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

Percentage Accurate: 99.0% → 98.7%

Time: 8.9s

Alternatives: 14

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

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

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 (* (- y z) (/ (- y t) 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(((y - z) * ((y - t) / 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 - (((y - z) * ((y - t) / 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(((y - z) * ((y - t) / x)), -1.0);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - math.pow(((y - z) * ((y - t) / 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(y - z) * Float64(Float64(y - t) / 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 - (((y - z) * ((y - t) / 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[(y - z), $MachinePrecision] * N[(N[(y - t), $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. Add Preprocessing

Alternative 2: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-67} \lor \neg \left(y \leq 3.5 \cdot 10^{-150}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e-67) (not (<= y 3.5e-150)))
   (+ 1.0 (/ x (* y (- t y))))
   (- 1.0 (/ x (* z t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-67) || !(y <= 3.5e-150)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5d-67)) .or. (.not. (y <= 3.5d-150))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-67) || !(y <= 3.5e-150)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -5e-67) or not (y <= 3.5e-150):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e-67) || !(y <= 3.5e-150))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5e-67) || ~((y <= 3.5e-150)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e-67], N[Not[LessEqual[y, 3.5e-150]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999999e-67 or 3.4999999999999998e-150 < 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 90.2%

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

   if -4.9999999999999999e-67 < y < 3.4999999999999998e-150

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 78.2%

      \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-67} \lor \neg \left(y \leq 3.5 \cdot 10^{-150}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t - y}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-57}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

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 -2e-162)
   (+ 1.0 (* (/ x z) (/ -1.0 (- t y))))
   (if (<= t 2.05e-57)
     (+ 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 <= -2e-162) {
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)));
	} else if (t <= 2.05e-57) {
		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 <= (-2d-162)) then
        tmp = 1.0d0 + ((x / z) * ((-1.0d0) / (t - y)))
    else if (t <= 2.05d-57) 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 <= -2e-162) {
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)));
	} else if (t <= 2.05e-57) {
		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 <= -2e-162:
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)))
	elif t <= 2.05e-57:
		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 <= -2e-162)
		tmp = Float64(1.0 + Float64(Float64(x / z) * Float64(-1.0 / Float64(t - y))));
	elseif (t <= 2.05e-57)
		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 <= -2e-162)
		tmp = 1.0 + ((x / z) * (-1.0 / (t - y)));
	elseif (t <= 2.05e-57)
		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, -2e-162], N[(1.0 + N[(N[(x / z), $MachinePrecision] * N[(-1.0 / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e-57], 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 < -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 < 2.0500000000000001e-57

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 84.5%

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

      1. associate-/r* 83.6%

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

   5. Simplified 83.6%

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

   if 2.0500000000000001e-57 < 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 95.3%

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

      1. associate-*r/ 95.3%

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

      2. neg-mul-1 95.3%

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

   5. Simplified 95.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-162}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t - y}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-57}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-57}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

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 -7.8e-162)
   (- 1.0 (/ x (* z (- t y))))
   (if (<= t 2.2e-57)
     (+ 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 <= -7.8e-162) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (t <= 2.2e-57) {
		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 <= (-7.8d-162)) then
        tmp = 1.0d0 - (x / (z * (t - y)))
    else if (t <= 2.2d-57) 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 <= -7.8e-162) {
		tmp = 1.0 - (x / (z * (t - y)));
	} else if (t <= 2.2e-57) {
		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 <= -7.8e-162:
		tmp = 1.0 - (x / (z * (t - y)))
	elif t <= 2.2e-57:
		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 <= -7.8e-162)
		tmp = Float64(1.0 - Float64(x / Float64(z * Float64(t - y))));
	elseif (t <= 2.2e-57)
		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 <= -7.8e-162)
		tmp = 1.0 - (x / (z * (t - y)));
	elseif (t <= 2.2e-57)
		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, -7.8e-162], N[(1.0 - N[(x / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-57], 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 < -7.7999999999999999e-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 79.2%

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

      1. associate-*r/ 79.2%

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

      2. neg-mul-1 79.2%

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

      3. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -7.7999999999999999e-162 < t < 2.19999999999999999e-57

