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

Percentage Accurate: 99.0% → 98.5%

Time: 12.8s

Alternatives: 13

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: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + ((1.0d0 / (y - z)) / ((t - y) / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. *-un-lft-identity 97.3%

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

   2. times-frac 98.8%

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

4. Applied egg-rr 98.8%

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

   1. clear-num 98.7%

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

   2. div-inv 98.8%

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

6. Applied egg-rr 98.8%

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

7. Final simplification 98.8%

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

Alternative 2: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-76} \lor \neg \left(y \leq 5.8 \cdot 10^{-55}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{y - z} \cdot \frac{x}{t}\\ \end{array} \end{array} \]

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 -1.26e-76) (not (<= y 5.8e-55)))
   (+ 1.0 (/ x (* y (- z y))))
   (+ 1.0 (* (/ 1.0 (- y z)) (/ x t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.26e-76) || !(y <= 5.8e-55)) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((1.0 / (y - z)) * (x / 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 <= (-1.26d-76)) .or. (.not. (y <= 5.8d-55))) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + ((1.0d0 / (y - z)) * (x / 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 <= -1.26e-76) || !(y <= 5.8e-55)) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((1.0 / (y - z)) * (x / t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.26e-76) or not (y <= 5.8e-55):
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + ((1.0 / (y - z)) * (x / t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.26e-76) || !(y <= 5.8e-55))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(1.0 / Float64(y - z)) * Float64(x / 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 <= -1.26e-76) || ~((y <= 5.8e-55)))
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + ((1.0 / (y - z)) * (x / 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, -1.26e-76], N[Not[LessEqual[y, 5.8e-55]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.26e-76 or 5.8e-55 < 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 t around 0 95.2%

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

   if -1.26e-76 < y < 5.8e-55

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf 84.4%

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

      1. associate-/r* 86.1%

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

      2. div-inv 86.1%

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

   5. Applied egg-rr 86.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{-76} \lor \neg \left(y \leq 5.8 \cdot 10^{-55}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{y - z} \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-69} \lor \neg \left(y \leq 2.3 \cdot 10^{-55}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e-69) (not (<= y 2.3e-55)))
   (+ 1.0 (/ x (* y (- z y))))
   (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-69) || !(y <= 2.3e-55)) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.5d-69)) .or. (.not. (y <= 2.3d-55))) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-69) || !(y <= 2.3e-55)) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e-69) or not (y <= 2.3e-55):
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e-69) || !(y <= 2.3e-55))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e-69) || ~((y <= 2.3e-55)))
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e-69], N[Not[LessEqual[y, 2.3e-55]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000017e-69 or 2.30000000000000011e-55 < 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 t around 0 95.2%

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

   if -2.50000000000000017e-69 < y < 2.30000000000000011e-55

   1. Initial program 92.6%

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

      1. *-un-lft-identity 92.6%

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

      2. times-frac 96.7%

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

   4. Applied egg-rr 96.7%

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

      1. clear-num 96.5%

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

      2. div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in t around inf 84.4%

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

      1. associate-/r* 86.1%

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

   9. Simplified 86.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-69} \lor \neg \left(y \leq 2.3 \cdot 10^{-55}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-69} \lor \neg \left(y \leq 2.2 \cdot 10^{-55}\right):\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e-69) (not (<= y 2.2e-55)))
   (+ 1.0 (/ (/ x y) (- t y)))
   (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-69) || !(y <= 2.2e-55)) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8d-69)) .or. (.not. (y <= 2.2d-55))) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-69) || !(y <= 2.2e-55)) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -8e-69) or not (y <= 2.2e-55):
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e-69) || !(y <= 2.2e-55))
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e-69) || ~((y <= 2.2e-55)))
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e-69], N[Not[LessEqual[y, 2.2e-55]], $MachinePrecision]], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999997e-69 or 2.2e-55 < 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 94.4%

