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

Percentage Accurate: 99.0% → 98.7%

Time: 13.6s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - 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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - 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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.1× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (- 1.0 (pow (* (- z y) (/ (- t y) x)) -1.0)))

C

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

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 = 1.0d0 - (((z - y) * ((t - y) / x)) ** (-1.0d0))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 - Math.pow(((z - y) * ((t - y) / x)), -1.0);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - math.pow(((z - y) * ((t - y) / x)), -1.0)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 - (Float64(Float64(z - y) * Float64(Float64(t - y) / x)) ^ -1.0))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - (((z - y) * ((t - y) / x)) ^ -1.0);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 - N[Power[N[(N[(z - y), $MachinePrecision] * N[(N[(t - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

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

   1. clear-num 98.3%

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

   2. inv-pow 98.3%

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

   3. associate-/l* 97.8%

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

4. Applied egg-rr 97.8%

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

5. Final simplification 97.8%

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

Alternative 2: 82.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 0.048:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= t -9.2e-39)
   (+ 1.0 (* x (/ (/ -1.0 t) z)))
   (if (<= t 9.8e-51)
     (- 1.0 (/ x (* y (- y z))))
     (if (<= t 1.75e-25)
       (/ x (* (- y z) t))
       (if (<= t 0.048)
         (/ (- z (/ x t)) z)
         (if (<= t 1.45e+31)
           (+ 1.0 (/ x (* y (- t y))))
           (if (<= t 2.4e+65) (- 1.0 (/ x (* z t))) 1.0)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e-39) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else if (t <= 9.8e-51) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (t <= 1.75e-25) {
		tmp = x / ((y - z) * t);
	} else if (t <= 0.048) {
		tmp = (z - (x / t)) / z;
	} else if (t <= 1.45e+31) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (t <= 2.4e+65) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	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 (t <= (-9.2d-39)) then
        tmp = 1.0d0 + (x * (((-1.0d0) / t) / z))
    else if (t <= 9.8d-51) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else if (t <= 1.75d-25) then
        tmp = x / ((y - z) * t)
    else if (t <= 0.048d0) then
        tmp = (z - (x / t)) / z
    else if (t <= 1.45d+31) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else if (t <= 2.4d+65) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    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 (t <= -9.2e-39) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else if (t <= 9.8e-51) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (t <= 1.75e-25) {
		tmp = x / ((y - z) * t);
	} else if (t <= 0.048) {
		tmp = (z - (x / t)) / z;
	} else if (t <= 1.45e+31) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (t <= 2.4e+65) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -9.2e-39:
		tmp = 1.0 + (x * ((-1.0 / t) / z))
	elif t <= 9.8e-51:
		tmp = 1.0 - (x / (y * (y - z)))
	elif t <= 1.75e-25:
		tmp = x / ((y - z) * t)
	elif t <= 0.048:
		tmp = (z - (x / t)) / z
	elif t <= 1.45e+31:
		tmp = 1.0 + (x / (y * (t - y)))
	elif t <= 2.4e+65:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.2e-39)
		tmp = Float64(1.0 + Float64(x * Float64(Float64(-1.0 / t) / z)));
	elseif (t <= 9.8e-51)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	elseif (t <= 1.75e-25)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (t <= 0.048)
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	elseif (t <= 1.45e+31)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	elseif (t <= 2.4e+65)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	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 (t <= -9.2e-39)
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	elseif (t <= 9.8e-51)
		tmp = 1.0 - (x / (y * (y - z)));
	elseif (t <= 1.75e-25)
		tmp = x / ((y - z) * t);
	elseif (t <= 0.048)
		tmp = (z - (x / t)) / z;
	elseif (t <= 1.45e+31)
		tmp = 1.0 + (x / (y * (t - y)));
	elseif (t <= 2.4e+65)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	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[t, -9.2e-39], N[(1.0 + N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e-51], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-25], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.048], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.45e+31], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+65], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -9.20000000000000033e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.3%

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

      1. clear-num 78.4%

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

      2. inv-pow 78.4%

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

      3. *-commutative 78.4%

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

      4. associate-/l* 78.4%

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

   5. Applied egg-rr 78.4%

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

      1. unpow-1 78.4%

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

      2. associate-*r/ 78.4%

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

      3. *-commutative 78.4%

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

      4. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

      1. associate-/r* 77.0%

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

      2. associate-/r/ 78.4%

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

   9. Applied egg-rr 78.4%

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

   if -9.20000000000000033e-39 < t < 9.79999999999999948e-51

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0 80.0%

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

   if 9.79999999999999948e-51 < t < 1.7500000000000001e-25

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in x around inf 62.8%

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

   if 1.7500000000000001e-25 < t < 0.048000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   if 0.048000000000000001 < t < 1.45e31