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 84.7%

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

      1. associate-/r* 83.8%

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

   5. Simplified 83.8%

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

   if 2.19999999999999999e-57 < 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 95.3%

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

      1. associate-*r/ 95.3%

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

      2. neg-mul-1 95.3%

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

   5. Simplified 95.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-57}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-81}:\\ \;\;\;\;1 - x \cdot \frac{\frac{1}{t}}{z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-57}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

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 -4.5e-81)
   (- 1.0 (* x (/ (/ 1.0 t) z)))
   (if (<= t 6e-57) (+ 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 <= -4.5e-81) {
		tmp = 1.0 - (x * ((1.0 / t) / z));
	} else if (t <= 6e-57) {
		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 <= (-4.5d-81)) then
        tmp = 1.0d0 - (x * ((1.0d0 / t) / z))
    else if (t <= 6d-57) 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 <= -4.5e-81) {
		tmp = 1.0 - (x * ((1.0 / t) / z));
	} else if (t <= 6e-57) {
		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 <= -4.5e-81:
		tmp = 1.0 - (x * ((1.0 / t) / z))
	elif t <= 6e-57:
		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 <= -4.5e-81)
		tmp = Float64(1.0 - Float64(x * Float64(Float64(1.0 / t) / z)));
	elseif (t <= 6e-57)
		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 <= -4.5e-81)
		tmp = 1.0 - (x * ((1.0 / t) / z));
	elseif (t <= 6e-57)
		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, -4.5e-81], N[(1.0 - N[(x * N[(N[(1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-57], 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 < -4.5e-81

   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 75.0%

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

      1. clear-num 75.1%

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

      2. inv-pow 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-/l* 72.9%

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

   5. Applied egg-rr 72.9%

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

      1. unpow-1 72.9%

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

      2. associate-*r/ 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

      1. associate-/r* 73.9%

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

      2. associate-/r/ 75.1%

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

   9. Applied egg-rr 75.1%

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

   if -4.5e-81 < t < 6.00000000000000001e-57

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0 82.4%

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

      1. associate-/r* 81.7%

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

   5. Simplified 81.7%

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

   if 6.00000000000000001e-57 < 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 95.3%

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

      1. associate-*r/ 95.3%

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

      2. neg-mul-1 95.3%

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

   5. Simplified 95.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-81}:\\ \;\;\;\;1 - x \cdot \frac{\frac{1}{t}}{z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-57}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-150}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

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 -8.6e-60)
   (+ 1.0 (/ (/ x y) (- z y)))
   (if (<= y 6.6e-150) (- 1.0 (/ x (* z t))) (- 1.0 (/ x (* y (- y t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.6e-60) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (y <= 6.6e-150) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - (x / (y * (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 (y <= (-8.6d-60)) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (y <= 6.6d-150) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 - (x / (y * (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 (y <= -8.6e-60) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (y <= 6.6e-150) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - (x / (y * (y - t)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -8.6e-60:
		tmp = 1.0 + ((x / y) / (z - y))
	elif y <= 6.6e-150:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 - (x / (y * (y - t)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.6e-60)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (y <= 6.6e-150)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * 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 (y <= -8.6e-60)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (y <= 6.6e-150)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 - (x / (y * (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[y, -8.6e-60], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-150], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.6000000000000001e-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 -8.6000000000000001e-60 < y < 6.6000000000000003e-150

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0 78.1%

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

   if 6.6000000000000003e-150 < 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 89.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-150}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-46}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e-101)
   (+ 1.0 (/ x (* y (- z y))))
   (if (<= z 7.2e-46) (- 1.0 (/ x (* y (- y t)))) (/ (- z (/ x t)) z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e-101) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (z <= 7.2e-46) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = (z - (x / t)) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.5d-101)) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else if (z <= 7.2d-46) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = (z - (x / t)) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e-101) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else if (z <= 7.2e-46) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = (z - (x / t)) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e-101:
		tmp = 1.0 + (x / (y * (z - y)))
	elif z <= 7.2e-46:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = (z - (x / t)) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e-101)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	elseif (z <= 7.2e-46)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e-101)
		tmp = 1.0 + (x / (y * (z - y)));
	elseif (z <= 7.2e-46)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = (z - (x / t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e-101], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-46], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000002e-101