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

      1. sub-neg 94.4%

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

      2. associate-/r* 94.4%

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

      3. distribute-neg-frac2 94.4%

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

      4. neg-sub0 94.4%

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

      5. sub-neg 94.4%

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

      6. +-commutative 94.4%

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

      7. associate--r+ 94.4%

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

      8. neg-sub0 94.4%

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

      9. remove-double-neg 94.4%

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

   5. Simplified 94.4%

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

   if -7.9999999999999997e-69 < y < 2.2e-55

   1. Initial program 92.6%

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

      1. *-un-lft-identity 92.6%

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

      2. times-frac 96.7%

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

   4. Applied egg-rr 96.7%

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

      1. clear-num 96.5%

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

      2. div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in t around inf 84.4%

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

      1. associate-/r* 86.1%

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

   9. Simplified 86.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-69} \lor \neg \left(y \leq 2.2 \cdot 10^{-55}\right):\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-126}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-226}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -2e-126)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= z 1.2e-226)
     (+ 1.0 (/ (/ x y) (- t y)))
     (+ 1.0 (/ x (* (- y z) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-126) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.2e-226) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + (x / ((y - 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 <= (-2d-126)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (z <= 1.2d-226) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 + (x / ((y - 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 <= -2e-126) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.2e-226) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2e-126:
		tmp = 1.0 - ((x / z) / (t - y))
	elif z <= 1.2e-226:
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 + (x / ((y - 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 <= -2e-126)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (z <= 1.2e-226)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - 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 <= -2e-126)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (z <= 1.2e-226)
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 + (x / ((y - 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, -2e-126], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-226], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e-126

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 88.3%

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

      1. associate-/r* 89.4%

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

   5. Simplified 89.4%

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

   if -1.9999999999999999e-126 < z < 1.2e-226

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 84.1%

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

      1. sub-neg 84.1%

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

      2. associate-/r* 85.3%

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

      3. distribute-neg-frac2 85.3%

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

      4. neg-sub0 85.3%

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

      5. sub-neg 85.3%

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

      6. +-commutative 85.3%

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

      7. associate--r+ 85.3%

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

      8. neg-sub0 85.3%

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

      9. remove-double-neg 85.3%

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

   5. Simplified 85.3%

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

   if 1.2e-226 < 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 t around inf 84.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-126}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-226}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-23}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-55}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -2.3e-23) 1.0 (if (<= y 8.5e-55) (+ 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 (y <= -2.3e-23) {
		tmp = 1.0;
	} else if (y <= 8.5e-55) {
		tmp = 1.0 + ((x / t) / (y - 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 <= (-2.3d-23)) then
        tmp = 1.0d0
    else if (y <= 8.5d-55) then
        tmp = 1.0d0 + ((x / t) / (y - 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 <= -2.3e-23) {
		tmp = 1.0;
	} else if (y <= 8.5e-55) {
		tmp = 1.0 + ((x / t) / (y - 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 <= -2.3e-23:
		tmp = 1.0
	elif y <= 8.5e-55:
		tmp = 1.0 + ((x / t) / (y - 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 <= -2.3e-23)
		tmp = 1.0;
	elseif (y <= 8.5e-55)
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - 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 <= -2.3e-23)
		tmp = 1.0;
	elseif (y <= 8.5e-55)
		tmp = 1.0 + ((x / t) / (y - 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, -2.3e-23], 1.0, If[LessEqual[y, 8.5e-55], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3000000000000001e-23 or 8.49999999999999968e-55 < 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 x around 0 90.7%

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

   if -2.3000000000000001e-23 < y < 8.49999999999999968e-55

   1. Initial program 93.4%

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

      1. *-un-lft-identity 93.4%

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

      2. times-frac 97.0%

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

   4. Applied egg-rr 97.0%

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

      1. clear-num 96.8%

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

      2. div-inv 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in t around inf 84.3%

