Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 88.7% → 97.0%

Time: 12.4s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - 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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - 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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{\frac{x}{y - z}}{t - z} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- y z)) (- t z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (y - z)) / (t - z);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (x / (y - z)) / (t - z);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (y - z)) / (t - z)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(y - z)) / Float64(t - z))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (y - z)) / (t - z);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.5%

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

3. Taylor expanded in x around 0 86.5%

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

   1. associate-/l/ 95.7%

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

5. Simplified 95.7%

   \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]
6. Add Preprocessing

Alternative 2: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-45} \lor \neg \left(z \leq 1.2 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.6e+141)
   (/ (/ x z) z)
   (if (or (<= z -3.3e-45) (not (<= z 1.2e-56)))
     (/ x (* z (- z t)))
     (/ x (* y (- t z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e+141) {
		tmp = (x / z) / z;
	} else if ((z <= -3.3e-45) || !(z <= 1.2e-56)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (y * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-5.6d+141)) then
        tmp = (x / z) / z
    else if ((z <= (-3.3d-45)) .or. (.not. (z <= 1.2d-56))) then
        tmp = x / (z * (z - t))
    else
        tmp = x / (y * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e+141) {
		tmp = (x / z) / z;
	} else if ((z <= -3.3e-45) || !(z <= 1.2e-56)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (y * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -5.6e+141:
		tmp = (x / z) / z
	elif (z <= -3.3e-45) or not (z <= 1.2e-56):
		tmp = x / (z * (z - t))
	else:
		tmp = x / (y * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.6e+141)
		tmp = Float64(Float64(x / z) / z);
	elseif ((z <= -3.3e-45) || !(z <= 1.2e-56))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(y * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.6e+141)
		tmp = (x / z) / z;
	elseif ((z <= -3.3e-45) || ~((z <= 1.2e-56)))
		tmp = x / (z * (z - t));
	else
		tmp = x / (y * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -5.6e+141], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, -3.3e-45], N[Not[LessEqual[z, 1.2e-56]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999982e141

   1. Initial program 72.2%

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

   3. Taylor expanded in t around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. associate-/r* 96.9%

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

      3. distribute-neg-frac2 96.9%

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

      4. neg-sub0 96.9%

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

      5. sub-neg 96.9%

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

      6. +-commutative 96.9%

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

      7. associate--r+ 96.9%

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

      8. neg-sub0 96.9%

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

      9. remove-double-neg 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around inf 93.9%

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

   if -5.59999999999999982e141 < z < -3.3000000000000001e-45 or 1.2e-56 < z

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-rgt-neg-in 69.6%

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

      3. sub-neg 69.6%

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

      4. +-commutative 69.6%

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

      5. distribute-neg-in 69.6%

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

      6. remove-double-neg 69.6%

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

      7. unsub-neg 69.6%

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

   5. Simplified 69.6%

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

   if -3.3000000000000001e-45 < z < 1.2e-56

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-45} \lor \neg \left(z \leq 1.2 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-46} \lor \neg \left(z \leq 8.5 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e+142)
   (/ (/ x z) z)
   (if (or (<= z -9.5e-46) (not (<= z 8.5e-55)))
     (/ x (* z (- z t)))
     (/ (/ x y) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+142) {
		tmp = (x / z) / z;
	} else if ((z <= -9.5e-46) || !(z <= 8.5e-55)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-8.5d+142)) then
        tmp = (x / z) / z
    else if ((z <= (-9.5d-46)) .or. (.not. (z <= 8.5d-55))) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+142) {
		tmp = (x / z) / z;
	} else if ((z <= -9.5e-46) || !(z <= 8.5e-55)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e+142:
		tmp = (x / z) / z
	elif (z <= -9.5e-46) or not (z <= 8.5e-55):
		tmp = x / (z * (z - t))
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e+142)
		tmp = Float64(Float64(x / z) / z);
	elseif ((z <= -9.5e-46) || !(z <= 8.5e-55))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.5e+142)
		tmp = (x / z) / z;
	elseif ((z <= -9.5e-46) || ~((z <= 8.5e-55)))
		tmp = x / (z * (z - t));
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e+142], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, -9.5e-46], N[Not[LessEqual[z, 8.5e-55]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.49999999999999955e142

