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

Percentage Accurate: 99.0% → 98.8%

Time: 9.5s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \sqrt[3]{y - z}\\ 1 - \frac{\frac{x}{\left(y - t\right) \cdot t_1}}{{t_1}^{2}} \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (cbrt (- y z)))) (- 1.0 (/ (/ x (* (- y t) t_1)) (pow t_1 2.0)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double t_1 = cbrt((y - z));
	return 1.0 - ((x / ((y - t) * t_1)) / pow(t_1, 2.0));
}

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.cbrt((y - z));
	return 1.0 - ((x / ((y - t) * t_1)) / Math.pow(t_1, 2.0));
}

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	t_1 = cbrt(Float64(y - z))
	return Float64(1.0 - Float64(Float64(x / Float64(Float64(y - t) * t_1)) / (t_1 ^ 2.0)))
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Power[N[(y - z), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 - N[(N[(x / N[(N[(y - t), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] / N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 98.5%

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

   1. associate-/l/ 99.2%

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

   2. div-inv 99.2%

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

   3. add-cube-cbrt 98.8%

      \[\leadsto 1 - \frac{x \cdot \frac{1}{y - t}}{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}} \]

   4. times-frac 99.2%

      \[\leadsto 1 - \color{blue}{\frac{x}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\frac{1}{y - t}}{\sqrt[3]{y - z}}} \]

   5. pow2 99.2%

      \[\leadsto 1 - \frac{x}{\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}}} \cdot \frac{\frac{1}{y - t}}{\sqrt[3]{y - z}} \]

3. Applied egg-rr 99.2%

   \[\leadsto 1 - \color{blue}{\frac{x}{{\left(\sqrt[3]{y - z}\right)}^{2}} \cdot \frac{\frac{1}{y - t}}{\sqrt[3]{y - z}}} \]
4. Step-by-step derivation

   1. associate-*l/ 99.2%

      \[\leadsto 1 - \color{blue}{\frac{x \cdot \frac{\frac{1}{y - t}}{\sqrt[3]{y - z}}}{{\left(\sqrt[3]{y - z}\right)}^{2}}} \]

   2. associate-/l/ 99.2%

      \[\leadsto 1 - \frac{x \cdot \color{blue}{\frac{1}{\sqrt[3]{y - z} \cdot \left(y - t\right)}}}{{\left(\sqrt[3]{y - z}\right)}^{2}} \]

   3. associate-*r/ 99.2%

      \[\leadsto 1 - \frac{\color{blue}{\frac{x \cdot 1}{\sqrt[3]{y - z} \cdot \left(y - t\right)}}}{{\left(\sqrt[3]{y - z}\right)}^{2}} \]

   4. *-rgt-identity 99.2%

      \[\leadsto 1 - \frac{\frac{\color{blue}{x}}{\sqrt[3]{y - z} \cdot \left(y - t\right)}}{{\left(\sqrt[3]{y - z}\right)}^{2}} \]

   5. *-commutative 99.2%

      \[\leadsto 1 - \frac{\frac{x}{\color{blue}{\left(y - t\right) \cdot \sqrt[3]{y - z}}}}{{\left(\sqrt[3]{y - z}\right)}^{2}} \]

5. Simplified 99.2%

   \[\leadsto 1 - \color{blue}{\frac{\frac{x}{\left(y - t\right) \cdot \sqrt[3]{y - z}}}{{\left(\sqrt[3]{y - z}\right)}^{2}}} \]

6. Final simplification 99.2%

   \[\leadsto 1 - \frac{\frac{x}{\left(y - t\right) \cdot \sqrt[3]{y - z}}}{{\left(\sqrt[3]{y - z}\right)}^{2}} \]

