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

Percentage Accurate: 94.5% → 94.5%

Time: 10.4s

Alternatives: 8

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.5% 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: 94.5% 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 93.7%

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

3. Final simplification 93.7%

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

Alternative 2: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.00056:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+158} \lor \neg \left(z \leq 1.4 \cdot 10^{+259}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -1.02e+14)
     t_1
     (if (<= z 8.5e-79)
       (* y (/ x z))
       (if (<= z 0.00056)
         (* x (- t))
         (if (or (<= z 2.2e+158) (not (<= z 1.4e+259))) (* x (/ y z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -1.02e+14) {
		tmp = t_1;
	} else if (z <= 8.5e-79) {
		tmp = y * (x / z);
	} else if (z <= 0.00056) {
		tmp = x * -t;
	} else if ((z <= 2.2e+158) || !(z <= 1.4e+259)) {
		tmp = x * (y / 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) :: tmp
    t_1 = x * (t / z)
    if (z <= (-1.02d+14)) then
        tmp = t_1
    else if (z <= 8.5d-79) then
        tmp = y * (x / z)
    else if (z <= 0.00056d0) then
        tmp = x * -t
    else if ((z <= 2.2d+158) .or. (.not. (z <= 1.4d+259))) then
        tmp = x * (y / 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 * (t / z);
	double tmp;
	if (z <= -1.02e+14) {
		tmp = t_1;
	} else if (z <= 8.5e-79) {
		tmp = y * (x / z);
	} else if (z <= 0.00056) {
		tmp = x * -t;
	} else if ((z <= 2.2e+158) || !(z <= 1.4e+259)) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -1.02e+14:
		tmp = t_1
	elif z <= 8.5e-79:
		tmp = y * (x / z)
	elif z <= 0.00056:
		tmp = x * -t
	elif (z <= 2.2e+158) or not (z <= 1.4e+259):
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -1.02e+14)
		tmp = t_1;
	elseif (z <= 8.5e-79)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 0.00056)
		tmp = Float64(x * Float64(-t));
	elseif ((z <= 2.2e+158) || !(z <= 1.4e+259))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (z <= -1.02e+14)
		tmp = t_1;
	elseif (z <= 8.5e-79)
		tmp = y * (x / z);
	elseif (z <= 0.00056)
		tmp = x * -t;
	elseif ((z <= 2.2e+158) || ~((z <= 1.4e+259)))
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+14], t$95$1, If[LessEqual[z, 8.5e-79], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00056], N[(x * (-t)), $MachinePrecision], If[Or[LessEqual[z, 2.2e+158], N[Not[LessEqual[z, 1.4e+259]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.02e14 or 2.2000000000000001e158 < z < 1.4e259

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 85.2%

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

   4. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   6. Simplified 66.0%

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

      1. associate-/l* 71.9%

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

      2. *-commutative 71.9%

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

   8. Applied egg-rr 71.9%

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

   if -1.02e14 < z < 8.50000000000000029e-79

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-/l* 77.0%

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

   5. Simplified 77.0%

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

   if 8.50000000000000029e-79 < z < 5.5999999999999995e-4

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-/l* 64.3%

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

      4. distribute-rgt-neg-out 64.3%

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

      5. distribute-neg-frac2 64.3%

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

      6. neg-sub0 64.3%

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

      7. associate--r- 64.3%

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

      8. metadata-eval 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in z around 0 59.0%

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

      1. *-commutative 59.0%

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

      2. neg-mul-1 59.0%

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

      3. distribute-lft-neg-in 59.0%

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

   8. Simplified 59.0%

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

   if 5.5999999999999995e-4 < z < 2.2000000000000001e158 or 1.4e259 < z

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 60.0%

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

      1. associate-*r/ 67.0%

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

   5. Simplified 67.0%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.00056:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+158} \lor \neg \left(z \leq 1.4 \cdot 10^{+259}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+164} \lor \neg \left(z \leq 1.2 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -3.6e+15)
     t_1
     (if (<= z 1.0)
       (* x (- (/ y z) t))
       (if (or (<= z 3e+164) (not (<= z 1.2e+253))) (* x (/ y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -3.6e+15) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else if ((z <= 3e+164) || !(z <= 1.2e+253)) {
		tmp = x * (y / 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) :: tmp
    t_1 = x * (t / z)
    if (z <= (-3.6d+15)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else if ((z <= 3d+164) .or. (.not. (z <= 1.2d+253))) then
        tmp = x * (y / 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 * (t / z);
	double tmp;
	if (z <= -3.6e+15) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else if ((z <= 3e+164) || !(z <= 1.2e+253)) {
		tmp = x * (y / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -3.6e+15:
		tmp = t_1
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	elif (z <= 3e+164) or not (z <= 1.2e+253):
		tmp = x * (y / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -3.6e+15)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif ((z <= 3e+164) || !(z <= 1.2e+253))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (z <= -3.6e+15)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	elseif ((z <= 3e+164) || ~((z <= 1.2e+253)))
		tmp = x * (y / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+15], t$95$1, If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3e+164], N[Not[LessEqual[z, 1.2e+253]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e15 or 3.00000000000000001e164 < z < 1.19999999999999996e253

