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

Percentage Accurate: 94.3% → 94.3%

Time: 10.0s

Alternatives: 12

Speedup: 1.0×

• 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: 94.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Final simplification 96.3%

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

Alternative 2: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -126 \lor \neg \left(z \leq 3 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -126.0) (not (<= z 3e-6)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -126.0) || !(z <= 3e-6)) {
		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 <= (-126.0d0)) .or. (.not. (z <= 3d-6))) 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 <= -126.0) || !(z <= 3e-6)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -126.0) or not (z <= 3e-6):
		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 <= -126.0) || !(z <= 3e-6))
		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 <= -126.0) || ~((z <= 3e-6)))
		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, -126.0], N[Not[LessEqual[z, 3e-6]], $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 < -126 or 3.0000000000000001e-6 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 85.8%

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

      1. associate-/l* 98.5%

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

      2. cancel-sign-sub-inv 98.5%

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

      3. metadata-eval 98.5%

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

      4. *-lft-identity 98.5%

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

      5. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   if -126 < z < 3.0000000000000001e-6

   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 0 92.1%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -126 \lor \neg \left(z \leq 3 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+74} \lor \neg \left(t \leq 4.8 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e+74) (not (<= t 4.8e+105)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+74) || !(t <= 4.8e+105)) {
		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 <= (-5d+74)) .or. (.not. (t <= 4.8d+105))) 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 <= -5e+74) || !(t <= 4.8e+105)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e+74) or not (t <= 4.8e+105):
		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 <= -5e+74) || !(t <= 4.8e+105))
		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 <= -5e+74) || ~((t <= 4.8e+105)))
		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, -5e+74], N[Not[LessEqual[t, 4.8e+105]], $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 < -4.99999999999999963e74 or 4.7999999999999995e105 < t

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. distribute-neg-frac2 75.6%

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

      3. neg-sub0 75.6%

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

      4. associate--r- 75.6%

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

      5. metadata-eval 75.6%

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

   5. Simplified 75.6%

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

   if -4.99999999999999963e74 < t < 4.7999999999999995e105

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. associate-*r/ 78.9%

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

   5. Simplified 78.9%

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

      1. clear-num 78.7%

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

      2. un-div-inv 79.5%

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

   7. Applied egg-rr 79.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+74} \lor \neg \left(t \leq 4.8 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+19} \lor \neg \left(z \leq 4.6 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.42e+19) (not (<= z 4.6e+54)))
   (* x (/ t z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.42e+19) || !(z <= 4.6e+54)) {
		tmp = x * (t / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.42d+19)) .or. (.not. (z <= 4.6d+54))) then
        tmp = x * (t / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.42e+19) || !(z <= 4.6e+54)) {
		tmp = x * (t / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.42e+19) or not (z <= 4.6e+54):
		tmp = x * (t / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.42e+19) || !(z <= 4.6e+54))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.42e+19) || ~((z <= 4.6e+54)))
		tmp = x * (t / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.42e+19], N[Not[LessEqual[z, 4.6e+54]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.42e19 or 4.59999999999999988e54 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 62.5%

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

      1. mul-1-neg 62.5%

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

      2. distribute-neg-frac2 62.5%

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

      3. neg-sub0 62.5%

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

      4. associate--r- 62.5%

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

      5. metadata-eval 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around inf 62.5%

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

   if -1.42e19 < z < 4.59999999999999988e54

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 88.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+19} \lor \neg \left(z \leq 4.6 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -126:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -126.0)
   (* x (+ (/ y z) (/ t z)))
   (if (<= z 3e-6) (* x (- (/ y z) t)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -126.0) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 3e-6) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-126.0d0)) then
        tmp = x * ((y / z) + (t / z))
    else if (z <= 3d-6) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -126.0) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 3e-6) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -126.0:
		tmp = x * ((y / z) + (t / z))
	elif z <= 3e-6:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -126.0)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	elseif (z <= 3e-6)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -126.0)
		tmp = x * ((y / z) + (t / z));
	elseif (z <= 3e-6)
		tmp = x * ((y / z) - t);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -126.0], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-6], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -126

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 98.7%

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

      1. associate-*r/ 98.7%

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

      2. neg-mul-1 98.7%

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

   5. Simplified 98.7%

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

   if -126 < z < 3.0000000000000001e-6

   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 0 92.1%

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

   if 3.0000000000000001e-6 < z

   1. Initial program 98.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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* 98.1%

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

      2. cancel-sign-sub-inv 98.1%

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

      3. metadata-eval 98.1%

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

      4. *-lft-identity 98.1%

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

      5. +-commutative 98.1%

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

   5. Simplified 98.1%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -126:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-47}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-47)
   (/ (* x y) z)
   (if (<= y 2.4e-166) (* t (/ x (+ z -1.0))) (/ x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-47) {
		tmp = (x * y) / z;
	} else if (y <= 2.4e-166) {
		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 (y <= (-1.45d-47)) then
        tmp = (x * y) / z
    else if (y <= 2.4d-166) 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 (y <= -1.45e-47) {
		tmp = (x * y) / z;
	} else if (y <= 2.4e-166) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-47:
		tmp = (x * y) / z
	elif y <= 2.4e-166:
		tmp = t * (x / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-47)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 2.4e-166)
		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 (y <= -1.45e-47)
		tmp = (x * y) / z;
	elseif (y <= 2.4e-166)
		tmp = t * (x / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-47], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.4e-166], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e-47

