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

Percentage Accurate: 99.2% → 98.6%

Time: 7.8s

Alternatives: 12

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: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.8%

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

   1. clear-num 98.8%

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

   2. inv-pow 98.8%

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

   3. *-commutative 98.8%

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

   4. associate-/l* 98.8%

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

3. Applied egg-rr 98.8%

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

   1. unpow-1 98.8%

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

   2. associate-/r/ 98.8%

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

5. Simplified 98.8%

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

6. Final simplification 98.8%

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

Alternative 2: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-85}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{y - t}\\ \mathbf{elif}\;t \leq 350:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot \left(y - t\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e-85)
   (- 1.0 (/ x (* t z)))
   (if (<= t 1.35e-58)
     (- 1.0 (/ (/ x y) (- y z)))
     (if (<= t 5.5e-26)
       (/ (/ (- x) (- y z)) (- y t))
       (if (<= t 350.0)
         (+ 1.0 (/ -1.0 (/ (* y (- y t)) x)))
         (+ 1.0 (/ (/ x t) (- y z))))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e-85) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 1.35e-58) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else if (t <= 5.5e-26) {
		tmp = (-x / (y - z)) / (y - t);
	} else if (t <= 350.0) {
		tmp = 1.0 + (-1.0 / ((y * (y - t)) / x));
	} 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 (t <= (-3.7d-85)) then
        tmp = 1.0d0 - (x / (t * z))
    else if (t <= 1.35d-58) then
        tmp = 1.0d0 - ((x / y) / (y - z))
    else if (t <= 5.5d-26) then
        tmp = (-x / (y - z)) / (y - t)
    else if (t <= 350.0d0) then
        tmp = 1.0d0 + ((-1.0d0) / ((y * (y - t)) / x))
    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 (t <= -3.7e-85) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 1.35e-58) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else if (t <= 5.5e-26) {
		tmp = (-x / (y - z)) / (y - t);
	} else if (t <= 350.0) {
		tmp = 1.0 + (-1.0 / ((y * (y - t)) / x));
	} 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 t <= -3.7e-85:
		tmp = 1.0 - (x / (t * z))
	elif t <= 1.35e-58:
		tmp = 1.0 - ((x / y) / (y - z))
	elif t <= 5.5e-26:
		tmp = (-x / (y - z)) / (y - t)
	elif t <= 350.0:
		tmp = 1.0 + (-1.0 / ((y * (y - t)) / x))
	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 (t <= -3.7e-85)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (t <= 1.35e-58)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - z)));
	elseif (t <= 5.5e-26)
		tmp = Float64(Float64(Float64(-x) / Float64(y - z)) / Float64(y - t));
	elseif (t <= 350.0)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(Float64(y * Float64(y - t)) / x)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / 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 (t <= -3.7e-85)
		tmp = 1.0 - (x / (t * z));
	elseif (t <= 1.35e-58)
		tmp = 1.0 - ((x / y) / (y - z));
	elseif (t <= 5.5e-26)
		tmp = (-x / (y - z)) / (y - t);
	elseif (t <= 350.0)
		tmp = 1.0 + (-1.0 / ((y * (y - t)) / x));
	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[t, -3.7e-85], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-58], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-26], N[(N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 350.0], N[(1.0 + N[(-1.0 / N[(N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.69999999999999983e-85

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.3%

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

   if -3.69999999999999983e-85 < t < 1.3499999999999999e-58

   1. Initial program 97.0%

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

   2. Taylor expanded in t around 0 85.2%

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

      1. associate-/r* 87.1%

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

   4. Simplified 87.1%

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

   if 1.3499999999999999e-58 < t < 5.5000000000000005e-26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