Alternative 2: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-112} \lor \neg \left(y \leq 7.2 \cdot 10^{-65}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e-112) (not (<= y 7.2e-65)))
   (- 1.0 (/ x (* y (- y z))))
   (- 1.0 (/ x (* t z)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-112) || !(y <= 7.2e-65)) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.05d-112)) .or. (.not. (y <= 7.2d-65))) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else
        tmp = 1.0d0 - (x / (t * z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-112) || !(y <= 7.2e-65)) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-112) or not (y <= 7.2e-65):
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 - (x / (t * z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e-112) || !(y <= 7.2e-65))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e-112) || ~((y <= 7.2e-65)))
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 - (x / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e-112], N[Not[LessEqual[y, 7.2e-65]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-112 or 7.1999999999999996e-65 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 90.6%

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

   if -1.05e-112 < y < 7.1999999999999996e-65

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 74.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-112} \lor \neg \left(y \leq 7.2 \cdot 10^{-65}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-124} \lor \neg \left(y \leq 5.6 \cdot 10^{-161}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.8e-124) (not (<= y 5.6e-161)))
   (- 1.0 (/ x (* y (- y t))))
   (- 1.0 (/ x (* t z)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-124) || !(y <= 5.6e-161)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.8d-124)) .or. (.not. (y <= 5.6d-161))) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 - (x / (t * z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-124) || !(y <= 5.6e-161)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -4.8e-124) or not (y <= 5.6e-161):
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 - (x / (t * z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.8e-124) || !(y <= 5.6e-161))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.8e-124) || ~((y <= 5.6e-161)))
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 - (x / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.8e-124], N[Not[LessEqual[y, 5.6e-161]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999985e-124 or 5.59999999999999984e-161 < y

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 89.6%

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

   if -4.79999999999999985e-124 < y < 5.59999999999999984e-161

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 83.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-124} \lor \neg \left(y \leq 5.6 \cdot 10^{-161}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]

Alternative 4: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-123} \lor \neg \left(y \leq 5.6 \cdot 10^{-161}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e-123) (not (<= y 5.6e-161)))
   (- 1.0 (/ (/ x y) (- y t)))
   (- 1.0 (/ x (* t z)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-123) || !(y <= 5.6e-161)) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.05d-123)) .or. (.not. (y <= 5.6d-161))) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else
        tmp = 1.0d0 - (x / (t * z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-123) || !(y <= 5.6e-161)) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 - (x / (t * z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-123) or not (y <= 5.6e-161):
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = 1.0 - (x / (t * z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e-123) || !(y <= 5.6e-161))
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e-123) || ~((y <= 5.6e-161)))
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = 1.0 - (x / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e-123], N[Not[LessEqual[y, 5.6e-161]], $MachinePrecision]], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-123 or 5.59999999999999984e-161 < y

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 89.6%

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

      1. associate-/l/ 89.8%

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

   4. Simplified 89.8%

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

   if -1.05e-123 < y < 5.59999999999999984e-161

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 83.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-123} \lor \neg \left(y \leq 5.6 \cdot 10^{-161}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]

Alternative 5: 91.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-61} \lor \neg \left(t \leq 2.4 \cdot 10^{-24}\right):\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.8e-61) (not (<= t 2.4e-24)))
   (+ 1.0 (/ x (* t (- y z))))
   (- 1.0 (/ x (* y (- y z))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.8e-61) || !(t <= 2.4e-24)) {
		tmp = 1.0 + (x / (t * (y - z)));
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8.8d-61)) .or. (.not. (t <= 2.4d-24))) then
        tmp = 1.0d0 + (x / (t * (y - z)))
    else
        tmp = 1.0d0 - (x / (y * (y - z)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.8e-61) || !(t <= 2.4e-24)) {
		tmp = 1.0 + (x / (t * (y - z)));
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -8.8e-61) or not (t <= 2.4e-24):
		tmp = 1.0 + (x / (t * (y - z)))
	else:
		tmp = 1.0 - (x / (y * (y - z)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.8e-61) || !(t <= 2.4e-24))
		tmp = Float64(1.0 + Float64(x / Float64(t * Float64(y - z))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.8e-61) || ~((t <= 2.4e-24)))
		tmp = 1.0 + (x / (t * (y - z)));
	else
		tmp = 1.0 - (x / (y * (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.8e-61], N[Not[LessEqual[t, 2.4e-24]], $MachinePrecision]], N[(1.0 + N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.80000000000000035e-61 or 2.3999999999999998e-24 < t

