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

Percentage Accurate: 99.0% → 98.6%

Time: 10.6s

Alternatives: 11

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: 98.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.7%

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

   1. associate-/r* 98.5%

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

   2. div-inv 98.5%

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

4. Applied egg-rr 98.5%

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

5. Final simplification 98.5%

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

Alternative 2: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-104}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x}{t}}{y} + 1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{z}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -2.6e-77)
   1.0
   (if (<= y 2.6e-104)
     (- 1.0 (/ (/ x z) t))
     (if (<= y 4.4e-39)
       (+ (/ (/ x t) y) 1.0)
       (if (<= y 5.5e+65) (+ (/ (/ x z) y) 1.0) 1.0)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-77) {
		tmp = 1.0;
	} else if (y <= 2.6e-104) {
		tmp = 1.0 - ((x / z) / t);
	} else if (y <= 4.4e-39) {
		tmp = ((x / t) / y) + 1.0;
	} else if (y <= 5.5e+65) {
		tmp = ((x / z) / y) + 1.0;
	} 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 <= (-2.6d-77)) then
        tmp = 1.0d0
    else if (y <= 2.6d-104) then
        tmp = 1.0d0 - ((x / z) / t)
    else if (y <= 4.4d-39) then
        tmp = ((x / t) / y) + 1.0d0
    else if (y <= 5.5d+65) then
        tmp = ((x / z) / y) + 1.0d0
    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 <= -2.6e-77) {
		tmp = 1.0;
	} else if (y <= 2.6e-104) {
		tmp = 1.0 - ((x / z) / t);
	} else if (y <= 4.4e-39) {
		tmp = ((x / t) / y) + 1.0;
	} else if (y <= 5.5e+65) {
		tmp = ((x / z) / y) + 1.0;
	} 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 <= -2.6e-77:
		tmp = 1.0
	elif y <= 2.6e-104:
		tmp = 1.0 - ((x / z) / t)
	elif y <= 4.4e-39:
		tmp = ((x / t) / y) + 1.0
	elif y <= 5.5e+65:
		tmp = ((x / z) / y) + 1.0
	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 <= -2.6e-77)
		tmp = 1.0;
	elseif (y <= 2.6e-104)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	elseif (y <= 4.4e-39)
		tmp = Float64(Float64(Float64(x / t) / y) + 1.0);
	elseif (y <= 5.5e+65)
		tmp = Float64(Float64(Float64(x / z) / y) + 1.0);
	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 <= -2.6e-77)
		tmp = 1.0;
	elseif (y <= 2.6e-104)
		tmp = 1.0 - ((x / z) / t);
	elseif (y <= 4.4e-39)
		tmp = ((x / t) / y) + 1.0;
	elseif (y <= 5.5e+65)
		tmp = ((x / z) / y) + 1.0;
	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, -2.6e-77], 1.0, If[LessEqual[y, 2.6e-104], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-39], N[(N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[y, 5.5e+65], N[(N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6000000000000001e-77 or 5.4999999999999996e65 < y

   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 45.1%

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

      1. frac-2neg 45.1%

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

      2. neg-sub0 45.1%

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

      3. div-sub 44.8%

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

      4. *-commutative 44.8%

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

      5. distribute-rgt-neg-in 44.8%

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

      6. add-sqr-sqrt 21.8%

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

      7. sqrt-unprod 45.0%

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

      8. sqr-neg 45.0%

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

      9. sqrt-unprod 22.9%

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

      10. add-sqr-sqrt 44.6%

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

      11. frac-2neg 44.6%

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

      12. *-commutative 44.6%

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

   5. Applied egg-rr 44.6%

      \[\leadsto 1 - \color{blue}{\left(\frac{0}{z \cdot \left(-t\right)} - \frac{x}{z \cdot t}\right)} \]
   6. Step-by-step derivation

      1. div0 44.9%

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

      2. neg-sub0 44.9%

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

      3. distribute-neg-frac2 44.9%

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

      4. distribute-rgt-neg-out 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in x around 0 96.4%