      3. *-commutative 80.8%

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

      4. associate-/r* 80.5%

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

   4. Simplified 80.5%

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

   if 5.5000000000000005e-26 < t < 350

   1. Initial program 99.8%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

      2. associate-/r/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

   if 350 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 98.4%

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

      1. +-commutative 98.4%

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

      2. associate-/r* 98.4%

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

   4. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y - z} + 1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-85}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{y - t}\\ \mathbf{elif}\;t \leq 350:\\ \;\;\;\;1 + \frac{-1}{\frac{y \cdot \left(y - t\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{y - t}\\ \mathbf{elif}\;t \leq 215:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ x y) (- y z)))))
   (if (<= t -1.05e-84)
     (- 1.0 (/ x (* t z)))
     (if (<= t 1.35e-58)
       t_1
       (if (<= t 5.6e-44)
         (/ (/ (- x) (- y z)) (- y t))
         (if (<= t 215.0) t_1 (+ 1.0 (/ (/ x t) (- y z)))))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((x / y) / (y - z));
	double tmp;
	if (t <= -1.05e-84) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 1.35e-58) {
		tmp = t_1;
	} else if (t <= 5.6e-44) {
		tmp = (-x / (y - z)) / (y - t);
	} else if (t <= 215.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((x / y) / (y - z))
    if (t <= (-1.05d-84)) then
        tmp = 1.0d0 - (x / (t * z))
    else if (t <= 1.35d-58) then
        tmp = t_1
    else if (t <= 5.6d-44) then
        tmp = (-x / (y - z)) / (y - t)
    else if (t <= 215.0d0) then
        tmp = t_1
    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 t_1 = 1.0 - ((x / y) / (y - z));
	double tmp;
	if (t <= -1.05e-84) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 1.35e-58) {
		tmp = t_1;
	} else if (t <= 5.6e-44) {
		tmp = (-x / (y - z)) / (y - t);
	} else if (t <= 215.0) {
		tmp = t_1;
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	t_1 = 1.0 - ((x / y) / (y - z))
	tmp = 0
	if t <= -1.05e-84:
		tmp = 1.0 - (x / (t * z))
	elif t <= 1.35e-58:
		tmp = t_1
	elif t <= 5.6e-44:
		tmp = (-x / (y - z)) / (y - t)
	elif t <= 215.0:
		tmp = t_1
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(Float64(x / y) / Float64(y - z)))
	tmp = 0.0
	if (t <= -1.05e-84)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (t <= 1.35e-58)
		tmp = t_1;
	elseif (t <= 5.6e-44)
		tmp = Float64(Float64(Float64(-x) / Float64(y - z)) / Float64(y - t));
	elseif (t <= 215.0)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - ((x / y) / (y - z));
	tmp = 0.0;
	if (t <= -1.05e-84)
		tmp = 1.0 - (x / (t * z));
	elseif (t <= 1.35e-58)
		tmp = t_1;
	elseif (t <= 5.6e-44)
		tmp = (-x / (y - z)) / (y - t);
	elseif (t <= 215.0)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-84], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-58], t$95$1, If[LessEqual[t, 5.6e-44], N[(N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 215.0], t$95$1, N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.04999999999999999e-84

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.3%

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

   if -1.04999999999999999e-84 < t < 1.3499999999999999e-58 or 5.6e-44 < t < 215

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 85.4%

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

      1. associate-/r* 87.1%

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

   4. Simplified 87.1%

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

   if 1.3499999999999999e-58 < t < 5.6e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.0%