   1. Initial program 72.2%

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

   3. Taylor expanded in t around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. associate-/r* 96.9%

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

      3. distribute-neg-frac2 96.9%

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

      4. neg-sub0 96.9%

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

      5. sub-neg 96.9%

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

      6. +-commutative 96.9%

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

      7. associate--r+ 96.9%

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

      8. neg-sub0 96.9%

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

      9. remove-double-neg 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around inf 93.9%

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

   if -8.49999999999999955e142 < z < -9.49999999999999993e-46 or 8.49999999999999968e-55 < z

   1. Initial program 82.2%

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

   3. Taylor expanded in y around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-rgt-neg-in 69.6%

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

      3. sub-neg 69.6%

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

      4. +-commutative 69.6%

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

      5. distribute-neg-in 69.6%

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

      6. remove-double-neg 69.6%

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

      7. unsub-neg 69.6%

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

   5. Simplified 69.6%

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

   if -9.49999999999999993e-46 < z < 8.49999999999999968e-55

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0 94.6%

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

      1. associate-/l/ 91.5%

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

   5. Simplified 91.5%

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

      1. clear-num 91.3%

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

      2. inv-pow 91.3%

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

   7. Applied egg-rr 91.3%

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

      1. unpow-1 91.3%

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

   9. Simplified 91.3%

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

   10. Taylor expanded in z around 0 67.5%

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

       1. *-commutative 67.5%

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

       2. associate-/r* 67.0%

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

   12. Simplified 67.0%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-46} \lor \neg \left(z \leq 8.5 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+97)
   (/ (/ x z) (- z y))
   (if (<= z 8e+78) (/ x (* (- y z) (- t z))) (/ (/ x z) (- z t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+97) {
		tmp = (x / z) / (z - y);
	} else if (z <= 8e+78) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.2d+97)) then
        tmp = (x / z) / (z - y)
    else if (z <= 8d+78) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / (z - t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+97) {
		tmp = (x / z) / (z - y);
	} else if (z <= 8e+78) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+97:
		tmp = (x / z) / (z - y)
	elif z <= 8e+78:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+97)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 8e+78)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+97)
		tmp = (x / z) / (z - y);
	elseif (z <= 8e+78)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+97], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+78], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e97

   1. Initial program 74.9%

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

   3. Taylor expanded in t around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. associate-/r* 97.5%

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

      3. distribute-neg-frac2 97.5%

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

      4. neg-sub0 97.5%

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

      5. sub-neg 97.5%

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

      6. +-commutative 97.5%

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

      7. associate--r+ 97.5%

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

      8. neg-sub0 97.5%

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

      9. remove-double-neg 97.5%

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

   5. Simplified 97.5%

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

   if -2.2000000000000001e97 < z < 8.00000000000000007e78

   1. Initial program 93.0%

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

   if 8.00000000000000007e78 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-/r* 94.5%

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

      3. distribute-neg-frac2 94.5%

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

      4. sub-neg 94.5%

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

      5. +-commutative 94.5%

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

      6. distribute-neg-in 94.5%

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

      7. remove-double-neg 94.5%

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

      8. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

Alternative 5: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.52e-6)
   (/ (/ x y) (- t z))
   (if (<= y 8e-290) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e-6) {
		tmp = (x / y) / (t - z);
	} else if (y <= 8e-290) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.52d-6)) then
        tmp = (x / y) / (t - z)
    else if (y <= 8d-290) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e-6) {
		tmp = (x / y) / (t - z);
	} else if (y <= 8e-290) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.52e-6:
		tmp = (x / y) / (t - z)
	elif y <= 8e-290:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.52e-6)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 8e-290)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.52e-6)
		tmp = (x / y) / (t - z);
	elseif (y <= 8e-290)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.52e-6], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-290], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.52000000000000006e-6