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 85.2%

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

   4. Taylor expanded in y around 0 66.0%

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

      1. *-commutative 66.0%

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

   6. Simplified 66.0%

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

      1. associate-/l* 71.9%

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

      2. *-commutative 71.9%

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

   8. Applied egg-rr 71.9%

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

   if -3.6e15 < z < 1

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*r/ 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*r* 85.9%

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

      5. neg-mul-1 85.9%

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

      6. distribute-rgt-out 91.0%

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

      7. unsub-neg 91.0%

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

   5. Simplified 91.0%

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

   if 1 < z < 3.00000000000000001e164 or 1.19999999999999996e253 < z

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf 60.0%

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

      1. associate-*r/ 67.0%

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

   5. Simplified 67.0%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+164} \lor \neg \left(z \leq 1.2 \cdot 10^{+253}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= t -4e+90)
     (* x (- t))
     (if (<= t 2e-152)
       t_1
       (if (<= t 1.4e+138)
         (* x (/ y z))
         (if (<= t 3.5e+222) t_1 (* t (/ x z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if (t <= -4e+90) {
		tmp = x * -t;
	} else if (t <= 2e-152) {
		tmp = t_1;
	} else if (t <= 1.4e+138) {
		tmp = x * (y / z);
	} else if (t <= 3.5e+222) {
		tmp = t_1;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / z)
    if (t <= (-4d+90)) then
        tmp = x * -t
    else if (t <= 2d-152) then
        tmp = t_1
    else if (t <= 1.4d+138) then
        tmp = x * (y / z)
    else if (t <= 3.5d+222) then
        tmp = t_1
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if (t <= -4e+90) {
		tmp = x * -t;
	} else if (t <= 2e-152) {
		tmp = t_1;
	} else if (t <= 1.4e+138) {
		tmp = x * (y / z);
	} else if (t <= 3.5e+222) {
		tmp = t_1;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	tmp = 0
	if t <= -4e+90:
		tmp = x * -t
	elif t <= 2e-152:
		tmp = t_1
	elif t <= 1.4e+138:
		tmp = x * (y / z)
	elif t <= 3.5e+222:
		tmp = t_1
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (t <= -4e+90)
		tmp = Float64(x * Float64(-t));
	elseif (t <= 2e-152)
		tmp = t_1;
	elseif (t <= 1.4e+138)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 3.5e+222)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (t <= -4e+90)
		tmp = x * -t;
	elseif (t <= 2e-152)
		tmp = t_1;
	elseif (t <= 1.4e+138)
		tmp = x * (y / z);
	elseif (t <= 3.5e+222)
		tmp = t_1;
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+90], N[(x * (-t)), $MachinePrecision], If[LessEqual[t, 2e-152], t$95$1, If[LessEqual[t, 1.4e+138], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+222], t$95$1, N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.99999999999999987e90

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. *-commutative 82.6%

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

      3. associate-/l* 86.4%

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

      4. distribute-rgt-neg-out 86.4%

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

      5. distribute-neg-frac2 86.4%

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

      6. neg-sub0 86.4%

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

      7. associate--r- 86.4%

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

      8. metadata-eval 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around 0 46.8%

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

      1. *-commutative 46.8%

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

      2. neg-mul-1 46.8%

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

      3. distribute-lft-neg-in 46.8%

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

   8. Simplified 46.8%

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

   if -3.99999999999999987e90 < t < 2.00000000000000013e-152 or 1.4e138 < t < 3.4999999999999998e222

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

   if 2.00000000000000013e-152 < t < 1.4e138

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. associate-*r/ 63.6%

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

   5. Simplified 63.6%

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

   if 3.4999999999999998e222 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-/l* 86.1%

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

      4. distribute-rgt-neg-out 86.1%

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

      5. distribute-neg-frac2 86.1%

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

      6. neg-sub0 86.1%

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

      7. associate--r- 86.1%

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

      8. metadata-eval 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in z around inf 51.3%

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

      1. associate-/l* 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-152}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1000000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1000000000000.0) (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 <= -1000000000000.0) || !(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 <= (-1000000000000.0d0)) .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 <= -1000000000000.0) || !(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 <= -1000000000000.0) 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 <= -1000000000000.0) || !(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 <= -1000000000000.0) || ~((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, -1000000000000.0], 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 < -1e12 or 1 < z

   1. Initial program 94.6%

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

   3. Taylor expanded in z around inf 87.0%

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

      1. *-commutative 87.0%

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

      2. remove-double-neg 87.0%

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

      3. cancel-sign-sub-inv 87.0%

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

      4. metadata-eval 87.0%

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

      5. *-lft-identity 87.0%

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

      6. distribute-neg-out 87.0%

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

      7. neg-mul-1 87.0%

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

      8. sub-neg 87.0%

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

      9. mul-1-neg 87.0%

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

      10. associate-*r* 87.0%

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

      11. *-commutative 87.0%

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

      12. associate-*r/ 87.0%

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

      13. mul-1-neg 87.0%

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

      14. associate-/l* 94.4%

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

      15. distribute-rgt-neg-in 94.4%

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

      16. distribute-neg-frac 94.4%

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

   5. Simplified 94.4%

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

   if -1e12 < z < 1

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*r/ 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*r* 85.9%