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 83.3%

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

   if 1.45e31 < t < 2.4000000000000002e65

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 99.7%

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

   if 2.4000000000000002e65 < t

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 73.1%

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

   4. Taylor expanded in x around 0 90.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 7 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-51}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 0.048:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-39}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;t \leq 860000000000 \lor \neg \left(t \leq 6.2 \cdot 10^{+29}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

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 (<= t -8.4e-39)
   (+ 1.0 (* x (/ (/ -1.0 t) z)))
   (if (<= t 2.9e-124)
     (+ 1.0 (/ (/ x y) (- z y)))
     (if (or (<= t 860000000000.0) (not (<= t 6.2e+29)))
       (- 1.0 (/ x (* t (- z y))))
       (+ 1.0 (/ x (* y (- t y))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.4e-39) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else if (t <= 2.9e-124) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if ((t <= 860000000000.0) || !(t <= 6.2e+29)) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + (x / (y * (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 (t <= (-8.4d-39)) then
        tmp = 1.0d0 + (x * (((-1.0d0) / t) / z))
    else if (t <= 2.9d-124) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if ((t <= 860000000000.0d0) .or. (.not. (t <= 6.2d+29))) then
        tmp = 1.0d0 - (x / (t * (z - y)))
    else
        tmp = 1.0d0 + (x / (y * (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 (t <= -8.4e-39) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else if (t <= 2.9e-124) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if ((t <= 860000000000.0) || !(t <= 6.2e+29)) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -8.4e-39:
		tmp = 1.0 + (x * ((-1.0 / t) / z))
	elif t <= 2.9e-124:
		tmp = 1.0 + ((x / y) / (z - y))
	elif (t <= 860000000000.0) or not (t <= 6.2e+29):
		tmp = 1.0 - (x / (t * (z - y)))
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.4e-39)
		tmp = Float64(1.0 + Float64(x * Float64(Float64(-1.0 / t) / z)));
	elseif (t <= 2.9e-124)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif ((t <= 860000000000.0) || !(t <= 6.2e+29))
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(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 (t <= -8.4e-39)
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	elseif (t <= 2.9e-124)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif ((t <= 860000000000.0) || ~((t <= 6.2e+29)))
		tmp = 1.0 - (x / (t * (z - y)));
	else
		tmp = 1.0 + (x / (y * (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[LessEqual[t, -8.4e-39], N[(1.0 + N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-124], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 860000000000.0], N[Not[LessEqual[t, 6.2e+29]], $MachinePrecision]], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.39999999999999973e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.3%

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

      1. clear-num 78.4%

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

      2. inv-pow 78.4%

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

      3. *-commutative 78.4%

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

      4. associate-/l* 78.4%

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

   5. Applied egg-rr 78.4%

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

      1. unpow-1 78.4%

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

      2. associate-*r/ 78.4%

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

      3. *-commutative 78.4%

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

      4. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

      1. associate-/r* 77.0%

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

      2. associate-/r/ 78.4%

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

   9. Applied egg-rr 78.4%

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

   if -8.39999999999999973e-39 < t < 2.9000000000000002e-124

   1. Initial program 96.1%

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

   3. Taylor expanded in t around 0 80.7%

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

      1. associate-/r* 79.9%

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

   5. Simplified 79.9%

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

   if 2.9000000000000002e-124 < t < 8.6e11 or 6.1999999999999998e29 < t

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 96.1%

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

      1. associate-*r/ 96.1%

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

      2. neg-mul-1 96.1%

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

   5. Simplified 96.1%

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

   if 8.6e11 < t < 6.1999999999999998e29

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 74.9%

      \[\leadsto 1 - \color{blue}{\frac{x}{y \cdot \left(y - t\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-39}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;t \leq 860000000000 \lor \neg \left(t \leq 6.2 \cdot 10^{+29}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t - y}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-192}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-142}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-32}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