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf 79.2%

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

      1. associate-/r* 84.9%

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

   5. Simplified 84.9%

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

   if -1.52000000000000006e-6 < y < 8.0000000000000006e-290

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. associate-/r* 77.2%

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

      3. distribute-neg-frac2 77.2%

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

      4. sub-neg 77.2%

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

      5. +-commutative 77.2%

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

      6. distribute-neg-in 77.2%

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

      7. remove-double-neg 77.2%

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

      8. unsub-neg 77.2%

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

   5. Simplified 77.2%

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

   if 8.0000000000000006e-290 < y

   1. Initial program 89.6%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 63.9%

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

Alternative 6: 78.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e-46)
   (/ (/ x y) (- t z))
   (if (<= y 7e-290) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-46) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7e-290) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.65d-46)) then
        tmp = (x / y) / (t - z)
    else if (y <= 7d-290) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-46) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7e-290) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e-46:
		tmp = (x / y) / (t - z)
	elif y <= 7e-290:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e-46)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 7e-290)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e-46)
		tmp = (x / y) / (t - z);
	elseif (y <= 7e-290)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e-46], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-290], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65000000000000007e-46

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 72.9%

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

      1. associate-/r* 76.4%

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

   5. Simplified 76.4%

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

   if -1.65000000000000007e-46 < y < 6.99999999999999963e-290

   1. Initial program 84.2%

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

   3. Taylor expanded in y around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. distribute-rgt-neg-in 66.5%

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

      3. sub-neg 66.5%

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

      4. +-commutative 66.5%

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

      5. distribute-neg-in 66.5%

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

      6. remove-double-neg 66.5%

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

      7. unsub-neg 66.5%

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

   5. Simplified 66.5%

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

   if 6.99999999999999963e-290 < y

   1. Initial program 89.7%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.2%

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

Alternative 7: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.4e-46)
   (/ x (* y (- t z)))
   (if (<= y 7.5e-290) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.4e-46) {
		tmp = x / (y * (t - z));
	} else if (y <= 7.5e-290) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-6.4d-46)) then
        tmp = x / (y * (t - z))
    else if (y <= 7.5d-290) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.4e-46) {
		tmp = x / (y * (t - z));
	} else if (y <= 7.5e-290) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -6.4e-46:
		tmp = x / (y * (t - z))
	elif y <= 7.5e-290:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.4e-46)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 7.5e-290)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.4e-46)
		tmp = x / (y * (t - z));
	elseif (y <= 7.5e-290)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -6.4e-46], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-290], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.3999999999999998e-46

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 72.9%

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

      1. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -6.3999999999999998e-46 < y < 7.4999999999999995e-290

   1. Initial program 84.2%

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

   3. Taylor expanded in y around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. distribute-rgt-neg-in 66.5%

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

      3. sub-neg 66.5%

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

      4. +-commutative 66.5%

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

      5. distribute-neg-in 66.5%

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

      6. remove-double-neg 66.5%

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

      7. unsub-neg 66.5%

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

   5. Simplified 66.5%

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

   if 7.4999999999999995e-290 < y

   1. Initial program 89.7%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.2%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+52} \lor \neg \left(z \leq 4.5 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.56e+52) (not (<= z 4.5e-53))) (/ (/ x z) z) (/ (/ x y) t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.56e+52) || !(z <= 4.5e-53)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.56d+52)) .or. (.not. (z <= 4.5d-53))) then
        tmp = (x / z) / z
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.56e+52) || !(z <= 4.5e-53)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.56e+52) or not (z <= 4.5e-53):
		tmp = (x / z) / z
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.56e+52) || !(z <= 4.5e-53))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.56e+52) || ~((z <= 4.5e-53)))
		tmp = (x / z) / z;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.56e+52], N[Not[LessEqual[z, 4.5e-53]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55999999999999994e52 or 4.49999999999999985e-53 < z

   1. Initial program 77.0%

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

   3. Taylor expanded in t around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-/r* 80.7%

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

      3. distribute-neg-frac2 80.7%

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

      4. neg-sub0 80.7%

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

      5. sub-neg 80.7%

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

      6. +-commutative 80.7%

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

      7. associate--r+ 80.7%

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

      8. neg-sub0 80.7%

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

      9. remove-double-neg 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in z around inf 71.5%