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

   if -2.6000000000000001e-77 < y < 2.60000000000000003e-104

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 81.4%

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

      1. associate-/r* 82.5%

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

      2. div-inv 82.5%

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

   5. Applied egg-rr 82.5%

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

      1. associate-*l/ 82.5%

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

      2. div-inv 82.5%

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

   7. Applied egg-rr 82.5%

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

   if 2.60000000000000003e-104 < y < 4.40000000000000002e-39

   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 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-/r* 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in y around 0 61.3%

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

      1. mul-1-neg 61.3%

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

      2. distribute-neg-frac2 61.3%

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

   8. Simplified 61.3%

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

   if 4.40000000000000002e-39 < y < 5.4999999999999996e65

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/r* 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in y around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. distribute-neg-frac2 65.0%

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

   8. Simplified 65.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-104}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x}{t}}{y} + 1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{z}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-67} \lor \neg \left(y \leq 1.7 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(t - y\right)} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.6e-67) (not (<= y 1.7e-124)))
   (+ (/ x (* y (- t y))) 1.0)
   (- 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 <= -7.6e-67) || !(y <= 1.7e-124)) {
		tmp = (x / (y * (t - y))) + 1.0;
	} 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 <= (-7.6d-67)) .or. (.not. (y <= 1.7d-124))) then
        tmp = (x / (y * (t - y))) + 1.0d0
    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 <= -7.6e-67) || !(y <= 1.7e-124)) {
		tmp = (x / (y * (t - y))) + 1.0;
	} 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 <= -7.6e-67) or not (y <= 1.7e-124):
		tmp = (x / (y * (t - y))) + 1.0
	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 <= -7.6e-67) || !(y <= 1.7e-124))
		tmp = Float64(Float64(x / Float64(y * Float64(t - y))) + 1.0);
	else
		tmp = Float64(1.0 - Float64(Float64(x / 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 <= -7.6e-67) || ~((y <= 1.7e-124)))
		tmp = (x / (y * (t - y))) + 1.0;
	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, -7.6e-67], N[Not[LessEqual[y, 1.7e-124]], $MachinePrecision]], N[(N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.59999999999999976e-67 or 1.7e-124 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.2%

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

   if -7.59999999999999976e-67 < y < 1.7e-124

   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 81.0%

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

      1. associate-/r* 82.0%

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

      2. div-inv 82.0%

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

   5. Applied egg-rr 82.0%

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

      1. associate-*l/ 82.1%

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

      2. div-inv 82.1%

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

   7. Applied egg-rr 82.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-67} \lor \neg \left(y \leq 1.7 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(t - y\right)} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-79}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - y\right)} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 (<= z -3.5e-79)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= z 9.6e-91) (+ (/ x (* y (- t y))) 1.0) (- 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 (z <= -3.5e-79) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 9.6e-91) {
		tmp = (x / (y * (t - y))) + 1.0;
	} 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 (z <= (-3.5d-79)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (z <= 9.6d-91) then
        tmp = (x / (y * (t - y))) + 1.0d0
    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 (z <= -3.5e-79) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 9.6e-91) {
		tmp = (x / (y * (t - y))) + 1.0;
	} 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 z <= -3.5e-79:
		tmp = 1.0 - ((x / z) / (t - y))
	elif z <= 9.6e-91:
		tmp = (x / (y * (t - y))) + 1.0
	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 (z <= -3.5e-79)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (z <= 9.6e-91)
		tmp = Float64(Float64(x / Float64(y * Float64(t - y))) + 1.0);
	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 (z <= -3.5e-79)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (z <= 9.6e-91)
		tmp = (x / (y * (t - y))) + 1.0;
	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[LessEqual[z, -3.5e-79], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-91], N[(N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000003e-79

   1. Initial program 99.9%

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

      1. associate-/r* 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. associate-/r* 97.9%

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

      3. distribute-neg-frac2 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in x around 0 97.9%