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 (<= t -2e-162)
   (+ 1.0 (* (/ x z) (/ -1.0 (- t y))))
   (if (<= t 2.2e-192)
     (+ 1.0 (/ (/ x y) (- z y)))
     (if (<= t 4.2e-142)
       (+ 1.0 (/ (/ x z) (- y t)))
       (if (<= t 3e-32)
         (+ 1.0 (/ (/ x y) (- t y)))
         (- 1.0 (/ x (* t (- z y)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e-162) {
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)));
	} else if (t <= 2.2e-192) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (t <= 4.2e-142) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 3e-32) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 - (x / (t * (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 (t <= (-2d-162)) then
        tmp = 1.0d0 + ((x / z) * ((-1.0d0) / (t - y)))
    else if (t <= 2.2d-192) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (t <= 4.2d-142) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 3d-32) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 - (x / (t * (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 (t <= -2e-162) {
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)));
	} else if (t <= 2.2e-192) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (t <= 4.2e-142) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 3e-32) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2e-162:
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)))
	elif t <= 2.2e-192:
		tmp = 1.0 + ((x / y) / (z - y))
	elif t <= 4.2e-142:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 3e-32:
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2e-162)
		tmp = Float64(1.0 + Float64(Float64(x / z) * Float64(-1.0 / Float64(t - y))));
	elseif (t <= 2.2e-192)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (t <= 4.2e-142)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 3e-32)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(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 (t <= -2e-162)
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)));
	elseif (t <= 2.2e-192)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (t <= 4.2e-142)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 3e-32)
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 - (x / (t * (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[t, -2e-162], N[(1.0 + N[(N[(x / z), $MachinePrecision] * N[(-1.0 / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-192], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-142], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-32], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.99999999999999991e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

      3. *-commutative 79.4%

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

   5. Simplified 79.4%

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

      1. neg-mul-1 79.4%

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

      2. times-frac 78.5%

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

   7. Applied egg-rr 78.5%

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

   if -1.99999999999999991e-162 < t < 2.20000000000000006e-192

   1. Initial program 93.4%

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

   3. Taylor expanded in t around 0 85.0%

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

      1. associate-/r* 85.2%

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

   5. Simplified 85.2%

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

   if 2.20000000000000006e-192 < t < 4.1999999999999999e-142

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac 100.0%

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

   5. Simplified 100.0%

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

   if 4.1999999999999999e-142 < t < 3e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 64.4%

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

      1. associate-/r* 64.8%

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

   5. Simplified 64.8%

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

   if 3e-32 < t

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 96.4%

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

      1. associate-*r/ 96.4%

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

      2. neg-mul-1 96.4%

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

   5. Simplified 96.4%

      \[\leadsto 1 - \color{blue}{\frac{-x}{t \cdot \left(y - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t - y}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-192}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-142}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-32}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-189}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-141}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-31}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

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 (<= t -4.3e-162)
   (- 1.0 (/ x (* z (- t y))))
   (if (<= t 1.4e-189)
     (+ 1.0 (/ (/ x y) (- z y)))
     (if (<= t 1.35e-141)
       (+ 1.0 (/ (/ x z) (- y t)))
       (if (<= t 1.86e-31)
         (+ 1.0 (/ (/ x y) (- t y)))
         (- 1.0 (/ x (* t (- z y)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.3e-162) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (t <= 1.4e-189) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (t <= 1.35e-141) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.86e-31) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 - (x / (t * (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 (t <= (-4.3d-162)) then
        tmp = 1.0d0 - (x / (z * (t - y)))
    else if (t <= 1.4d-189) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (t <= 1.35d-141) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.86d-31) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 - (x / (t * (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 (t <= -4.3e-162) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (t <= 1.4e-189) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (t <= 1.35e-141) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.86e-31) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.3e-162:
		tmp = 1.0 - (x / (z * (t - y)))
	elif t <= 1.4e-189:
		tmp = 1.0 + ((x / y) / (z - y))
	elif t <= 1.35e-141:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.86e-31:
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.3e-162)
		tmp = Float64(1.0 - Float64(x / Float64(z * Float64(t - y))));
	elseif (t <= 1.4e-189)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (t <= 1.35e-141)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.86e-31)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(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 (t <= -4.3e-162)
		tmp = 1.0 - (x / (z * (t - y)));
	elseif (t <= 1.4e-189)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (t <= 1.35e-141)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.86e-31)
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 - (x / (t * (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[t, -4.3e-162], N[(1.0 - N[(x / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-189], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-141], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.86e-31], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.29999999999999996e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

      3. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   if -4.29999999999999996e-162 < t < 1.4e-189