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

   if -1.55999999999999994e52 < z < 4.49999999999999985e-53

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 94.8%

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

      1. associate-/l/ 92.2%

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

   5. Simplified 92.2%

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

      1. clear-num 92.0%

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

      2. inv-pow 92.0%

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

   7. Applied egg-rr 92.0%

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

      1. unpow-1 92.0%

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

   9. Simplified 92.0%

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

   10. Taylor expanded in z around 0 61.5%

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

       1. *-commutative 61.5%

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

       2. associate-/r* 62.9%

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

   12. Simplified 62.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+52} \lor \neg \left(z \leq 4.5 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+97} \lor \neg \left(z \leq 2 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e+97) (not (<= z 2e+135))) (/ x (* y z)) (/ (/ x y) t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+97) || !(z <= 2e+135)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-8.5d+97)) .or. (.not. (z <= 2d+135))) then
        tmp = x / (y * z)
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+97) || !(z <= 2e+135)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e+97) or not (z <= 2e+135):
		tmp = x / (y * z)
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e+97) || !(z <= 2e+135))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.5e+97) || ~((z <= 2e+135)))
		tmp = x / (y * z);
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e+97], N[Not[LessEqual[z, 2e+135]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999993e97 or 1.99999999999999992e135 < z

   1. Initial program 74.0%

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

   3. Taylor expanded in t around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-/r* 91.8%

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

      3. distribute-neg-frac2 91.8%

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

      4. neg-sub0 91.8%

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

      5. sub-neg 91.8%

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

      6. +-commutative 91.8%

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

      7. associate--r+ 91.8%

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

      8. neg-sub0 91.8%

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

      9. remove-double-neg 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in z around 0 38.7%

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

      1. associate-*r/ 38.7%

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

      2. neg-mul-1 38.7%

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

      3. *-commutative 38.7%

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

   8. Simplified 38.7%

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

      1. frac-2neg 38.7%

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

      2. remove-double-neg 38.7%

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

      3. *-commutative 38.7%

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

      4. distribute-lft-neg-in 38.7%

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

      5. un-div-inv 38.7%

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

      6. associate-/l/ 38.7%

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

      7. associate-/l/ 38.7%

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

      8. add-sqr-sqrt 23.2%

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

      9. sqrt-unprod 38.2%

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

      10. sqr-neg 38.2%

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

      11. sqrt-unprod 15.3%

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

      12. add-sqr-sqrt 38.8%

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

   10. Applied egg-rr 38.8%

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

       1. associate-*r/ 38.8%

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

       2. *-rgt-identity 38.8%

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

       3. *-commutative 38.8%

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

   12. Simplified 38.8%

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

   if -8.4999999999999993e97 < z < 1.99999999999999992e135

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 91.2%

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

      1. associate-/l/ 94.2%

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

   5. Simplified 94.2%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

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

   7. Applied egg-rr 94.1%

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

      1. unpow-1 94.1%

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

   9. Simplified 94.1%

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

   10. Taylor expanded in z around 0 51.5%

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

       1. *-commutative 51.5%

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

       2. associate-/r* 54.9%

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

   12. Simplified 54.9%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+97} \lor \neg \left(z \leq 2 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+51} \lor \neg \left(z \leq 7 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.75e+51) (not (<= z 7e+134))) (/ x (* y z)) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.75e+51) || !(z <= 7e+134)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.75d+51)) .or. (.not. (z <= 7d+134))) then
        tmp = x / (y * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.75e+51) || !(z <= 7e+134)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.75e+51) or not (z <= 7e+134):
		tmp = x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.75e+51) || !(z <= 7e+134))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.75e+51) || ~((z <= 7e+134)))
		tmp = x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.75e+51], N[Not[LessEqual[z, 7e+134]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e51 or 7.00000000000000006e134 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-/r* 91.5%

