tmp = t_1
    else if (t <= (-1.9d+45)) then
        tmp = t * (x / z)
    else if (t <= (-5.5d-103)) then
        tmp = t_1
    else if (t <= 3.4d+71) then
        tmp = (y / z) * x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double t_2 = x / (z / t);
	double tmp;
	if (t <= -2.65e+244) {
		tmp = t_2;
	} else if (t <= -1.16e+206) {
		tmp = t * -x;
	} else if (t <= -2.3e+133) {
		tmp = t_2;
	} else if (t <= -6.1e+85) {
		tmp = t_1;
	} else if (t <= -1.9e+45) {
		tmp = t * (x / z);
	} else if (t <= -5.5e-103) {
		tmp = t_1;
	} else if (t <= 3.4e+71) {
		tmp = (y / z) * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	t_2 = x / (z / t)
	tmp = 0
	if t <= -2.65e+244:
		tmp = t_2
	elif t <= -1.16e+206:
		tmp = t * -x
	elif t <= -2.3e+133:
		tmp = t_2
	elif t <= -6.1e+85:
		tmp = t_1
	elif t <= -1.9e+45:
		tmp = t * (x / z)
	elif t <= -5.5e-103:
		tmp = t_1
	elif t <= 3.4e+71:
		tmp = (y / z) * x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	t_2 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -2.65e+244)
		tmp = t_2;
	elseif (t <= -1.16e+206)
		tmp = Float64(t * Float64(-x));
	elseif (t <= -2.3e+133)
		tmp = t_2;
	elseif (t <= -6.1e+85)
		tmp = t_1;
	elseif (t <= -1.9e+45)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= -5.5e-103)
		tmp = t_1;
	elseif (t <= 3.4e+71)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	t_2 = x / (z / t);
	tmp = 0.0;
	if (t <= -2.65e+244)
		tmp = t_2;
	elseif (t <= -1.16e+206)
		tmp = t * -x;
	elseif (t <= -2.3e+133)
		tmp = t_2;
	elseif (t <= -6.1e+85)
		tmp = t_1;
	elseif (t <= -1.9e+45)
		tmp = t * (x / z);
	elseif (t <= -5.5e-103)
		tmp = t_1;
	elseif (t <= 3.4e+71)
		tmp = (y / z) * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e+244], t$95$2, If[LessEqual[t, -1.16e+206], N[(t * (-x)), $MachinePrecision], If[LessEqual[t, -2.3e+133], t$95$2, If[LessEqual[t, -6.1e+85], t$95$1, If[LessEqual[t, -1.9e+45], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-103], t$95$1, If[LessEqual[t, 3.4e+71], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.6499999999999999e244 or -1.1600000000000001e206 < t < -2.2999999999999999e133 or 3.3999999999999998e71 < t

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 55.3%

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

      1. associate-/l* 68.7%

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

      2. cancel-sign-sub-inv 68.7%

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

      3. metadata-eval 68.7%

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

      4. *-lft-identity 68.7%

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

      5. +-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

   if -2.6499999999999999e244 < t < -1.1600000000000001e206

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*r/ 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*r* 90.5%

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

      5. neg-mul-1 90.5%

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

      6. distribute-rgt-out 90.4%

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

      7. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in y around 0 62.9%

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

      1. associate-*r* 62.9%

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

      2. mul-1-neg 62.9%

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

   8. Simplified 62.9%

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

   if -2.2999999999999999e133 < t < -6.09999999999999981e85 or -1.9000000000000001e45 < t < -5.50000000000000032e-103

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf 76.2%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 82.1%

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

   5. Simplified 82.1%

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

   if -6.09999999999999981e85 < t < -1.9000000000000001e45

   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 87.6%

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

      1. associate-/l* 87.6%

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

      2. cancel-sign-sub-inv 87.6%

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

      3. metadata-eval 87.6%

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

      4. *-lft-identity 87.6%

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

      5. +-commutative 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in t around inf 75.5%