   1. Initial program 93.4%

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

   3. Taylor expanded in t around 0 85.0%

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

      1. associate-/r* 85.2%

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

   5. Simplified 85.2%

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

   if 1.4e-189 < t < 1.3500000000000001e-141

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac 100.0%

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

   5. Simplified 100.0%

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

   if 1.3500000000000001e-141 < t < 1.85999999999999995e-31

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 64.4%

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

      1. associate-/r* 64.8%

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

   5. Simplified 64.8%

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

   if 1.85999999999999995e-31 < t

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 96.4%

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

      1. associate-*r/ 96.4%

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

      2. neg-mul-1 96.4%

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

   5. Simplified 96.4%

      \[\leadsto 1 - \color{blue}{\frac{-x}{t \cdot \left(y - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-189}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-141}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-31}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-204}:\\ \;\;\;\;1 - \frac{1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.86 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

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 (<= y -1.45e-60)
   (+ 1.0 (/ (/ x y) (- z y)))
   (if (<= y -8e-204)
     (- 1.0 (/ 1.0 (* t (/ z x))))
     (if (<= y -1.86e-211)
       (/ x (* (- y z) t))
       (if (<= y 2.6e-188) (/ (- z (/ x t)) z) (+ 1.0 (/ x (* y (- t y)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-60) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (y <= -8e-204) {
		tmp = 1.0 - (1.0 / (t * (z / x)));
	} else if (y <= -1.86e-211) {
		tmp = x / ((y - z) * t);
	} else if (y <= 2.6e-188) {
		tmp = (z - (x / t)) / z;
	} else {
		tmp = 1.0 + (x / (y * (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 (y <= (-1.45d-60)) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (y <= (-8d-204)) then
        tmp = 1.0d0 - (1.0d0 / (t * (z / x)))
    else if (y <= (-1.86d-211)) then
        tmp = x / ((y - z) * t)
    else if (y <= 2.6d-188) then
        tmp = (z - (x / t)) / z
    else
        tmp = 1.0d0 + (x / (y * (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 (y <= -1.45e-60) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (y <= -8e-204) {
		tmp = 1.0 - (1.0 / (t * (z / x)));
	} else if (y <= -1.86e-211) {
		tmp = x / ((y - z) * t);
	} else if (y <= 2.6e-188) {
		tmp = (z - (x / t)) / z;
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-60:
		tmp = 1.0 + ((x / y) / (z - y))
	elif y <= -8e-204:
		tmp = 1.0 - (1.0 / (t * (z / x)))
	elif y <= -1.86e-211:
		tmp = x / ((y - z) * t)
	elif y <= 2.6e-188:
		tmp = (z - (x / t)) / z
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-60)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (y <= -8e-204)
		tmp = Float64(1.0 - Float64(1.0 / Float64(t * Float64(z / x))));
	elseif (y <= -1.86e-211)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (y <= 2.6e-188)
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(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 (y <= -1.45e-60)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (y <= -8e-204)
		tmp = 1.0 - (1.0 / (t * (z / x)));
	elseif (y <= -1.86e-211)
		tmp = x / ((y - z) * t);
	elseif (y <= 2.6e-188)
		tmp = (z - (x / t)) / z;
	else
		tmp = 1.0 + (x / (y * (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[LessEqual[y, -1.45e-60], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-204], N[(1.0 - N[(1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.86e-211], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-188], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.45e-60

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 90.3%

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

      1. associate-/r* 90.3%

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

   5. Simplified 90.3%

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

   if -1.45e-60 < y < -8.00000000000000001e-204

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 71.8%

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

      1. clear-num 71.8%

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

      2. inv-pow 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-/l* 69.7%

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

   5. Applied egg-rr 69.7%

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

      1. unpow-1 69.7%

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

      2. associate-*r/ 71.8%

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

      3. *-commutative 71.8%

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

      4. associate-/l* 69.6%

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

   7. Simplified 69.6%

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

   if -8.00000000000000001e-204 < y < -1.85999999999999993e-211

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 61.0%

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

      1. associate-*r/ 61.0%

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

      2. neg-mul-1 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in x around inf 61.0%