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 77.8%

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

   if -1.45e-47 < y < 2.3999999999999999e-166

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. associate-/l* 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

      4. distribute-neg-frac2 73.0%

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

      5. neg-sub0 73.0%

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

      6. associate--r- 73.0%

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

      7. metadata-eval 73.0%

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

   5. Simplified 73.0%

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

   if 2.3999999999999999e-166 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 70.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   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 75.2%

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

      2. un-div-inv 75.2%

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

   7. Applied egg-rr 75.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-47}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+75} \lor \neg \left(t \leq 1.8 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.5e+75) (not (<= t 1.8e+106))) (* x (/ t z)) (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e+75) || !(t <= 1.8e+106)) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.5d+75)) .or. (.not. (t <= 1.8d+106))) then
        tmp = x * (t / z)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e+75) || !(t <= 1.8e+106)) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e+75) or not (t <= 1.8e+106):
		tmp = x * (t / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.5e+75) || !(t <= 1.8e+106))
		tmp = Float64(x * Float64(t / z));
	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 <= -1.5e+75) || ~((t <= 1.8e+106)))
		tmp = x * (t / z);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.5e+75], N[Not[LessEqual[t, 1.8e+106]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e75 or 1.8e106 < t

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. distribute-neg-frac2 75.6%

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

      3. neg-sub0 75.6%

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

      4. associate--r- 75.6%

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

      5. metadata-eval 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in z around inf 57.1%

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

   if -1.5e75 < t < 1.8e106

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. associate-*r/ 78.9%

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

   5. Simplified 78.9%

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

      1. clear-num 78.7%

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

      2. un-div-inv 79.5%

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

   7. Applied egg-rr 79.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+75} \lor \neg \left(t \leq 1.8 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+71} \lor \neg \left(t \leq 1.65 \cdot 10^{+107}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e+71) (not (<= t 1.65e+107))) (* x (/ t z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e+71) || !(t <= 1.65e+107)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.6d+71)) .or. (.not. (t <= 1.65d+107))) then
        tmp = x * (t / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e+71) || !(t <= 1.65e+107)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e+71) or not (t <= 1.65e+107):
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e+71) || !(t <= 1.65e+107))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.6e+71) || ~((t <= 1.65e+107)))
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.6e+71], N[Not[LessEqual[t, 1.65e+107]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5999999999999996e71 or 1.65000000000000016e107 < t

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. distribute-neg-frac2 75.6%

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

      3. neg-sub0 75.6%

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

      4. associate--r- 75.6%

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

      5. metadata-eval 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in z around inf 57.1%

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

   if -6.5999999999999996e71 < t < 1.65000000000000016e107

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. associate-*r/ 78.9%

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

   5. Simplified 78.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+71} \lor \neg \left(t \leq 1.65 \cdot 10^{+107}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17000000000000 \lor \neg \left(z \leq 0.00135\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -17000000000000.0) (not (<= z 0.00135)))
   (* x (/ t z))
   (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17000000000000.0) || !(z <= 0.00135)) {
		tmp = x * (t / 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 <= (-17000000000000.0d0)) .or. (.not. (z <= 0.00135d0))) then
        tmp = x * (t / 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 <= -17000000000000.0) || !(z <= 0.00135)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -17000000000000.0) or not (z <= 0.00135):
		tmp = x * (t / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -17000000000000.0) || !(z <= 0.00135))
		tmp = Float64(x * Float64(t / 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 <= -17000000000000.0) || ~((z <= 0.00135)))
		tmp = x * (t / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -17000000000000.0], N[Not[LessEqual[z, 0.00135]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e13 or 0.0013500000000000001 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac2 60.4%

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

      3. neg-sub0 60.4%

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

      4. associate--r- 60.4%

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

      5. metadata-eval 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in z around inf 60.4%

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

   if -1.7e13 < z < 0.0013500000000000001

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 29.3%

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

      1. mul-1-neg 29.3%

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

      2. distribute-neg-frac2 29.3%

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

      3. neg-sub0 29.3%

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

      4. associate--r- 29.3%

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

      5. metadata-eval 29.3%

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

   5. Simplified 29.3%

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

   6. Taylor expanded in z around 0 27.9%

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

      1. *-commutative 27.9%

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

      2. neg-mul-1 27.9%

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

      3. distribute-rgt-neg-in 27.9%

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

   8. Simplified 27.9%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000000000000 \lor \neg \left(z \leq 0.00135\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17000000000000 \lor \neg \left(z \leq 0.00135\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -17000000000000.0) (not (<= z 0.00135)))
   (* t (/ x z))
   (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -17000000000000.0) || !(z <= 0.00135)) {
		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 <= (-17000000000000.0d0)) .or. (.not. (z <= 0.00135d0))) 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 <= -17000000000000.0) || !(z <= 0.00135)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -17000000000000.0) or not (z <= 0.00135):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -17000000000000.0) || !(z <= 0.00135))
		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 <= -17000000000000.0) || ~((z <= 0.00135)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -17000000000000.0], N[Not[LessEqual[z, 0.00135]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e13 or 0.0013500000000000001 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac2 60.4%

