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

Percentage Accurate: 94.3% → 94.9%

Time: 9.7s

Alternatives: 11

Speedup: 0.3×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+266} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (or (<= t_1 -5e+266) (not (<= t_1 INFINITY))) (* y (/ x z)) (* t_1 x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if ((t_1 <= -5e+266) || !(t_1 <= ((double) INFINITY))) {
		tmp = y * (x / z);
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if ((t_1 <= -5e+266) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = y * (x / z);
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if (t_1 <= -5e+266) or not (t_1 <= math.inf):
		tmp = y * (x / z)
	else:
		tmp = t_1 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if ((t_1 <= -5e+266) || !(t_1 <= Inf))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t_1 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if ((t_1 <= -5e+266) || ~((t_1 <= Inf)))
		tmp = y * (x / z);
	else
		tmp = t_1 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+266], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -4.9999999999999999e266 or +inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 76.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate-*r/ 76.5%

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

   5. Simplified 76.5%

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

      1. clear-num 76.6%

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

      2. un-div-inv 76.8%

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

   7. Applied egg-rr 76.8%

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

      1. associate-/r/ 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -4.9999999999999999e266 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < +inf.0

   1. Initial program 95.4%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -5 \cdot 10^{+266} \lor \neg \left(\frac{y}{z} + \frac{t}{z + -1} \leq \infty\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14600 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -14600.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -14600.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-14600.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -14600.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -14600.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -14600.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -14600.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -14600.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -14600 or 1 < z

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 85.7%

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

      1. associate-/l* 96.6%

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

      2. cancel-sign-sub-inv 96.6%

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

      3. metadata-eval 96.6%

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

      4. *-lft-identity 96.6%

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

      5. +-commutative 96.6%

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

   5. Simplified 96.6%

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

   if -14600 < z < 1

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0 89.2%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14600 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+117} \lor \neg \left(t \leq 5 \cdot 10^{+52}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e+117) (not (<= t 5e+52)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e+117) || !(t <= 5e+52)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.6d+117)) .or. (.not. (t <= 5d+52))) then
        tmp = x * (t / (z + (-1.0d0)))
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e+117) || !(t <= 5e+52)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e+117) or not (t <= 5e+52):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e+117) || !(t <= 5e+52))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e+117) || ~((t <= 5e+52)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e+117], N[Not[LessEqual[t, 5e+52]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000002e117 or 5e52 < t

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-neg-frac2 75.4%

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

      3. neg-sub0 75.4%

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

      4. associate--r- 75.4%

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

      5. metadata-eval 75.4%

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

   5. Simplified 75.4%

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

   if -1.60000000000000002e117 < t < 5e52

   1. Initial program 93.7%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

      1. clear-num 84.1%

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

      2. un-div-inv 84.6%

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

   7. Applied egg-rr 84.6%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+117} \lor \neg \left(t \leq 5 \cdot 10^{+52}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+171} \lor \neg \left(t \leq 1.4 \cdot 10^{+56}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.7e+171) (not (<= t 1.4e+56)))
   (* t (/ x (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.7e+171) || !(t <= 1.4e+56)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.7d+171)) .or. (.not. (t <= 1.4d+56))) then
        tmp = t * (x / (z + (-1.0d0)))
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.7e+171) || !(t <= 1.4e+56)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.7e+171) or not (t <= 1.4e+56):
		tmp = t * (x / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.7e+171) || !(t <= 1.4e+56))
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.7e+171) || ~((t <= 1.4e+56)))
		tmp = t * (x / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.7e+171], N[Not[LessEqual[t, 1.4e+56]], $MachinePrecision]], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.69999999999999998e171 or 1.40000000000000004e56 < t

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. associate-/l* 73.3%

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

      3. distribute-rgt-neg-in 73.3%

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

      4. distribute-neg-frac2 73.3%

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

      5. neg-sub0 73.3%

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

      6. associate--r- 73.3%

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

      7. metadata-eval 73.3%

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

   5. Simplified 73.3%

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

   if -3.69999999999999998e171 < t < 1.40000000000000004e56

   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 74.7%

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

      1. associate-*r/ 81.5%

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

   5. Simplified 81.5%

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

      1. clear-num 81.4%

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

      2. un-div-inv 81.9%

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

   7. Applied egg-rr 81.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+171} \lor \neg \left(t \leq 1.4 \cdot 10^{+56}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+109)
   (* (/ y z) x)
   (if (<= z 6.5e+37) (* x (- (/ y z) t)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+109) {
		tmp = (y / z) * x;
	} else if (z <= 6.5e+37) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d+109)) then
        tmp = (y / z) * x
    else if (z <= 6.5d+37) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+109) {
		tmp = (y / z) * x;
	} else if (z <= 6.5e+37) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+109:
		tmp = (y / z) * x
	elif z <= 6.5e+37:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+109)
		tmp = Float64(Float64(y / z) * x);
	elseif (z <= 6.5e+37)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+109)
		tmp = (y / z) * x;
	elseif (z <= 6.5e+37)
		tmp = x * ((y / z) - t);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+109], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 6.5e+37], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999994e109