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

      1. associate-/r* 85.8%

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

   9. Simplified 85.8%

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

Alternative 7: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -8.6e-23) 1.0 (if (<= y 7.6e-56) (+ 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 (y <= -8.6e-23) {
		tmp = 1.0;
	} else if (y <= 7.6e-56) {
		tmp = 1.0 + (x / ((y - 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 <= (-8.6d-23)) then
        tmp = 1.0d0
    else if (y <= 7.6d-56) then
        tmp = 1.0d0 + (x / ((y - 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 <= -8.6e-23) {
		tmp = 1.0;
	} else if (y <= 7.6e-56) {
		tmp = 1.0 + (x / ((y - 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 <= -8.6e-23:
		tmp = 1.0
	elif y <= 7.6e-56:
		tmp = 1.0 + (x / ((y - 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 <= -8.6e-23)
		tmp = 1.0;
	elseif (y <= 7.6e-56)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - 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 <= -8.6e-23)
		tmp = 1.0;
	elseif (y <= 7.6e-56)
		tmp = 1.0 + (x / ((y - 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, -8.6e-23], 1.0, If[LessEqual[y, 7.6e-56], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.60000000000000004e-23 or 7.6000000000000004e-56 < 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 x around 0 90.7%

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

   if -8.60000000000000004e-23 < y < 7.6000000000000004e-56

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 84.3%

      \[\leadsto \color{blue}{1 + \frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -1.5e-48) 1.0 (if (<= y 7.6e-56) (- 1.0 (/ (/ 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 <= -1.5e-48) {
		tmp = 1.0;
	} else if (y <= 7.6e-56) {
		tmp = 1.0 - ((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 <= (-1.5d-48)) then
        tmp = 1.0d0
    else if (y <= 7.6d-56) then
        tmp = 1.0d0 - ((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 <= -1.5e-48) {
		tmp = 1.0;
	} else if (y <= 7.6e-56) {
		tmp = 1.0 - ((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 <= -1.5e-48:
		tmp = 1.0
	elif y <= 7.6e-56:
		tmp = 1.0 - ((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 <= -1.5e-48)
		tmp = 1.0;
	elseif (y <= 7.6e-56)
		tmp = Float64(1.0 - Float64(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 <= -1.5e-48)
		tmp = 1.0;
	elseif (y <= 7.6e-56)
		tmp = 1.0 - ((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, -1.5e-48], 1.0, If[LessEqual[y, 7.6e-56], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e-48 or 7.6000000000000004e-56 < 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 x around 0 89.8%

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

   if -1.5e-48 < y < 7.6000000000000004e-56

   1. Initial program 93.1%

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

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

      3. associate-/l* 97.0%

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

   4. Applied egg-rr 97.0%

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

      1. unpow-1 97.0%

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

   6. Simplified 97.0%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. associate-/r* 76.4%

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

   9. Simplified 76.4%

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

Alternative 9: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -1.6e-48) 1.0 (if (<= y 1.6e-55) (- 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 <= -1.6e-48) {
		tmp = 1.0;
	} else if (y <= 1.6e-55) {
		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 <= (-1.6d-48)) then
        tmp = 1.0d0
    else if (y <= 1.6d-55) 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 <= -1.6e-48) {
		tmp = 1.0;
	} else if (y <= 1.6e-55) {
		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 <= -1.6e-48:
		tmp = 1.0
	elif y <= 1.6e-55:
		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 <= -1.6e-48)
		tmp = 1.0;
	elseif (y <= 1.6e-55)
		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 <= -1.6e-48)
		tmp = 1.0;
	elseif (y <= 1.6e-55)
		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, -1.6e-48], 1.0, If[LessEqual[y, 1.6e-55], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5999999999999999e-48 or 1.6000000000000001e-55 < 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 x around 0 89.8%

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

   if -1.5999999999999999e-48 < y < 1.6000000000000001e-55

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 75.3%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + (1.0d0 / ((y - z) * ((t - y) / x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 97.3%

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

   1. clear-num 97.3%

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

   2. inv-pow 97.3%

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

   3. associate-/l* 98.8%

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

4. Applied egg-rr 98.8%

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

   1. unpow-1 98.8%

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

6. Simplified 98.8%

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

7. Final simplification 98.8%

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

Alternative 11: 98.4% accurate, 0.8× speedup

Math

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

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 97.3%

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

   1. *-un-lft-identity 97.3%

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

   2. times-frac 98.8%

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

4. Applied egg-rr 98.8%

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

5. Final simplification 98.8%

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

Alternative 12: 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 97.3%

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

3. Final simplification 97.3%

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

Alternative 13: 74.9% 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 97.3%

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

3. Taylor expanded in x around 0 72.4%

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

Reproduce

herbie shell --seed 2024146 
(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)))))