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

   if -1.85999999999999993e-211 < y < 2.6000000000000001e-188

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 85.2%

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

   4. Taylor expanded in z around 0 83.4%

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

   if 2.6000000000000001e-188 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 80.3%

      \[\leadsto 1 - \color{blue}{\frac{x}{y \cdot \left(y - t\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-60}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-204}:\\ \;\;\;\;1 - \frac{1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.86 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-211}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* y (- t y))))))
   (if (<= y -1.85e-59)
     t_1
     (if (<= y -9.6e-211)
       (- 1.0 (/ x (* z t)))
       (if (<= y 3.5e-188) (/ (- z (/ x t)) z) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (y * (t - y)));
	double tmp;
	if (y <= -1.85e-59) {
		tmp = t_1;
	} else if (y <= -9.6e-211) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 3.5e-188) {
		tmp = (z - (x / t)) / z;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (x / (y * (t - y)))
    if (y <= (-1.85d-59)) then
        tmp = t_1
    else if (y <= (-9.6d-211)) then
        tmp = 1.0d0 - (x / (z * t))
    else if (y <= 3.5d-188) then
        tmp = (z - (x / t)) / z
    else
        tmp = t_1
    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 t_1 = 1.0 + (x / (y * (t - y)));
	double tmp;
	if (y <= -1.85e-59) {
		tmp = t_1;
	} else if (y <= -9.6e-211) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 3.5e-188) {
		tmp = (z - (x / t)) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + (x / (y * (t - y)))
	tmp = 0
	if y <= -1.85e-59:
		tmp = t_1
	elif y <= -9.6e-211:
		tmp = 1.0 - (x / (z * t))
	elif y <= 3.5e-188:
		tmp = (z - (x / t)) / z
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))))
	tmp = 0.0
	if (y <= -1.85e-59)
		tmp = t_1;
	elseif (y <= -9.6e-211)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (y <= 3.5e-188)
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (x / (y * (t - y)));
	tmp = 0.0;
	if (y <= -1.85e-59)
		tmp = t_1;
	elseif (y <= -9.6e-211)
		tmp = 1.0 - (x / (z * t));
	elseif (y <= 3.5e-188)
		tmp = (z - (x / t)) / z;
	else
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-59], t$95$1, If[LessEqual[y, -9.6e-211], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-188], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85e-59 or 3.5e-188 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 86.4%

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

   if -1.85e-59 < y < -9.6000000000000008e-211

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 70.0%

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

   if -9.6000000000000008e-211 < y < 3.5e-188

   1. Initial program 91.7%

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

   3. Taylor expanded in y around 0 83.4%

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

   4. Taylor expanded in z around 0 81.7%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-59}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-211}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+178}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+171}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+201}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

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 (<= x -1.9e+178)
   (+ 1.0 (* x (/ (/ -1.0 t) z)))
   (if (<= x 7.5e+171)
     1.0
     (if (<= x 3e+201) (+ 1.0 (/ x (* y t))) (- 1.0 (/ (/ x y) y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e+178) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else if (x <= 7.5e+171) {
		tmp = 1.0;
	} else if (x <= 3e+201) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / y) / 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 (x <= (-1.9d+178)) then
        tmp = 1.0d0 + (x * (((-1.0d0) / t) / z))
    else if (x <= 7.5d+171) then
        tmp = 1.0d0
    else if (x <= 3d+201) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0 - ((x / y) / 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 (x <= -1.9e+178) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else if (x <= 7.5e+171) {
		tmp = 1.0;
	} else if (x <= 3e+201) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if x <= -1.9e+178:
		tmp = 1.0 + (x * ((-1.0 / t) / z))
	elif x <= 7.5e+171:
		tmp = 1.0
	elif x <= 3e+201:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.9e+178)
		tmp = Float64(1.0 + Float64(x * Float64(Float64(-1.0 / t) / z)));
	elseif (x <= 7.5e+171)
		tmp = 1.0;
	elseif (x <= 3e+201)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / 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 (x <= -1.9e+178)
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	elseif (x <= 7.5e+171)
		tmp = 1.0;
	elseif (x <= 3e+201)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 - ((x / y) / 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[x, -1.9e+178], N[(1.0 + N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+171], 1.0, If[LessEqual[x, 3e+201], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.89999999999999999e178

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 61.2%

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

      1. clear-num 61.2%

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

      2. inv-pow 61.2%

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

      3. *-commutative 61.2%

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

      4. associate-/l* 53.6%

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

   5. Applied egg-rr 53.6%

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

      1. unpow-1 53.6%

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

      2. associate-*r/ 61.2%

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

      3. *-commutative 61.2%

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

      4. associate-/l* 58.5%

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

   7. Simplified 58.5%

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

      1. associate-/r* 58.6%

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

      2. associate-/r/ 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -1.89999999999999999e178 < x < 7.4999999999999998e171