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

      1. associate-/r* 97.9%

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

   10. Simplified 97.9%

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

   if -3.5000000000000003e-79 < z < 9.60000000000000043e-91

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 91.5%

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

   if 9.60000000000000043e-91 < 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 70.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-79}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - y\right)} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t - y}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

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 (<= z -4.2e-80)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= z 9.6e-91) (+ (/ (/ x (- t y)) y) 1.0) (- 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 (z <= -4.2e-80) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 9.6e-91) {
		tmp = ((x / (t - y)) / y) + 1.0;
	} 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 (z <= (-4.2d-80)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (z <= 9.6d-91) then
        tmp = ((x / (t - y)) / y) + 1.0d0
    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 (z <= -4.2e-80) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 9.6e-91) {
		tmp = ((x / (t - y)) / y) + 1.0;
	} 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 z <= -4.2e-80:
		tmp = 1.0 - ((x / z) / (t - y))
	elif z <= 9.6e-91:
		tmp = ((x / (t - y)) / y) + 1.0
	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 (z <= -4.2e-80)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (z <= 9.6e-91)
		tmp = Float64(Float64(Float64(x / Float64(t - y)) / y) + 1.0);
	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 (z <= -4.2e-80)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (z <= 9.6e-91)
		tmp = ((x / (t - y)) / y) + 1.0;
	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[LessEqual[z, -4.2e-80], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-91], N[(N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000003e-80

   1. Initial program 99.9%

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

      1. associate-/r* 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 96.8%

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

      1. mul-1-neg 96.8%

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

      2. associate-/r* 96.8%

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

      3. distribute-neg-frac2 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in x around 0 96.8%

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

      1. associate-/r* 96.8%

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

   10. Simplified 96.8%

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

   if -4.20000000000000003e-80 < z < 9.60000000000000043e-91

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-/r* 92.6%

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

   5. Simplified 92.6%

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

   if 9.60000000000000043e-91 < 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 70.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t - y}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-80}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{\frac{x}{t - y}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e-80)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= z 8.6e-191)
     (+ (/ (/ x (- t y)) y) 1.0)
     (+ (/ x (* (- y 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 (z <= -9e-80) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 8.6e-191) {
		tmp = ((x / (t - y)) / y) + 1.0;
	} else {
		tmp = (x / ((y - z) * t)) + 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 (z <= (-9d-80)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (z <= 8.6d-191) then
        tmp = ((x / (t - y)) / y) + 1.0d0
    else
        tmp = (x / ((y - z) * t)) + 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 (z <= -9e-80) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 8.6e-191) {
		tmp = ((x / (t - y)) / y) + 1.0;
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -9e-80:
		tmp = 1.0 - ((x / z) / (t - y))
	elif z <= 8.6e-191:
		tmp = ((x / (t - y)) / y) + 1.0
	else:
		tmp = (x / ((y - z) * t)) + 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e-80)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (z <= 8.6e-191)
		tmp = Float64(Float64(Float64(x / Float64(t - y)) / y) + 1.0);
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 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 (z <= -9e-80)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (z <= 8.6e-191)
		tmp = ((x / (t - y)) / y) + 1.0;
	else
		tmp = (x / ((y - z) * t)) + 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[z, -9e-80], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-191], N[(N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.0000000000000006e-80

   1. Initial program 99.9%

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

      1. associate-/r* 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. associate-/r* 97.9%

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

      3. distribute-neg-frac2 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in x around 0 97.9%

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

      1. associate-/r* 97.9%

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

   10. Simplified 97.9%

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

   if -9.0000000000000006e-80 < z < 8.59999999999999966e-191

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-/r* 93.2%

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

   5. Simplified 93.2%

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

   if 8.59999999999999966e-191 < z

   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 inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-80}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{\frac{x}{t - y}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-82}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-191}:\\ \;\;\;\;\frac{\frac{x}{t - y}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \end{array} \end{array} \]