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

      1. associate-*r/ 75.8%

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

   8. Simplified 75.8%

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

   if -5.50000000000000032e-103 < t < 3.3999999999999998e71

   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 inf 83.9%

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

      1. associate-*r/ 89.9%

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

   5. Simplified 89.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+244}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+206}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+133}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -7e+241)
     t_1
     (if (<= t -5.2e+208)
       (* t (- x))
       (if (<= t -2e+136)
         t_1
         (if (<= t -6.6e+84)
           (/ y (/ z x))
           (if (<= t -1.5e+44)
             (* t (/ x z))
             (if (<= t -4.2e-99)
               (* y (/ x z))
               (if (<= t 1.95e+71) (* (/ y z) x) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -7e+241) {
		tmp = t_1;
	} else if (t <= -5.2e+208) {
		tmp = t * -x;
	} else if (t <= -2e+136) {
		tmp = t_1;
	} else if (t <= -6.6e+84) {
		tmp = y / (z / x);
	} else if (t <= -1.5e+44) {
		tmp = t * (x / z);
	} else if (t <= -4.2e-99) {
		tmp = y * (x / z);
	} else if (t <= 1.95e+71) {
		tmp = (y / z) * x;
	} 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 / (z / t)
    if (t <= (-7d+241)) then
        tmp = t_1
    else if (t <= (-5.2d+208)) then
        tmp = t * -x
    else if (t <= (-2d+136)) then
        tmp = t_1
    else if (t <= (-6.6d+84)) then
        tmp = y / (z / x)
    else if (t <= (-1.5d+44)) then
        tmp = t * (x / z)
    else if (t <= (-4.2d-99)) then
        tmp = y * (x / z)
    else if (t <= 1.95d+71) then
        tmp = (y / z) * x
    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 / (z / t);
	double tmp;
	if (t <= -7e+241) {
		tmp = t_1;
	} else if (t <= -5.2e+208) {
		tmp = t * -x;
	} else if (t <= -2e+136) {
		tmp = t_1;
	} else if (t <= -6.6e+84) {
		tmp = y / (z / x);
	} else if (t <= -1.5e+44) {
		tmp = t * (x / z);
	} else if (t <= -4.2e-99) {
		tmp = y * (x / z);
	} else if (t <= 1.95e+71) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -7e+241:
		tmp = t_1
	elif t <= -5.2e+208:
		tmp = t * -x
	elif t <= -2e+136:
		tmp = t_1
	elif t <= -6.6e+84:
		tmp = y / (z / x)
	elif t <= -1.5e+44:
		tmp = t * (x / z)
	elif t <= -4.2e-99:
		tmp = y * (x / z)
	elif t <= 1.95e+71:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -7e+241)
		tmp = t_1;
	elseif (t <= -5.2e+208)
		tmp = Float64(t * Float64(-x));
	elseif (t <= -2e+136)
		tmp = t_1;
	elseif (t <= -6.6e+84)
		tmp = Float64(y / Float64(z / x));
	elseif (t <= -1.5e+44)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= -4.2e-99)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 1.95e+71)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -7e+241)
		tmp = t_1;
	elseif (t <= -5.2e+208)
		tmp = t * -x;
	elseif (t <= -2e+136)
		tmp = t_1;
	elseif (t <= -6.6e+84)
		tmp = y / (z / x);
	elseif (t <= -1.5e+44)
		tmp = t * (x / z);
	elseif (t <= -4.2e-99)
		tmp = y * (x / z);
	elseif (t <= 1.95e+71)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+241], t$95$1, If[LessEqual[t, -5.2e+208], N[(t * (-x)), $MachinePrecision], If[LessEqual[t, -2e+136], t$95$1, If[LessEqual[t, -6.6e+84], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e+44], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-99], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+71], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7e241 or -5.2000000000000001e208 < t < -2.00000000000000012e136 or 1.9500000000000001e71 < t

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 55.3%

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

      1. associate-/l* 68.7%

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

      2. cancel-sign-sub-inv 68.7%

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

      3. metadata-eval 68.7%

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

      4. *-lft-identity 68.7%

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

      5. +-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

   if -7e241 < t < -5.2000000000000001e208

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*r/ 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*r* 90.5%

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

      5. neg-mul-1 90.5%

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

      6. distribute-rgt-out 90.4%

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

      7. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in y around 0 62.9%

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

      1. associate-*r* 62.9%

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

      2. mul-1-neg 62.9%

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

   8. Simplified 62.9%

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

   if -2.00000000000000012e136 < t < -6.60000000000000034e84

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.8%

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

      1. associate-*r/ 81.8%

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

   5. Simplified 81.8%

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

      1. associate-*r/ 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-/l* 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -6.60000000000000034e84 < t < -1.49999999999999993e44