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. associate-*r/ 84.0%

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

   5. Simplified 84.0%

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

   if -1.19999999999999994e109 < z < 6.4999999999999998e37

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 83.5%

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

   if 6.4999999999999998e37 < z

   1. Initial program 97.8%

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

      1. clear-num 97.7%

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

      2. associate-/r/ 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. cancel-sign-sub-inv 90.7%

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

      2. metadata-eval 90.7%

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

      3. *-lft-identity 90.7%

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

      4. associate-*r/ 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around 0 64.4%

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

      1. *-commutative 64.4%

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

      2. associate-/l* 69.8%

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

   10. Simplified 69.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-9} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e-9) (not (<= z 1.0))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-9) || !(z <= 1.0)) {
		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 <= (-1.45d-9)) .or. (.not. (z <= 1.0d0))) 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 <= -1.45e-9) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.45e-9) or not (z <= 1.0):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.45e-9) || !(z <= 1.0))
		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 <= -1.45e-9) || ~((z <= 1.0)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.45e-9], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.44999999999999996e-9 or 1 < z

   1. Initial program 97.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. neg-mul-1 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in y around 0 52.0%

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

      1. associate-/l* 51.2%

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

   8. Simplified 51.2%

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

   if -1.44999999999999996e-9 < z < 1

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 89.0%

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

   4. Taylor expanded in y around 0 36.5%

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

      1. associate-*r* 36.5%

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

      2. neg-mul-1 36.5%

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

   6. Simplified 36.5%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-9} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+182}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e+174)
   (* x (/ t z))
   (if (<= t 7.6e+182) (/ x (/ z y)) (* t (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e+174) {
		tmp = x * (t / z);
	} else if (t <= 7.6e+182) {
		tmp = x / (z / y);
	} 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 (t <= (-3.5d+174)) then
        tmp = x * (t / z)
    else if (t <= 7.6d+182) then
        tmp = x / (z / y)
    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 (t <= -3.5e+174) {
		tmp = x * (t / z);
	} else if (t <= 7.6e+182) {
		tmp = x / (z / y);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.5e+174:
		tmp = x * (t / z)
	elif t <= 7.6e+182:
		tmp = x / (z / y)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e+174)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 7.6e+182)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.5e+174)
		tmp = x * (t / z);
	elseif (t <= 7.6e+182)
		tmp = x / (z / y);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e+174], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+182], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5000000000000001e174

   1. Initial program 96.7%

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

      1. clear-num 96.7%

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

      2. associate-/r/ 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in z around inf 62.2%

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

      1. cancel-sign-sub-inv 62.2%

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

      2. metadata-eval 62.2%

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

      3. *-lft-identity 62.2%

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

      4. associate-*r/ 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

      2. associate-/l* 61.2%

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

   10. Simplified 61.2%

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

   if -3.5000000000000001e174 < t < 7.60000000000000025e182

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. associate-*r/ 75.2%

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

   5. Simplified 75.2%

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

      1. clear-num 75.1%

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

      2. un-div-inv 75.8%

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

   7. Applied egg-rr 75.8%

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

   if 7.60000000000000025e182 < t

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 71.1%

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

   4. Taylor expanded in y around 0 70.8%

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

      1. associate-*r* 70.8%

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

      2. neg-mul-1 70.8%

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

   6. Simplified 70.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+182}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 10^{+183}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2e+175)
   (* x (/ t z))
   (if (<= t 1e+183) (* (/ y z) x) (* t (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e+175) {
		tmp = x * (t / z);
	} else if (t <= 1e+183) {
		tmp = (y / z) * x;
	} 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 (t <= (-2d+175)) then
        tmp = x * (t / z)
    else if (t <= 1d+183) then
        tmp = (y / z) * x
    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 (t <= -2e+175) {
		tmp = x * (t / z);
	} else if (t <= 1e+183) {
		tmp = (y / z) * x;
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2e+175:
		tmp = x * (t / z)
	elif t <= 1e+183:
		tmp = (y / z) * x
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2e+175)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 1e+183)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2e+175)
		tmp = x * (t / z);
	elseif (t <= 1e+183)
		tmp = (y / z) * x;
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2e+175], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+183], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9999999999999999e175

   1. Initial program 96.7%

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

      1. clear-num 96.7%

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

      2. associate-/r/ 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in z around inf 62.2%