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

      3. distribute-neg-frac2 91.5%

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

      4. neg-sub0 91.5%

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

      5. sub-neg 91.5%

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

      6. +-commutative 91.5%

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

      7. associate--r+ 91.5%

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

      8. neg-sub0 91.5%

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

      9. remove-double-neg 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 40.9%

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

      1. associate-*r/ 40.9%

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

      2. neg-mul-1 40.9%

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

      3. *-commutative 40.9%

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

   8. Simplified 40.9%

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

      1. frac-2neg 40.9%

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

      2. remove-double-neg 40.9%

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

      3. *-commutative 40.9%

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

      4. distribute-lft-neg-in 40.9%

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

      5. un-div-inv 40.9%

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

      6. associate-/l/ 40.9%

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

      7. associate-/l/ 40.9%

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

      8. add-sqr-sqrt 23.2%

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

      9. sqrt-unprod 39.2%

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

      10. sqr-neg 39.2%

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

      11. sqrt-unprod 16.3%

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

      12. add-sqr-sqrt 38.4%

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

   10. Applied egg-rr 38.4%

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

       1. associate-*r/ 38.4%

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

       2. *-rgt-identity 38.4%

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

       3. *-commutative 38.4%

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

   12. Simplified 38.4%

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

   if -2.75e51 < z < 7.00000000000000006e134

   1. Initial program 91.2%

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

      1. associate-/l/ 95.5%

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

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 71.4%

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

   6. Taylor expanded in y around inf 57.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+51} \lor \neg \left(z \leq 7 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+50} \lor \neg \left(z \leq 1.75 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e+50) (not (<= z 1.75e+132))) (/ x (* y z)) (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+50) || !(z <= 1.75e+132)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.9d+50)) .or. (.not. (z <= 1.75d+132))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+50) || !(z <= 1.75e+132)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.9e+50) or not (z <= 1.75e+132):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e+50) || !(z <= 1.75e+132))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.9e+50) || ~((z <= 1.75e+132)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e+50], N[Not[LessEqual[z, 1.75e+132]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999994e50 or 1.7500000000000001e132 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-/r* 91.5%

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

      3. distribute-neg-frac2 91.5%

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

      4. neg-sub0 91.5%

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

      5. sub-neg 91.5%

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

      6. +-commutative 91.5%

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

      7. associate--r+ 91.5%

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

      8. neg-sub0 91.5%

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

      9. remove-double-neg 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 40.9%

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

      1. associate-*r/ 40.9%

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

      2. neg-mul-1 40.9%

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

      3. *-commutative 40.9%

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

   8. Simplified 40.9%

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

      1. frac-2neg 40.9%

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

      2. remove-double-neg 40.9%

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

      3. *-commutative 40.9%

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

      4. distribute-lft-neg-in 40.9%

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

      5. un-div-inv 40.9%

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

      6. associate-/l/ 40.9%

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

      7. associate-/l/ 40.9%

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

      8. add-sqr-sqrt 23.2%

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

      9. sqrt-unprod 39.2%

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

      10. sqr-neg 39.2%

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

      11. sqrt-unprod 16.3%

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

      12. add-sqr-sqrt 38.4%

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

   10. Applied egg-rr 38.4%

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

       1. associate-*r/ 38.4%

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

       2. *-rgt-identity 38.4%

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

       3. *-commutative 38.4%

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

   12. Simplified 38.4%

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

   if -1.89999999999999994e50 < z < 1.7500000000000001e132

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 52.8%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+50} \lor \neg \left(z \leq 1.75 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+29} \lor \neg \left(z \leq 10^{+52}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+29) (not (<= z 1e+52))) (/ x (* z t)) (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+29) || !(z <= 1e+52)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d+29)) .or. (.not. (z <= 1d+52))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+29) || !(z <= 1e+52)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e+29) or not (z <= 1e+52):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+29) || !(z <= 1e+52))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e+29) || ~((z <= 1e+52)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+29], N[Not[LessEqual[z, 1e+52]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999993e29 or 9.9999999999999999e51 < z