   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 87.6%

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

      1. associate-/l* 87.6%

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

      2. cancel-sign-sub-inv 87.6%

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

      3. metadata-eval 87.6%

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

      4. *-lft-identity 87.6%

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

      5. +-commutative 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in t around inf 75.5%

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

      1. associate-*r/ 75.8%

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

   8. Simplified 75.8%

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

   if -1.49999999999999993e44 < t < -4.19999999999999968e-99

   1. Initial program 74.0%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. associate-/l* 54.8%

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

      2. associate-/r/ 78.1%

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

   5. Simplified 78.1%

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

   if -4.19999999999999968e-99 < t < 1.9500000000000001e71

   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 inf 83.9%

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

      1. associate-*r/ 89.9%

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

   5. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -2e+243)
     t_1
     (if (<= t -7.3e+208)
       (* t (- x))
       (if (<= t -1.3e+136)
         t_1
         (if (<= t -6.3e+84)
           (/ y (/ z x))
           (if (<= t -4.4e+27)
             (* t (/ x z))
             (if (<= t -3.5e-99)
               (/ (* y x) z)
               (if (<= t 2.6e+71) (* (/ y z) x) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -2e+243) {
		tmp = t_1;
	} else if (t <= -7.3e+208) {
		tmp = t * -x;
	} else if (t <= -1.3e+136) {
		tmp = t_1;
	} else if (t <= -6.3e+84) {
		tmp = y / (z / x);
	} else if (t <= -4.4e+27) {
		tmp = t * (x / z);
	} else if (t <= -3.5e-99) {
		tmp = (y * x) / z;
	} else if (t <= 2.6e+71) {
		tmp = (y / z) * x;
	} 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 / (z / t)
    if (t <= (-2d+243)) then
        tmp = t_1
    else if (t <= (-7.3d+208)) then
        tmp = t * -x
    else if (t <= (-1.3d+136)) then
        tmp = t_1
    else if (t <= (-6.3d+84)) then
        tmp = y / (z / x)
    else if (t <= (-4.4d+27)) then
        tmp = t * (x / z)
    else if (t <= (-3.5d-99)) then
        tmp = (y * x) / z
    else if (t <= 2.6d+71) then
        tmp = (y / z) * x
    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 / (z / t);
	double tmp;
	if (t <= -2e+243) {
		tmp = t_1;
	} else if (t <= -7.3e+208) {
		tmp = t * -x;
	} else if (t <= -1.3e+136) {
		tmp = t_1;
	} else if (t <= -6.3e+84) {
		tmp = y / (z / x);
	} else if (t <= -4.4e+27) {
		tmp = t * (x / z);
	} else if (t <= -3.5e-99) {
		tmp = (y * x) / z;
	} else if (t <= 2.6e+71) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -2e+243:
		tmp = t_1
	elif t <= -7.3e+208:
		tmp = t * -x
	elif t <= -1.3e+136:
		tmp = t_1
	elif t <= -6.3e+84:
		tmp = y / (z / x)
	elif t <= -4.4e+27:
		tmp = t * (x / z)
	elif t <= -3.5e-99:
		tmp = (y * x) / z
	elif t <= 2.6e+71:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -2e+243)
		tmp = t_1;
	elseif (t <= -7.3e+208)
		tmp = Float64(t * Float64(-x));
	elseif (t <= -1.3e+136)
		tmp = t_1;
	elseif (t <= -6.3e+84)
		tmp = Float64(y / Float64(z / x));
	elseif (t <= -4.4e+27)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= -3.5e-99)
		tmp = Float64(Float64(y * x) / z);
	elseif (t <= 2.6e+71)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -2e+243)
		tmp = t_1;
	elseif (t <= -7.3e+208)
		tmp = t * -x;
	elseif (t <= -1.3e+136)
		tmp = t_1;
	elseif (t <= -6.3e+84)
		tmp = y / (z / x);
	elseif (t <= -4.4e+27)
		tmp = t * (x / z);
	elseif (t <= -3.5e-99)
		tmp = (y * x) / z;
	elseif (t <= 2.6e+71)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+243], t$95$1, If[LessEqual[t, -7.3e+208], N[(t * (-x)), $MachinePrecision], If[LessEqual[t, -1.3e+136], t$95$1, If[LessEqual[t, -6.3e+84], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e+27], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-99], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 2.6e+71], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.0000000000000001e243 or -7.29999999999999991e208 < t < -1.3000000000000001e136 or 2.59999999999999991e71 < t