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 65.2%

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

   4. Taylor expanded in x around 0 82.6%

      \[\leadsto \color{blue}{1} \]

   if 7.4999999999999998e171 < x < 3.00000000000000025e201

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 60.2%

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

      1. associate-*r/ 60.2%

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

      2. neg-mul-1 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in y around inf 60.0%

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

      1. *-commutative 60.0%

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

   8. Simplified 60.0%

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

   if 3.00000000000000025e201 < x

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

      3. associate-/l* 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 85.7%

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

      1. *-rgt-identity 85.7%

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

      2. times-frac 79.8%

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

      3. associate-*l/ 85.7%

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

      4. associate-*r/ 85.8%

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

      5. *-rgt-identity 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in y around inf 61.2%

      \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+178}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+171}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+201}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+179}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+171}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+197}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

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 (<= x -2.1e+179)
   (- 1.0 (/ x (* z t)))
   (if (<= x 3.6e+171)
     1.0
     (if (<= x 2.65e+197) (+ 1.0 (/ x (* y t))) (- 1.0 (/ (/ x y) y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.1e+179) {
		tmp = 1.0 - (x / (z * t));
	} else if (x <= 3.6e+171) {
		tmp = 1.0;
	} else if (x <= 2.65e+197) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / y) / 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 (x <= (-2.1d+179)) then
        tmp = 1.0d0 - (x / (z * t))
    else if (x <= 3.6d+171) then
        tmp = 1.0d0
    else if (x <= 2.65d+197) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0 - ((x / y) / 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 (x <= -2.1e+179) {
		tmp = 1.0 - (x / (z * t));
	} else if (x <= 3.6e+171) {
		tmp = 1.0;
	} else if (x <= 2.65e+197) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if x <= -2.1e+179:
		tmp = 1.0 - (x / (z * t))
	elif x <= 3.6e+171:
		tmp = 1.0
	elif x <= 2.65e+197:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.1e+179)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (x <= 3.6e+171)
		tmp = 1.0;
	elseif (x <= 2.65e+197)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / 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 (x <= -2.1e+179)
		tmp = 1.0 - (x / (z * t));
	elseif (x <= 3.6e+171)
		tmp = 1.0;
	elseif (x <= 2.65e+197)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 - ((x / y) / 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[x, -2.1e+179], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+171], 1.0, If[LessEqual[x, 2.65e+197], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.0999999999999999e179

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 61.2%

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

   if -2.0999999999999999e179 < x < 3.60000000000000018e171

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 65.2%

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

   4. Taylor expanded in x around 0 82.6%

      \[\leadsto \color{blue}{1} \]

   if 3.60000000000000018e171 < x < 2.6500000000000001e197

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 60.2%

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

      1. associate-*r/ 60.2%

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

      2. neg-mul-1 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in y around inf 60.0%

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

      1. *-commutative 60.0%

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

   8. Simplified 60.0%

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

   if 2.6500000000000001e197 < x

   1. Initial program 99.6%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

      3. associate-/l* 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 85.7%

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

      1. *-rgt-identity 85.7%

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

      2. times-frac 79.8%

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

      3. associate-*l/ 85.7%

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

      4. associate-*r/ 85.8%

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

      5. *-rgt-identity 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in y around inf 61.2%

      \[\leadsto 1 - \frac{\color{blue}{\frac{x}{y}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+179}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+171}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+197}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

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 (<= t -3e-162)
   (- 1.0 (/ x (* z (- t y))))
   (if (<= t 3.2e-124)
     (+ 1.0 (/ (/ x y) (- z y)))
     (- 1.0 (/ x (* t (- z y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e-162) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (t <= 3.2e-124) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else {
		tmp = 1.0 - (x / (t * (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 (t <= (-3d-162)) then
        tmp = 1.0d0 - (x / (z * (t - y)))
    else if (t <= 3.2d-124) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else
        tmp = 1.0d0 - (x / (t * (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 (t <= -3e-162) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (t <= 3.2e-124) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3e-162:
		tmp = 1.0 - (x / (z * (t - y)))
	elif t <= 3.2e-124:
		tmp = 1.0 + ((x / y) / (z - y))
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3e-162)
		tmp = Float64(1.0 - Float64(x / Float64(z * Float64(t - y))));
	elseif (t <= 3.2e-124)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(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 (t <= -3e-162)
		tmp = 1.0 - (x / (z * (t - y)));
	elseif (t <= 3.2e-124)
		tmp = 1.0 + ((x / y) / (z - y));
	else
		tmp = 1.0 - (x / (t * (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[t, -3e-162], N[(1.0 - N[(x / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-124], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.99999999999999999e-162