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 98.3%

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

      1. associate-*r/ 98.3%

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

      2. neg-mul-1 98.3%

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

   4. Simplified 98.3%

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

   if -8.80000000000000035e-61 < t < 2.3999999999999998e-24

   1. Initial program 96.9%

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

   2. Taylor expanded in t around 0 84.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-61} \lor \neg \left(t \leq 2.4 \cdot 10^{-24}\right):\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 6: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-24}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e-126)
   1.0
   (if (<= y 6.6e-24) (+ 1.0 (/ -1.0 (* z (/ t x)))) (- 1.0 (/ (/ x y) y)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-126) {
		tmp = 1.0;
	} else if (y <= 6.6e-24) {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-3d-126)) then
        tmp = 1.0d0
    else if (y <= 6.6d-24) then
        tmp = 1.0d0 + ((-1.0d0) / (z * (t / x)))
    else
        tmp = 1.0d0 - ((x / y) / y)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-126) {
		tmp = 1.0;
	} else if (y <= 6.6e-24) {
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3e-126:
		tmp = 1.0
	elif y <= 6.6e-24:
		tmp = 1.0 + (-1.0 / (z * (t / x)))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e-126)
		tmp = 1.0;
	elseif (y <= 6.6e-24)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(z * Float64(t / x))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e-126)
		tmp = 1.0;
	elseif (y <= 6.6e-24)
		tmp = 1.0 + (-1.0 / (z * (t / x)));
	else
		tmp = 1.0 - ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3e-126], 1.0, If[LessEqual[y, 6.6e-24], N[(1.0 + N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000002e-126

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 88.7%

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

   3. Taylor expanded in x around 0 87.5%

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

   if -3.0000000000000002e-126 < y < 6.59999999999999968e-24

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 72.1%

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

      1. associate-/r* 72.0%

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

      2. div-inv 71.9%

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

   4. Applied egg-rr 71.9%

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

      1. clear-num 72.4%

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

      2. frac-times 72.5%

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

      3. metadata-eval 72.5%

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

   6. Applied egg-rr 72.5%

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

   if 6.59999999999999968e-24 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 94.4%

      \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 94.4%

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

      2. associate-/r* 94.4%

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

   4. Simplified 94.4%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-24}:\\ \;\;\;\;1 + \frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]

Alternative 7: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-129}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-161}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e-129)
   (- 1.0 (/ (/ x y) (- y t)))
   (if (<= y 5.6e-161) (- 1.0 (/ x (* t z))) (- 1.0 (/ (/ x (- y t)) y)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e-129) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else if (y <= 5.6e-161) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7d-129)) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else if (y <= 5.6d-161) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = 1.0d0 - ((x / (y - t)) / y)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e-129) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else if (y <= 5.6e-161) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -7e-129:
		tmp = 1.0 - ((x / y) / (y - t))
	elif y <= 5.6e-161:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0 - ((x / (y - t)) / y)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e-129)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	elseif (y <= 5.6e-161)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7e-129)
		tmp = 1.0 - ((x / y) / (y - t));
	elseif (y <= 5.6e-161)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0 - ((x / (y - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -7e-129], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-161], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999995e-129