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

      5. neg-mul-1 85.9%

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

      6. distribute-rgt-out 91.0%

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

      7. unsub-neg 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-55} \lor \neg \left(z \leq 7.2\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7e-55) (not (<= z 7.2))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e-55) || !(z <= 7.2)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7d-55)) .or. (.not. (z <= 7.2d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e-55) || !(z <= 7.2)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7e-55) or not (z <= 7.2):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7e-55) || !(z <= 7.2))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7e-55) || ~((z <= 7.2)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7e-55], N[Not[LessEqual[z, 7.2]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000051e-55 or 7.20000000000000018 < z

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. *-commutative 56.2%

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

      3. associate-/l* 58.9%

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

      4. distribute-rgt-neg-out 58.9%

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

      5. distribute-neg-frac2 58.9%

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

      6. neg-sub0 58.9%

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

      7. associate--r- 58.9%

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

      8. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around inf 54.8%

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

      1. associate-/l* 54.2%

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

   8. Simplified 54.2%

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

   if -7.00000000000000051e-55 < z < 7.20000000000000018

   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 0 29.9%

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

      1. mul-1-neg 29.9%

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

      2. *-commutative 29.9%

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

      3. associate-/l* 30.0%

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

      4. distribute-rgt-neg-out 30.0%

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

      5. distribute-neg-frac2 30.0%

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

      6. neg-sub0 30.0%

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

      7. associate--r- 30.0%

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

      8. metadata-eval 30.0%

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

   5. Simplified 30.0%

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

   6. Taylor expanded in z around 0 29.0%

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

      1. *-commutative 29.0%

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

      2. neg-mul-1 29.0%

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

      3. distribute-lft-neg-in 29.0%

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

   8. Simplified 29.0%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-55} \lor \neg \left(z \leq 7.2\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.6e+90)
   (* x (- t))
   (if (<= t 3.5e+222) (* x (/ y z)) (* t (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.6e+90) {
		tmp = x * -t;
	} else if (t <= 3.5e+222) {
		tmp = x * (y / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.6d+90)) then
        tmp = x * -t
    else if (t <= 3.5d+222) then
        tmp = x * (y / z)
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.6e+90) {
		tmp = x * -t;
	} else if (t <= 3.5e+222) {
		tmp = x * (y / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.6e+90:
		tmp = x * -t
	elif t <= 3.5e+222:
		tmp = x * (y / z)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.6e+90)
		tmp = Float64(x * Float64(-t));
	elseif (t <= 3.5e+222)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.6e+90)
		tmp = x * -t;
	elseif (t <= 3.5e+222)
		tmp = x * (y / z);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.6e+90], N[(x * (-t)), $MachinePrecision], If[LessEqual[t, 3.5e+222], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5999999999999998e90

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. *-commutative 82.6%

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

      3. associate-/l* 86.4%

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

      4. distribute-rgt-neg-out 86.4%

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

      5. distribute-neg-frac2 86.4%

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

      6. neg-sub0 86.4%

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

      7. associate--r- 86.4%

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

      8. metadata-eval 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around 0 46.8%

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

      1. *-commutative 46.8%

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

      2. neg-mul-1 46.8%

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

      3. distribute-lft-neg-in 46.8%

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

   8. Simplified 46.8%

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

   if -2.5999999999999998e90 < t < 3.4999999999999998e222

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. associate-*r/ 70.8%

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

   5. Simplified 70.8%

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

   if 3.4999999999999998e222 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-/l* 86.1%

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

      4. distribute-rgt-neg-out 86.1%

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

      5. distribute-neg-frac2 86.1%

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

      6. neg-sub0 86.1%

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

      7. associate--r- 86.1%

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

      8. metadata-eval 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in z around inf 51.3%

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

      1. associate-/l* 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 23.2% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

3. Taylor expanded in y around 0 43.0%

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

   1. mul-1-neg 43.0%

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

   2. *-commutative 43.0%

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

   3. associate-/l* 44.3%

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

   4. distribute-rgt-neg-out 44.3%

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

   5. distribute-neg-frac2 44.3%

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

   6. neg-sub0 44.3%

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

   7. associate--r- 44.3%

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

   8. metadata-eval 44.3%

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

5. Simplified 44.3%

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

6. Taylor expanded in z around 0 20.0%

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

   1. *-commutative 20.0%

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

   2. neg-mul-1 20.0%

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

   3. distribute-lft-neg-in 20.0%

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

8. Simplified 20.0%

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

9. Final simplification 20.0%

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

Developer target: 95.0% 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 2024045 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

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