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

      1. cancel-sign-sub-inv 62.2%

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

      2. metadata-eval 62.2%

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

      3. *-lft-identity 62.2%

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

      4. associate-*r/ 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

      2. associate-/l* 61.2%

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

   10. Simplified 61.2%

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

   if -1.9999999999999999e175 < t < 9.99999999999999947e182

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. associate-*r/ 75.2%

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

   5. Simplified 75.2%

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

   if 9.99999999999999947e182 < t

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 71.1%

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

   4. Taylor expanded in y around 0 70.8%

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

      1. associate-*r* 70.8%

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

      2. neg-mul-1 70.8%

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

   6. Simplified 70.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 10^{+183}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.1:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e-9) (* t (/ x z)) (if (<= z 1.1) (* t (- x)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e-9) {
		tmp = t * (x / z);
	} else if (z <= 1.1) {
		tmp = t * -x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.45d-9)) then
        tmp = t * (x / z)
    else if (z <= 1.1d0) then
        tmp = t * -x
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e-9) {
		tmp = t * (x / z);
	} else if (z <= 1.1) {
		tmp = t * -x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e-9:
		tmp = t * (x / z)
	elif z <= 1.1:
		tmp = t * -x
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e-9)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 1.1)
		tmp = Float64(t * Float64(-x));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e-9)
		tmp = t * (x / z);
	elseif (z <= 1.1)
		tmp = t * -x;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e-9], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1], N[(t * (-x)), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999996e-9

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. neg-mul-1 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in y around 0 45.8%

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

      1. associate-/l* 47.1%

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

   8. Simplified 47.1%

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

   if -1.44999999999999996e-9 < z < 1.1000000000000001

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 89.0%

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

   4. Taylor expanded in y around 0 36.5%

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

      1. associate-*r* 36.5%

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

      2. neg-mul-1 36.5%

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

   6. Simplified 36.5%

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

   if 1.1000000000000001 < z

   1. Initial program 98.2%

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

      1. clear-num 98.1%

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

      2. associate-/r/ 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 92.2%

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

      1. cancel-sign-sub-inv 92.2%

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

      2. metadata-eval 92.2%

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

      3. *-lft-identity 92.2%

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

      4. associate-*r/ 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in y around 0 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-/l* 63.1%

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

   10. Simplified 63.1%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.1:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 24.6% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < 1

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 77.6%

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

   4. Taylor expanded in y around 0 30.0%

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

      1. associate-*r* 30.0%

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

      2. neg-mul-1 30.0%

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

   6. Simplified 30.0%

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

   if 1 < z

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 38.3%

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

   4. Taylor expanded in y around 0 12.6%

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

      1. associate-*r* 12.6%

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

      2. neg-mul-1 12.6%

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

   6. Simplified 12.6%

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

      1. add-cube-cbrt 12.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(-t\right) \cdot x} \cdot \sqrt[3]{\left(-t\right) \cdot x}\right) \cdot \sqrt[3]{\left(-t\right) \cdot x}} \]

      2. pow3 12.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(-t\right) \cdot x}\right)}^{3}} \]

      3. add-sqr-sqrt 9.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot x}\right)}^{3} \]

      4. sqrt-unprod 17.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot x}\right)}^{3} \]

      5. sqr-neg 17.5%

         \[\leadsto {\left(\sqrt[3]{\sqrt{\color{blue}{t \cdot t}} \cdot x}\right)}^{3} \]

      6. sqrt-unprod 8.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot x}\right)}^{3} \]

      7. add-sqr-sqrt 20.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{t} \cdot x}\right)}^{3} \]

      8. *-commutative 20.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot t}}\right)}^{3} \]

   8. Applied egg-rr 20.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot t}\right)}^{3}} \]
   9. Step-by-step derivation

      1. rem-cube-cbrt 20.1%

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

   10. Simplified 20.1%

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

4. Final simplification 27.6%

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

Alternative 11: 9.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ t \cdot x \end{array} \]

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 * 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 94.0%

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

3. Taylor expanded in z around 0 67.9%

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

4. Taylor expanded in y around 0 25.7%

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

   1. associate-*r* 25.7%

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

   2. neg-mul-1 25.7%

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

6. Simplified 25.7%

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

   1. add-cube-cbrt 25.5%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\left(-t\right) \cdot x} \cdot \sqrt[3]{\left(-t\right) \cdot x}\right) \cdot \sqrt[3]{\left(-t\right) \cdot x}} \]

   2. pow3 25.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(-t\right) \cdot x}\right)}^{3}} \]

   3. add-sqr-sqrt 12.7%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot x}\right)}^{3} \]

   4. sqrt-unprod 14.0%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot x}\right)}^{3} \]

   5. sqr-neg 14.0%

      \[\leadsto {\left(\sqrt[3]{\sqrt{\color{blue}{t \cdot t}} \cdot x}\right)}^{3} \]

   6. sqrt-unprod 4.5%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot x}\right)}^{3} \]

   7. add-sqr-sqrt 9.9%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{t} \cdot x}\right)}^{3} \]

   8. *-commutative 9.9%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot t}}\right)}^{3} \]

8. Applied egg-rr 9.9%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot t}\right)}^{3}} \]
9. Step-by-step derivation

   1. rem-cube-cbrt 9.9%

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

10. Simplified 9.9%

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

11. Final simplification 9.9%

    \[\leadsto t \cdot x \]
12. Add Preprocessing

Developer Target 1: 95.2% 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 2024118 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

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