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

      3. neg-sub0 60.4%

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

      4. associate--r- 60.4%

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

      5. metadata-eval 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in z around inf 50.4%

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

      1. associate-/l* 53.9%

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

   8. Simplified 53.9%

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

   if -1.7e13 < z < 0.0013500000000000001

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 29.3%

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

      1. mul-1-neg 29.3%

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

      2. distribute-neg-frac2 29.3%

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

      3. neg-sub0 29.3%

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

      4. associate--r- 29.3%

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

      5. metadata-eval 29.3%

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

   5. Simplified 29.3%

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

   6. Taylor expanded in z around 0 27.9%

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

      1. *-commutative 27.9%

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

      2. neg-mul-1 27.9%

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

      3. distribute-rgt-neg-in 27.9%

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

   8. Simplified 27.9%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000000000000 \lor \neg \left(z \leq 0.00135\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 23.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.00135:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= z 0.00135) (* t (- x)) (* x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 0.00135) {
		tmp = t * -x;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 0.00135d0) then
        tmp = t * -x
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 0.00135) {
		tmp = t * -x;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 0.00135:
		tmp = t * -x
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 0.00135)
		tmp = Float64(t * Float64(-x));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 0.00135)
		tmp = t * -x;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 0.00135], N[(t * (-x)), $MachinePrecision], N[(x * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.0013500000000000001

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. distribute-neg-frac2 41.2%

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

      3. neg-sub0 41.2%

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

      4. associate--r- 41.2%

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

      5. metadata-eval 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in z around 0 21.8%

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

      1. *-commutative 21.8%

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

      2. neg-mul-1 21.8%

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

      3. distribute-rgt-neg-in 21.8%

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

   8. Simplified 21.8%

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

   if 0.0013500000000000001 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-neg-frac2 58.8%

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

      3. neg-sub0 58.8%

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

      4. associate--r- 58.8%

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

      5. metadata-eval 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around 0 12.9%

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

      1. *-commutative 12.9%

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

      2. neg-mul-1 12.9%

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

      3. distribute-rgt-neg-in 12.9%

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

   8. Simplified 12.9%

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

      1. neg-sub0 12.9%

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

      2. sub-neg 12.9%

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

      3. add-sqr-sqrt 6.8%

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

      4. sqrt-unprod 19.0%

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

      5. sqr-neg 19.0%

         \[\leadsto x \cdot \left(0 + \sqrt{\color{blue}{t \cdot t}}\right) \]

      6. sqrt-unprod 10.0%

         \[\leadsto x \cdot \left(0 + \color{blue}{\sqrt{t} \cdot \sqrt{t}}\right) \]

      7. add-sqr-sqrt 21.7%

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

   10. Applied egg-rr 21.7%

       \[\leadsto x \cdot \color{blue}{\left(0 + t\right)} \]
   11. Step-by-step derivation

       1. +-lft-identity 21.7%

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

   12. Simplified 21.7%

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

4. Final simplification 21.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.00135:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 9.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in y around 0 45.3%

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

   1. mul-1-neg 45.3%

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

   2. distribute-neg-frac2 45.3%

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

   3. neg-sub0 45.3%

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

   4. associate--r- 45.3%

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

   5. metadata-eval 45.3%

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

5. Simplified 45.3%

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

6. Taylor expanded in z around 0 19.7%

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

   1. *-commutative 19.7%

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

   2. neg-mul-1 19.7%

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

   3. distribute-rgt-neg-in 19.7%

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

8. Simplified 19.7%

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

   1. neg-sub0 19.7%

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

   2. sub-neg 19.7%

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

   3. add-sqr-sqrt 10.0%

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

   4. sqrt-unprod 16.6%

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

   5. sqr-neg 16.6%

      \[\leadsto x \cdot \left(0 + \sqrt{\color{blue}{t \cdot t}}\right) \]

   6. sqrt-unprod 6.2%

      \[\leadsto x \cdot \left(0 + \color{blue}{\sqrt{t} \cdot \sqrt{t}}\right) \]

   7. add-sqr-sqrt 10.8%

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

10. Applied egg-rr 10.8%

    \[\leadsto x \cdot \color{blue}{\left(0 + t\right)} \]
11. Step-by-step derivation

    1. +-lft-identity 10.8%

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

12. Simplified 10.8%

    \[\leadsto x \cdot \color{blue}{t} \]
13. Add Preprocessing

Developer Target 1: 94.9% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(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)))))