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0 77.6%

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

   if -1.5000000000000002e-101 < z < 7.2e-46

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0 87.1%

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

   if 7.2e-46 < z

   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 78.8%

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

   4. Taylor expanded in z around 0 75.7%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-46}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-64}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= y -4.5e-79) 1.0 (if (<= y 7e-64) (/ (- z (/ 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 (y <= -4.5e-79) {
		tmp = 1.0;
	} else if (y <= 7e-64) {
		tmp = (z - (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 (y <= (-4.5d-79)) then
        tmp = 1.0d0
    else if (y <= 7d-64) then
        tmp = (z - (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 (y <= -4.5e-79) {
		tmp = 1.0;
	} else if (y <= 7e-64) {
		tmp = (z - (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 y <= -4.5e-79:
		tmp = 1.0
	elif y <= 7e-64:
		tmp = (z - (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 (y <= -4.5e-79)
		tmp = 1.0;
	elseif (y <= 7e-64)
		tmp = Float64(Float64(z - Float64(x / 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 (y <= -4.5e-79)
		tmp = 1.0;
	elseif (y <= 7e-64)
		tmp = (z - (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[y, -4.5e-79], 1.0, If[LessEqual[y, 7e-64], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000003e-79 or 7.0000000000000006e-64 < 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 y around 0 51.1%

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

   4. Taylor expanded in x around 0 86.4%

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

   if -4.5000000000000003e-79 < y < 7.0000000000000006e-64

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 73.3%

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

   4. Taylor expanded in z around 0 71.1%

      \[\leadsto \color{blue}{\frac{z - \frac{x}{t}}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= y -7e-67) 1.0 (if (<= y 1.05e-60) (- 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 (y <= -7e-67) {
		tmp = 1.0;
	} else if (y <= 1.05e-60) {
		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 (y <= (-7d-67)) then
        tmp = 1.0d0
    else if (y <= 1.05d-60) 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 (y <= -7e-67) {
		tmp = 1.0;
	} else if (y <= 1.05e-60) {
		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 y <= -7e-67:
		tmp = 1.0
	elif y <= 1.05e-60:
		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 (y <= -7e-67)
		tmp = 1.0;
	elseif (y <= 1.05e-60)
		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 (y <= -7e-67)
		tmp = 1.0;
	elseif (y <= 1.05e-60)
		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[y, -7e-67], 1.0, If[LessEqual[y, 1.05e-60], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000001e-67 or 1.04999999999999996e-60 < 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 y around 0 50.1%

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

   4. Taylor expanded in x around 0 86.6%

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

   if -7.0000000000000001e-67 < y < 1.04999999999999996e-60

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 73.6%

      \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+171}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 (* t (- z)))
   (if (<= x 3.6e+171) 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 / (t * -z);
	} else if (x <= 3.6e+171) {
		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 / (t * -z)
    else if (x <= 3.6d+171) 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 / (t * -z);
	} else if (x <= 3.6e+171) {
		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 / (t * -z)
	elif x <= 3.6e+171:
		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(t * Float64(-z)));
	elseif (x <= 3.6e+171)
		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 / (t * -z);
	elseif (x <= 3.6e+171)
		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[(t * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+171], 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%

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

   if -1.35e174 < 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 65.4%

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

   4. Taylor expanded in x around 0 83.4%

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

   if 3.60000000000000018e171 < 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 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+171}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.5% accurate, 0.8× speedup

Math

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

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

C

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

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 - t)) * (1.0d0 / (z - y)))
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 - t)) * (1.0 / (z - y)));
}

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 + ((x / (y - t)) * (1.0 / (z - y)));
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[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z - y), $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. Final simplification 97.4%

   \[\leadsto 1 + \frac{x}{y - t} \cdot \frac{1}{z - y} \]
6. Add Preprocessing

Alternative 12: 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 13: 99.0% accurate, 1.0× speedup

Math

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

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) (- t y)))))

C

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

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) * (t - y)))
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) * (t - y)));
}

Python

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

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(t - y))))
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) * (t - y)));
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[(t - y), $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. Final simplification 98.3%

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

Alternative 14: 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)))))