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 (<= z -7.5e-82)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= z 1.15e-191)
     (+ (/ (/ x (- t y)) y) 1.0)
     (+ (/ (/ x t) (- y z)) 1.0))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-82) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.15e-191) {
		tmp = ((x / (t - y)) / y) + 1.0;
	} else {
		tmp = ((x / t) / (y - z)) + 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 (z <= (-7.5d-82)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (z <= 1.15d-191) then
        tmp = ((x / (t - y)) / y) + 1.0d0
    else
        tmp = ((x / t) / (y - z)) + 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 (z <= -7.5e-82) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.15e-191) {
		tmp = ((x / (t - y)) / y) + 1.0;
	} else {
		tmp = ((x / t) / (y - z)) + 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-82:
		tmp = 1.0 - ((x / z) / (t - y))
	elif z <= 1.15e-191:
		tmp = ((x / (t - y)) / y) + 1.0
	else:
		tmp = ((x / t) / (y - z)) + 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-82)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (z <= 1.15e-191)
		tmp = Float64(Float64(Float64(x / Float64(t - y)) / y) + 1.0);
	else
		tmp = Float64(Float64(Float64(x / t) / Float64(y - z)) + 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 (z <= -7.5e-82)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (z <= 1.15e-191)
		tmp = ((x / (t - y)) / y) + 1.0;
	else
		tmp = ((x / t) / (y - z)) + 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[z, -7.5e-82], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-191], N[(N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4999999999999997e-82

   1. Initial program 99.9%

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

      1. associate-/r* 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 96.8%

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

      1. mul-1-neg 96.8%

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

      2. associate-/r* 96.8%

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

      3. distribute-neg-frac2 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in x around 0 96.8%

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

      1. associate-/r* 96.8%

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

   10. Simplified 96.8%

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

   if -7.4999999999999997e-82 < z < 1.15000000000000005e-191

   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 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-/r* 93.0%

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

   5. Simplified 93.0%

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

   if 1.15000000000000005e-191 < z

   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. associate-/r* 97.9%

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

      2. div-inv 97.9%

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

   4. Applied egg-rr 97.9%

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

      1. associate-*l/ 98.9%

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

      2. div-inv 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in y around 0 77.3%

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

      1. mul-1-neg 53.2%

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

      2. distribute-neg-frac2 53.2%

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

   9. Simplified 77.3%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-82}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-191}:\\ \;\;\;\;\frac{\frac{x}{t - y}}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-122}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -2.45e-78) 1.0 (if (<= y 4e-122) (- 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 <= -2.45e-78) {
		tmp = 1.0;
	} else if (y <= 4e-122) {
		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 <= (-2.45d-78)) then
        tmp = 1.0d0
    else if (y <= 4d-122) 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 <= -2.45e-78) {
		tmp = 1.0;
	} else if (y <= 4e-122) {
		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 <= -2.45e-78:
		tmp = 1.0
	elif y <= 4e-122:
		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 <= -2.45e-78)
		tmp = 1.0;
	elseif (y <= 4e-122)
		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 <= -2.45e-78)
		tmp = 1.0;
	elseif (y <= 4e-122)
		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, -2.45e-78], 1.0, If[LessEqual[y, 4e-122], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.45000000000000015e-78 or 4.00000000000000024e-122 < y

   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 45.7%

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

      1. frac-2neg 45.7%

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

      2. neg-sub0 45.7%

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

      3. div-sub 45.4%

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

      4. *-commutative 45.4%

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

      5. distribute-rgt-neg-in 45.4%

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

      6. add-sqr-sqrt 21.6%

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

      7. sqrt-unprod 46.1%

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

      8. sqr-neg 46.1%

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

      9. sqrt-unprod 24.3%

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

      10. add-sqr-sqrt 45.8%

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

      11. frac-2neg 45.8%

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

      12. *-commutative 45.8%

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

   5. Applied egg-rr 45.8%

      \[\leadsto 1 - \color{blue}{\left(\frac{0}{z \cdot \left(-t\right)} - \frac{x}{z \cdot t}\right)} \]
   6. Step-by-step derivation