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 55.3%

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

      1. associate-/l* 68.7%

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

      2. cancel-sign-sub-inv 68.7%

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

      3. metadata-eval 68.7%

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

      4. *-lft-identity 68.7%

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

      5. +-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 62.6%

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

   8. Simplified 62.6%

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

   if -2.0000000000000001e243 < t < -7.29999999999999991e208

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-*r/ 90.5%

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

      3. *-commutative 90.5%

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

      4. associate-*r* 90.5%

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

      5. neg-mul-1 90.5%

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

      6. distribute-rgt-out 90.4%

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

      7. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in y around 0 62.9%

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

      1. associate-*r* 62.9%

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

      2. mul-1-neg 62.9%

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

   8. Simplified 62.9%

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

   if -1.3000000000000001e136 < t < -6.30000000000000013e84

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.8%

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

      1. associate-*r/ 81.8%

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

   5. Simplified 81.8%

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

      1. associate-*r/ 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-/l* 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -6.30000000000000013e84 < t < -4.3999999999999997e27

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 88.9%

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

      1. associate-/l* 88.9%

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

      2. cancel-sign-sub-inv 88.9%

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

      3. metadata-eval 88.9%

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

      4. *-lft-identity 88.9%

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

      5. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in t around inf 78.2%

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

      1. associate-*r/ 78.5%

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

   8. Simplified 78.5%

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

   if -4.3999999999999997e27 < t < -3.4999999999999999e-99

   1. Initial program 72.8%

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

   3. Taylor expanded in y around inf 78.2%

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

   if -3.4999999999999999e-99 < t < 2.59999999999999991e71

   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 inf 83.9%

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

      1. associate-*r/ 89.9%

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

   5. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+243}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e+142)
   (/ x (/ z t))
   (if (<= z -4.6e+92)
     (/ (* y x) z)
     (if (<= z -8.2e+78)
       (/ (* t x) z)
       (if (<= z 4.6e+33)
         (* x (- (/ y z) t))
         (if (<= z 4.7e+143) (* t (/ x z)) (* (/ y z) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+142) {
		tmp = x / (z / t);
	} else if (z <= -4.6e+92) {
		tmp = (y * x) / z;
	} else if (z <= -8.2e+78) {
		tmp = (t * x) / z;
	} else if (z <= 4.6e+33) {
		tmp = x * ((y / z) - t);
	} else if (z <= 4.7e+143) {
		tmp = t * (x / z);
	} else {
		tmp = (y / z) * 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 <= (-3.3d+142)) then
        tmp = x / (z / t)
    else if (z <= (-4.6d+92)) then
        tmp = (y * x) / z
    else if (z <= (-8.2d+78)) then
        tmp = (t * x) / z
    else if (z <= 4.6d+33) then
        tmp = x * ((y / z) - t)
    else if (z <= 4.7d+143) then
        tmp = t * (x / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+142) {
		tmp = x / (z / t);
	} else if (z <= -4.6e+92) {
		tmp = (y * x) / z;
	} else if (z <= -8.2e+78) {
		tmp = (t * x) / z;
	} else if (z <= 4.6e+33) {
		tmp = x * ((y / z) - t);
	} else if (z <= 4.7e+143) {
		tmp = t * (x / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e+142:
		tmp = x / (z / t)
	elif z <= -4.6e+92:
		tmp = (y * x) / z
	elif z <= -8.2e+78:
		tmp = (t * x) / z
	elif z <= 4.6e+33:
		tmp = x * ((y / z) - t)
	elif z <= 4.7e+143:
		tmp = t * (x / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e+142)
		tmp = Float64(x / Float64(z / t));
	elseif (z <= -4.6e+92)
		tmp = Float64(Float64(y * x) / z);
	elseif (z <= -8.2e+78)
		tmp = Float64(Float64(t * x) / z);
	elseif (z <= 4.6e+33)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 4.7e+143)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.3e+142)
		tmp = x / (z / t);
	elseif (z <= -4.6e+92)
		tmp = (y * x) / z;
	elseif (z <= -8.2e+78)
		tmp = (t * x) / z;
	elseif (z <= 4.6e+33)
		tmp = x * ((y / z) - t);
	elseif (z <= 4.7e+143)
		tmp = t * (x / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e+142], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e+92], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8.2e+78], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.6e+33], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+143], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.3000000000000002e142