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 91.7%

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

      1. associate-/l/ 92.1%

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

   4. Simplified 92.1%

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

   if -6.9999999999999995e-129 < y < 5.59999999999999984e-161

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 83.3%

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

   if 5.59999999999999984e-161 < y

   1. Initial program 99.3%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. clear-num 99.8%

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

      2. frac-times 99.9%

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

      3. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 87.8%

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

      1. associate-/r* 88.0%

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

   8. Simplified 88.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-129}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-161}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 8: 92.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-53}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-219}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e-53)
   (+ 1.0 (/ x (* (- y t) z)))
   (if (<= z 1.65e-219)
     (- 1.0 (/ (/ x y) (- y t)))
     (+ 1.0 (/ x (* t (- y z)))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e-53) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 1.65e-219) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 + (x / (t * (y - z)));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.45d-53)) then
        tmp = 1.0d0 + (x / ((y - t) * z))
    else if (z <= 1.65d-219) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else
        tmp = 1.0d0 + (x / (t * (y - z)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e-53) {
		tmp = 1.0 + (x / ((y - t) * z));
	} else if (z <= 1.65e-219) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = 1.0 + (x / (t * (y - z)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e-53:
		tmp = 1.0 + (x / ((y - t) * z))
	elif z <= 1.65e-219:
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = 1.0 + (x / (t * (y - z)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e-53)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - t) * z)));
	elseif (z <= 1.65e-219)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(t * Float64(y - z))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e-53)
		tmp = 1.0 + (x / ((y - t) * z));
	elseif (z <= 1.65e-219)
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = 1.0 + (x / (t * (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e-53], N[(1.0 + N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-219], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e-53

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. neg-mul-1 93.5%

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

   4. Simplified 93.5%

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

   if -1.4499999999999999e-53 < z < 1.6500000000000001e-219

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 87.9%

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

      1. associate-/l/ 88.1%

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

   4. Simplified 88.1%

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

   if 1.6500000000000001e-219 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in t around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   4. Simplified 80.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-53}:\\ \;\;\;\;1 + \frac{x}{\left(y - t\right) \cdot z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-219}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 9: 98.4% accurate, 0.8× speedup

Math

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

FPCore

NOTE: 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)) (/ -1.0 (- y t)))))

C

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

Fortran

NOTE: 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)) * ((-1.0d0) / (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. associate-/r* 98.8%

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

   2. div-inv 98.8%

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

3. Applied egg-rr 98.8%

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

4. Final simplification 98.8%

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

Alternative 10: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-61}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-124) 1.0 (if (<= y 6e-61) (- 1.0 (/ x (* t z))) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-124) {
		tmp = 1.0;
	} else if (y <= 6e-61) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.8d-124)) then
        tmp = 1.0d0
    else if (y <= 6d-61) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-124) {
		tmp = 1.0;
	} else if (y <= 6e-61) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-124:
		tmp = 1.0
	elif y <= 6e-61:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-124)
		tmp = 1.0;
	elseif (y <= 6e-61)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e-124)
		tmp = 1.0;
	elseif (y <= 6e-61)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-124], 1.0, If[LessEqual[y, 6e-61], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999985e-124 or 6.00000000000000024e-61 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 89.5%

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

   3. Taylor expanded in x around 0 87.5%

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

   if -4.79999999999999985e-124 < y < 6.00000000000000024e-61

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 74.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-61}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-26}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-123)
   1.0
   (if (<= y 6.6e-26) (- 1.0 (/ x (* t z))) (- 1.0 (/ (/ x y) y)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-123) {
		tmp = 1.0;
	} else if (y <= 6.6e-26) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-1.05d-123)) then
        tmp = 1.0d0
    else if (y <= 6.6d-26) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = 1.0d0 - ((x / y) / y)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-123) {
		tmp = 1.0;
	} else if (y <= 6.6e-26) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-123:
		tmp = 1.0
	elif y <= 6.6e-26:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-123)
		tmp = 1.0;
	elseif (y <= 6.6e-26)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e-123)
		tmp = 1.0;
	elseif (y <= 6.6e-26)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0 - ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-123], 1.0, If[LessEqual[y, 6.6e-26], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-123

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 88.7%

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

   3. Taylor expanded in x around 0 87.5%

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

   if -1.05e-123 < y < 6.5999999999999997e-26

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 72.1%

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

   if 6.5999999999999997e-26 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 94.4%

      \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 94.4%

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

      2. associate-/r* 94.4%

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

   4. Simplified 94.4%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-26}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]

Alternative 12: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: 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 - t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

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

2. Final simplification 98.5%

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

Alternative 13: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. associate-/l/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 14: 74.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

2. Taylor expanded in t around 0 73.3%

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

3. Taylor expanded in x around 0 74.6%

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

4. Final simplification 74.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023199 
(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)))))