   1. Initial program 77.3%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 45.8%

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

   6. Taylor expanded in y around 0 41.3%

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

      1. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

      1. *-un-lft-identity 41.3%

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

      2. associate-/l/ 36.9%

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

      3. associate-/r* 44.0%

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

      4. add-sqr-sqrt 16.7%

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

      5. sqrt-unprod 51.7%

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

      6. sqr-neg 51.7%

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

      7. sqrt-unprod 18.5%

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

      8. add-sqr-sqrt 35.2%

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

   10. Applied egg-rr 35.2%

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

       1. *-lft-identity 35.2%

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

       2. associate-/l/ 35.0%

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

       3. *-commutative 35.0%

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

   12. Simplified 35.0%

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

   if -1.59999999999999993e29 < z < 9.9999999999999999e51

   1. Initial program 93.3%

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

   3. Taylor expanded in z around 0 57.7%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+29} \lor \neg \left(z \leq 10^{+52}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e+97)
   (/ x (* y z))
   (if (<= z 6.2e+131) (/ (/ x y) t) (/ (/ x z) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+97) {
		tmp = x / (y * z);
	} else if (z <= 6.2e+131) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.1d+97)) then
        tmp = x / (y * z)
    else if (z <= 6.2d+131) then
        tmp = (x / y) / t
    else
        tmp = (x / z) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+97) {
		tmp = x / (y * z);
	} else if (z <= 6.2e+131) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e+97:
		tmp = x / (y * z)
	elif z <= 6.2e+131:
		tmp = (x / y) / t
	else:
		tmp = (x / z) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e+97)
		tmp = Float64(x / Float64(y * z));
	elseif (z <= 6.2e+131)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(x / z) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e+97)
		tmp = x / (y * z);
	elseif (z <= 6.2e+131)
		tmp = (x / y) / t;
	else
		tmp = (x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e+97], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+131], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e97

   1. Initial program 74.9%

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

   3. Taylor expanded in t around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. associate-/r* 97.5%

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

      3. distribute-neg-frac2 97.5%

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

      4. neg-sub0 97.5%

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

      5. sub-neg 97.5%

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

      6. +-commutative 97.5%

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

      7. associate--r+ 97.5%

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

      8. neg-sub0 97.5%

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

      9. remove-double-neg 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around 0 31.8%

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

      1. associate-*r/ 31.8%

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

      2. neg-mul-1 31.8%

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

      3. *-commutative 31.8%

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

   8. Simplified 31.8%

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

      1. frac-2neg 31.8%

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

      2. remove-double-neg 31.8%

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

      3. *-commutative 31.8%

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

      4. distribute-lft-neg-in 31.8%

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

      5. un-div-inv 31.8%

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

      6. associate-/l/ 31.8%

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

      7. associate-/l/ 31.8%

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

      8. add-sqr-sqrt 14.6%

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

      9. sqrt-unprod 31.1%

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

      10. sqr-neg 31.1%

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

      11. sqrt-unprod 16.9%

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

      12. add-sqr-sqrt 32.0%

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

   10. Applied egg-rr 32.0%

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

       1. associate-*r/ 32.0%

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

       2. *-rgt-identity 32.0%

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

       3. *-commutative 32.0%

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

   12. Simplified 32.0%

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

   if -1.1e97 < z < 6.20000000000000032e131

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 91.2%

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

      1. associate-/l/ 94.2%

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

   5. Simplified 94.2%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

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

   7. Applied egg-rr 94.1%

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

      1. unpow-1 94.1%

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

   9. Simplified 94.1%

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

   10. Taylor expanded in z around 0 51.5%

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

       1. *-commutative 51.5%

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

       2. associate-/r* 54.9%

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

   12. Simplified 54.9%

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

   if 6.20000000000000032e131 < z

   1. Initial program 72.9%

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

   3. Taylor expanded in t around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. associate-/r* 84.8%

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

      3. distribute-neg-frac2 84.8%

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

      4. neg-sub0 84.8%

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

      5. sub-neg 84.8%

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

      6. +-commutative 84.8%

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

      7. associate--r+ 84.8%

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

      8. neg-sub0 84.8%

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

      9. remove-double-neg 84.8%

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

   5. Simplified 84.8%

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

      1. div-inv 84.8%

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

      2. associate-/l* 72.9%

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

   7. Applied egg-rr 72.9%

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

   8. Taylor expanded in z around 0 47.2%

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

      1. neg-mul-1 47.2%

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

   10. Simplified 47.2%

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

       1. associate-*r/ 49.5%

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

       2. add-sqr-sqrt 42.0%

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

       3. div-inv 42.0%

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

       4. sqrt-unprod 46.0%

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

       5. sqr-neg 46.0%

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

       6. sqrt-unprod 7.6%

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

       7. add-sqr-sqrt 49.5%

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

   12. Applied egg-rr 49.5%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- t z)) (- y z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 - z)) / (y - z)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (t - z)) / (y - z)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(t - z)) / Float64(y - z))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (t - z)) / (y - z);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.5%

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

   1. associate-/l/ 96.8%

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

3. Simplified 96.8%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 15: 38.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y \cdot t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* y t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / (y * t);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 * t)
end function

Java

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (y * t)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(y * t))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (y * t);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.5%

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

3. Taylor expanded in z around 0 42.2%

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

4. Final simplification 42.2%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer Target 1: 87.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / 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 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

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