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

      3. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   if -2.99999999999999999e-162 < t < 3.20000000000000004e-124

   1. Initial program 94.4%

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

   3. Taylor expanded in t around 0 86.3%

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

      1. associate-/r* 85.1%

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

   5. Simplified 85.1%

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

   if 3.20000000000000004e-124 < t

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 93.6%

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

      1. associate-*r/ 93.6%

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

      2. neg-mul-1 93.6%

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

   5. Simplified 93.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-124}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+180}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+170}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 (<= x -2.2e+180)
   (- 1.0 (/ x (* z t)))
   (if (<= x 6.8e+170) 1.0 (+ 1.0 (/ x (* y t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e+180) {
		tmp = 1.0 - (x / (z * t));
	} else if (x <= 6.8e+170) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (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 (x <= (-2.2d+180)) then
        tmp = 1.0d0 - (x / (z * t))
    else if (x <= 6.8d+170) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + (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 (x <= -2.2e+180) {
		tmp = 1.0 - (x / (z * t));
	} else if (x <= 6.8e+170) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e+180:
		tmp = 1.0 - (x / (z * t))
	elif x <= 6.8e+170:
		tmp = 1.0
	else:
		tmp = 1.0 + (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 (x <= -2.2e+180)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (x <= 6.8e+170)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + 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 (x <= -2.2e+180)
		tmp = 1.0 - (x / (z * t));
	elseif (x <= 6.8e+170)
		tmp = 1.0;
	else
		tmp = 1.0 + (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[x, -2.2e+180], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+170], 1.0, N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1999999999999999e180

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 61.2%

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

   if -2.1999999999999999e180 < x < 6.8000000000000003e170

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 65.2%

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

   4. Taylor expanded in x around 0 82.6%

      \[\leadsto \color{blue}{1} \]

   if 6.8000000000000003e170 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 53.8%

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

      1. associate-*r/ 53.8%

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

      2. neg-mul-1 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

   8. Simplified 45.5%

      \[\leadsto \color{blue}{1 + \frac{x}{y \cdot t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+180}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+170}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;x \leq 10^{+172}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 (<= x -1.35e+174)
   (* x (/ (/ -1.0 t) z))
   (if (<= x 1e+172) 1.0 (+ 1.0 (/ x (* y t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e+174) {
		tmp = x * ((-1.0 / t) / z);
	} else if (x <= 1e+172) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (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 (x <= (-1.35d+174)) then
        tmp = x * (((-1.0d0) / t) / z)
    else if (x <= 1d+172) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + (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 (x <= -1.35e+174) {
		tmp = x * ((-1.0 / t) / z);
	} else if (x <= 1e+172) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e+174:
		tmp = x * ((-1.0 / t) / z)
	elif x <= 1e+172:
		tmp = 1.0
	else:
		tmp = 1.0 + (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 (x <= -1.35e+174)
		tmp = Float64(x * Float64(Float64(-1.0 / t) / z));
	elseif (x <= 1e+172)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + 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 (x <= -1.35e+174)
		tmp = x * ((-1.0 / t) / z);
	elseif (x <= 1e+172)
		tmp = 1.0;
	else
		tmp = 1.0 + (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[x, -1.35e+174], N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+172], 1.0, N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e174

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 60.5%

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

   4. Taylor expanded in x around inf 43.1%

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

      1. associate-*r/ 43.1%

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

      2. mul-1-neg 43.1%

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

   6. Simplified 43.1%

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

      1. add-sqr-sqrt 43.0%

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

      2. sqrt-unprod 18.6%

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

      3. sqr-neg 18.6%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 4.9%

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

      6. frac-2neg 4.9%

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

      7. distribute-lft-neg-in 4.9%

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

      8. associate-/l/ 5.1%

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

      9. div-inv 5.1%

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

      10. associate-/l* 5.0%

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

      11. add-sqr-sqrt 5.0%

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

      12. sqrt-unprod 4.2%

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

      13. sqr-neg 4.2%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 43.2%

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

   8. Applied egg-rr 43.2%

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

   9. Taylor expanded in z around 0 43.0%

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

       1. associate-/r* 43.2%

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

   11. Simplified 43.2%

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

   if -1.35e174 < x < 1.0000000000000001e172

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 65.4%

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

   4. Taylor expanded in x around 0 83.4%

      \[\leadsto \color{blue}{1} \]

   if 1.0000000000000001e172 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 53.8%