      1. div0 46.1%

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

      2. neg-sub0 46.1%

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

      3. distribute-neg-frac2 46.1%

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

      4. distribute-rgt-neg-out 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in x around 0 91.1%

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

   if -2.45000000000000015e-78 < y < 4.00000000000000024e-122

   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 80.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-122}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-116}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -1.72e-77) 1.0 (if (<= y 4.4e-116) (- 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 <= -1.72e-77) {
		tmp = 1.0;
	} else if (y <= 4.4e-116) {
		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 <= (-1.72d-77)) then
        tmp = 1.0d0
    else if (y <= 4.4d-116) 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 <= -1.72e-77) {
		tmp = 1.0;
	} else if (y <= 4.4e-116) {
		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 <= -1.72e-77:
		tmp = 1.0
	elif y <= 4.4e-116:
		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 <= -1.72e-77)
		tmp = 1.0;
	elseif (y <= 4.4e-116)
		tmp = Float64(1.0 - Float64(Float64(x / 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 <= -1.72e-77)
		tmp = 1.0;
	elseif (y <= 4.4e-116)
		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, -1.72e-77], 1.0, If[LessEqual[y, 4.4e-116], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.71999999999999997e-77 or 4.4000000000000002e-116 < y

   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 45.7%

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

      1. frac-2neg 45.7%

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

      2. neg-sub0 45.7%

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

      3. div-sub 45.4%

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

      4. *-commutative 45.4%

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

      5. distribute-rgt-neg-in 45.4%

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

      6. add-sqr-sqrt 21.6%

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

      7. sqrt-unprod 46.1%

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

      8. sqr-neg 46.1%

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

      9. sqrt-unprod 24.3%

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

      10. add-sqr-sqrt 45.8%

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

      11. frac-2neg 45.8%

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

      12. *-commutative 45.8%

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

   5. Applied egg-rr 45.8%

      \[\leadsto 1 - \color{blue}{\left(\frac{0}{z \cdot \left(-t\right)} - \frac{x}{z \cdot t}\right)} \]
   6. Step-by-step derivation

      1. div0 46.1%

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

      2. neg-sub0 46.1%

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

      3. distribute-neg-frac2 46.1%

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

      4. distribute-rgt-neg-out 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in x around 0 91.1%

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

   if -1.71999999999999997e-77 < y < 4.4000000000000002e-116

   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 80.9%

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

      1. associate-/r* 82.1%

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

      2. div-inv 82.0%

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

   5. Applied egg-rr 82.0%

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

      1. associate-*l/ 82.0%

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

      2. div-inv 82.1%

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

   7. Applied egg-rr 82.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.72 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-116}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.7%

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

3. Final simplification 98.7%

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

Alternative 11: 76.0% 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 98.7%

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

3. Taylor expanded in y around 0 57.0%

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

   1. frac-2neg 57.0%

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

   2. neg-sub0 57.0%

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

   3. div-sub 55.5%

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

   4. *-commutative 55.5%

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

   5. distribute-rgt-neg-in 55.5%

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

   6. add-sqr-sqrt 24.2%

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

   7. sqrt-unprod 51.0%

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

   8. sqr-neg 51.0%

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

   9. sqrt-unprod 26.8%

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

   10. add-sqr-sqrt 46.6%

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

   11. frac-2neg 46.6%

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

   12. *-commutative 46.6%

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

5. Applied egg-rr 46.6%

   \[\leadsto 1 - \color{blue}{\left(\frac{0}{z \cdot \left(-t\right)} - \frac{x}{z \cdot t}\right)} \]
6. Step-by-step derivation

   1. div0 47.2%

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

   2. neg-sub0 47.2%

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

   3. distribute-neg-frac2 47.2%

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

   4. distribute-rgt-neg-out 47.2%

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

7. Simplified 47.2%

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

8. Taylor expanded in x around 0 78.4%

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

9. Final simplification 78.4%

   \[\leadsto 1 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024043 
(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)))))