   1. Initial program 93.6%

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

   3. Taylor expanded in z around inf 82.1%

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

      1. associate-/l* 93.8%

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

      2. cancel-sign-sub-inv 93.8%

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

      3. metadata-eval 93.8%

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

      4. *-lft-identity 93.8%

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

      5. +-commutative 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in t around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-/l* 72.9%

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

   8. Simplified 72.9%

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

   if -3.3000000000000002e142 < z < -4.59999999999999997e92

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 83.6%

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

   if -4.59999999999999997e92 < z < -8.1999999999999994e78

   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 99.2%

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

      1. associate-/l* 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-lft-identity 100.0%

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

      5. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 99.2%

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

   if -8.1999999999999994e78 < z < 4.60000000000000021e33

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-*r/ 89.0%

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

      3. *-commutative 89.0%

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

      4. associate-*r* 89.0%

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

      5. neg-mul-1 89.0%

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

      6. distribute-rgt-out 90.4%

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

      7. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   if 4.60000000000000021e33 < z < 4.7e143

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 89.4%

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

      1. associate-/l* 96.5%

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

      2. cancel-sign-sub-inv 96.5%

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

      3. metadata-eval 96.5%

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

      4. *-lft-identity 96.5%

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

      5. +-commutative 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in t around inf 67.0%

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

      1. associate-*r/ 73.9%

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

   8. Simplified 73.9%

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

   if 4.7e143 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. associate-*r/ 67.7%

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

   5. Simplified 67.7%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -1.06e+14)
     t_1
     (if (<= t -3.8e-99)
       (/ (* y x) z)
       (if (<= t 2.15e+71) (* (/ y z) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.06e+14) {
		tmp = t_1;
	} else if (t <= -3.8e-99) {
		tmp = (y * x) / z;
	} else if (t <= 2.15e+71) {
		tmp = (y / z) * x;
	} 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 * (t / (z + (-1.0d0)))
    if (t <= (-1.06d+14)) then
        tmp = t_1
    else if (t <= (-3.8d-99)) then
        tmp = (y * x) / z
    else if (t <= 2.15d+71) then
        tmp = (y / z) * x
    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 * (t / (z + -1.0));
	double tmp;
	if (t <= -1.06e+14) {
		tmp = t_1;
	} else if (t <= -3.8e-99) {
		tmp = (y * x) / z;
	} else if (t <= 2.15e+71) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -1.06e+14:
		tmp = t_1
	elif t <= -3.8e-99:
		tmp = (y * x) / z
	elif t <= 2.15e+71:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -1.06e+14)
		tmp = t_1;
	elseif (t <= -3.8e-99)
		tmp = Float64(Float64(y * x) / z);
	elseif (t <= 2.15e+71)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z + -1.0));
	tmp = 0.0;
	if (t <= -1.06e+14)
		tmp = t_1;
	elseif (t <= -3.8e-99)
		tmp = (y * x) / z;
	elseif (t <= 2.15e+71)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.06e+14], t$95$1, If[LessEqual[t, -3.8e-99], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 2.15e+71], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.06e14 or 2.14999999999999992e71 < t