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

      1. associate-*r/ 53.8%

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

      2. neg-mul-1 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

   8. Simplified 45.5%

      \[\leadsto \color{blue}{1 + \frac{x}{y \cdot t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 - \frac{1}{y - z} \cdot \frac{x}{y - t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (- 1.0 (* (/ 1.0 (- y z)) (/ x (- y t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 - ((1.0 / (y - z)) * (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 = 1.0d0 - ((1.0d0 / (y - z)) * (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 1.0 - ((1.0 / (y - z)) * (x / (y - t)));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - ((1.0 / (y - z)) * (x / (y - t)))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 - Float64(Float64(1.0 / Float64(y - z)) * 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 = 1.0 - ((1.0 / (y - z)) * (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[(1.0 - N[(N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

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

   1. *-un-lft-identity 98.3%

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

   2. times-frac 97.4%

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

4. Applied egg-rr 97.4%

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

Alternative 14: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= x -1.35e+174) (* x (/ (/ -1.0 t) z)) 1.0))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e+174) {
		tmp = x * ((-1.0 / t) / z);
	} else {
		tmp = 1.0;
	}
	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 (x <= (-1.35d+174)) then
        tmp = x * (((-1.0d0) / t) / z)
    else
        tmp = 1.0d0
    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 (x <= -1.35e+174) {
		tmp = x * ((-1.0 / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e+174:
		tmp = x * ((-1.0 / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e+174)
		tmp = Float64(x * Float64(Float64(-1.0 / t) / z));
	else
		tmp = 1.0;
	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 (x <= -1.35e+174)
		tmp = x * ((-1.0 / t) / z);
	else
		tmp = 1.0;
	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[x, -1.35e+174], N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e174

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 60.5%

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

   4. Taylor expanded in x around inf 43.1%

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

      1. associate-*r/ 43.1%

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

      2. mul-1-neg 43.1%

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

   6. Simplified 43.1%

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

      1. add-sqr-sqrt 43.0%

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

      2. sqrt-unprod 18.6%

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

      3. sqr-neg 18.6%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 4.9%

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

      6. frac-2neg 4.9%

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

      7. distribute-lft-neg-in 4.9%

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

      8. associate-/l/ 5.1%

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

      9. div-inv 5.1%

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

      10. associate-/l* 5.0%

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

      11. add-sqr-sqrt 5.0%

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

      12. sqrt-unprod 4.2%

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

      13. sqr-neg 4.2%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 43.2%

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

   8. Applied egg-rr 43.2%

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

   9. Taylor expanded in z around 0 43.0%

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

       1. associate-/r* 43.2%

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

   11. Simplified 43.2%

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

   if -1.35e174 < x

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 60.7%

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

   4. Taylor expanded in x around 0 77.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= x -1.35e+174) (/ x (* t (- z))) 1.0))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e+174) {
		tmp = x / (t * -z);
	} else {
		tmp = 1.0;
	}
	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 (x <= (-1.35d+174)) then
        tmp = x / (t * -z)
    else
        tmp = 1.0d0
    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 (x <= -1.35e+174) {
		tmp = x / (t * -z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e+174:
		tmp = x / (t * -z)
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e+174)
		tmp = Float64(x / Float64(t * Float64(-z)));
	else
		tmp = 1.0;
	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 (x <= -1.35e+174)
		tmp = x / (t * -z);
	else
		tmp = 1.0;
	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[x, -1.35e+174], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e174

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 60.5%

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

   4. Taylor expanded in x around inf 43.1%

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

      1. associate-*r/ 43.1%

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

      2. mul-1-neg 43.1%

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

   6. Simplified 43.1%

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

   if -1.35e174 < x

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 60.7%

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

   4. Taylor expanded in x around 0 77.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (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 = 1.0d0 - (x / ((y - z) * (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 1.0 - (x / ((y - z) * (y - t)));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / ((y - z) * (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[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

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

Alternative 17: 74.7% accurate, 11.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 1.0)

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0;
}

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 = 1.0d0
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return 1.0
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in y around 0 60.6%

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

4. Taylor expanded in x around 0 71.7%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))