   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 72.1%

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

      1. associate-*r/ 72.1%

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

      2. associate-*r* 72.1%

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

      3. neg-mul-1 72.1%

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

      4. associate-*l/ 80.0%

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

      5. *-commutative 80.0%

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

      6. distribute-frac-neg 80.0%

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

      7. mul-1-neg 80.0%

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

      8. associate-*r/ 80.0%

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

      9. *-commutative 80.0%

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

      10. associate-*r/ 79.9%

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

      11. metadata-eval 79.9%

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

      12. associate-/r* 79.9%

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

      13. neg-mul-1 79.9%

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

      14. associate-*r/ 80.0%

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

      15. *-rgt-identity 80.0%

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

      16. neg-sub0 80.0%

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

      17. associate--r- 80.0%

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

      18. metadata-eval 80.0%

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

   5. Simplified 80.0%

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

   if -1.06e14 < t < -3.7999999999999997e-99

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf 80.2%

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

   if -3.7999999999999997e-99 < t < 2.14999999999999992e71

   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 inf 83.9%

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

      1. associate-*r/ 89.9%

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

   5. Simplified 89.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.86 \lor \neg \left(z \leq 1.1 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.86) (not (<= z 1.1e-11)))
   (* (/ x z) (+ y t))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.86) || !(z <= 1.1e-11)) {
		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 <= (-0.86d0)) .or. (.not. (z <= 1.1d-11))) 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 <= -0.86) || !(z <= 1.1e-11)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.86) or not (z <= 1.1e-11):
		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 <= -0.86) || !(z <= 1.1e-11))
		tmp = Float64(Float64(x / 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 <= -0.86) || ~((z <= 1.1e-11)))
		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, -0.86], N[Not[LessEqual[z, 1.1e-11]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.859999999999999987 or 1.1000000000000001e-11 < z

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 96.4%

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

      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%

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

   5. Simplified 88.8%

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

   if -0.859999999999999987 < z < 1.1000000000000001e-11

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-*r/ 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*r* 91.5%

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

      5. neg-mul-1 91.5%

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

      6. distribute-rgt-out 92.2%

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

      7. unsub-neg 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.86 \lor \neg \left(z \leq 1.1 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 1.1 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1) (not (<= z 1.1e-11)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1) || !(z <= 1.1e-11)) {
		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 <= (-1.1d0)) .or. (.not. (z <= 1.1d-11))) 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 <= -1.1) || !(z <= 1.1e-11)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1) or not (z <= 1.1e-11):
		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 <= -1.1) || !(z <= 1.1e-11))
		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 <= -1.1) || ~((z <= 1.1e-11)))
		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, -1.1], N[Not[LessEqual[z, 1.1e-11]], $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 < -1.1000000000000001 or 1.1000000000000001e-11 < z

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 96.4%

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

      2. cancel-sign-sub-inv 96.4%

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

      3. metadata-eval 96.4%

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

      4. *-lft-identity 96.4%

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

      5. +-commutative 96.4%

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

   5. Simplified 96.4%

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

   if -1.1000000000000001 < z < 1.1000000000000001e-11

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-*r/ 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*r* 91.5%

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

      5. neg-mul-1 91.5%

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

      6. distribute-rgt-out 92.2%

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

      7. unsub-neg 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 1.1 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 500000000000\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 500000000000.0))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 500000000000.0)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 500000000000.0d0))) 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 <= -1.0) || !(z <= 500000000000.0)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 500000000000.0):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 500000000000.0))
		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 <= -1.0) || ~((z <= 500000000000.0)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 500000000000.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 5e11 < z

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 86.0%

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

      1. associate-/l* 96.3%

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

      2. cancel-sign-sub-inv 96.3%

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

      3. metadata-eval 96.3%

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

      4. *-lft-identity 96.3%

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

      5. +-commutative 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in t around inf 55.3%

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

      1. associate-*r/ 54.6%

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

   8. Simplified 54.6%

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

   if -1 < z < 5e11

   1. Initial program 93.3%

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

   3. Taylor expanded in z around 0 94.4%

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

      1. +-commutative 94.4%

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

      2. associate-*r/ 91.3%

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

      3. *-commutative 91.3%

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

      4. associate-*r* 91.3%

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

      5. neg-mul-1 91.3%

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

      6. distribute-rgt-out 92.1%

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

      7. unsub-neg 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in y around 0 34.6%

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

      1. associate-*r* 34.6%

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

      2. mul-1-neg 34.6%

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

   8. Simplified 34.6%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 500000000000\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 23.1% 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 94.9%

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

3. Taylor expanded in z around 0 64.0%

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

   1. +-commutative 64.0%

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

   2. associate-*r/ 65.7%

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

   3. *-commutative 65.7%

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

   4. associate-*r* 65.7%

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

   5. neg-mul-1 65.7%

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

   6. distribute-rgt-out 66.9%

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

   7. unsub-neg 66.9%

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

5. Simplified 66.9%

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

6. Taylor expanded in y around 0 26.2%

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

   1. associate-*r* 26.2%

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

   2. mul-1-neg 26.2%

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

8. Simplified 26.2%

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

9. Final simplification 26.2%

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

Developer target: 95.3% 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 2024018 
(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)))))