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

      1. associate-*r/ 76.0%

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

      2. neg-mul-1 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-/r* 75.6%

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

   4. Simplified 75.6%

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

   if 215 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 98.4%

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

      1. +-commutative 98.4%

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

      2. associate-/r* 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{y - t}\\ \mathbf{elif}\;t \leq 215:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 4: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-103}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-39}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-22)
   1.0
   (if (<= y -4e-103)
     (+ 1.0 (/ x (* y t)))
     (if (<= y 2e-39) (- 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 <= -2.5e-22) {
		tmp = 1.0;
	} else if (y <= -4e-103) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 2e-39) {
		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 <= (-2.5d-22)) then
        tmp = 1.0d0
    else if (y <= (-4d-103)) then
        tmp = 1.0d0 + (x / (y * t))
    else if (y <= 2d-39) 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 <= -2.5e-22) {
		tmp = 1.0;
	} else if (y <= -4e-103) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 2e-39) {
		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 <= -2.5e-22:
		tmp = 1.0
	elif y <= -4e-103:
		tmp = 1.0 + (x / (y * t))
	elif y <= 2e-39:
		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 <= -2.5e-22)
		tmp = 1.0;
	elseif (y <= -4e-103)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	elseif (y <= 2e-39)
		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 <= -2.5e-22)
		tmp = 1.0;
	elseif (y <= -4e-103)
		tmp = 1.0 + (x / (y * t));
	elseif (y <= 2e-39)
		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, -2.5e-22], 1.0, If[LessEqual[y, -4e-103], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-39], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999977e-22 or 1.99999999999999986e-39 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.0%

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

   if -2.49999999999999977e-22 < y < -3.99999999999999983e-103

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/r* 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in y around inf 70.0%

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

   if -3.99999999999999983e-103 < y < 1.99999999999999986e-39

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 78.2%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-103}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-39}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1650:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-103}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-39}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1650.0)
   (- 1.0 (/ x (* y y)))
   (if (<= y -2.1e-103)
     (+ 1.0 (/ x (* y t)))
     (if (<= y 1.95e-39) (- 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 <= -1650.0) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= -2.1e-103) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 1.95e-39) {
		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 <= (-1650.0d0)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= (-2.1d-103)) then
        tmp = 1.0d0 + (x / (y * t))
    else if (y <= 1.95d-39) 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 <= -1650.0) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= -2.1e-103) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 1.95e-39) {
		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 <= -1650.0:
		tmp = 1.0 - (x / (y * y))
	elif y <= -2.1e-103:
		tmp = 1.0 + (x / (y * t))
	elif y <= 1.95e-39:
		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 <= -1650.0)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= -2.1e-103)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	elseif (y <= 1.95e-39)
		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 <= -1650.0)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= -2.1e-103)
		tmp = 1.0 + (x / (y * t));
	elseif (y <= 1.95e-39)
		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, -1650.0], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-103], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-39], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 4 regimes

2. if y < -1650

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.8%

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

      1. unpow2 93.8%

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

   4. Simplified 93.8%

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

   if -1650 < y < -2.10000000000000005e-103

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-/r* 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in y around inf 69.9%

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

   if -2.10000000000000005e-103 < y < 1.95000000000000015e-39

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 78.2%

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

   if 1.95000000000000015e-39 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1650:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-103}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-39}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -36000000000 \lor \neg \left(y \leq 3.5 \cdot 10^{-37}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -36000000000.0) (not (<= y 3.5e-37)))
   (- 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 ((y <= -36000000000.0) || !(y <= 3.5e-37)) {
		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 ((y <= (-36000000000.0d0)) .or. (.not. (y <= 3.5d-37))) 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 ((y <= -36000000000.0) || !(y <= 3.5e-37)) {
		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 (y <= -36000000000.0) or not (y <= 3.5e-37):
		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 ((y <= -36000000000.0) || !(y <= 3.5e-37))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / 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 ((y <= -36000000000.0) || ~((y <= 3.5e-37)))
		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[Or[LessEqual[y, -36000000000.0], N[Not[LessEqual[y, 3.5e-37]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $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 < -3.6e10 or 3.5000000000000001e-37 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.9%

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

   if -3.6e10 < y < 3.5000000000000001e-37

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-/r* 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -36000000000 \lor \neg \left(y \leq 3.5 \cdot 10^{-37}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -49000000000000:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -49000000000000.0)
   (- 1.0 (/ x (* y y)))
   (if (<= y 2.35e-39) (+ 1.0 (/ (/ x t) (- y z))) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -49000000000000.0) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 2.35e-39) {
		tmp = 1.0 + ((x / t) / (y - 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 <= (-49000000000000.0d0)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 2.35d-39) then
        tmp = 1.0d0 + ((x / t) / (y - 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 <= -49000000000000.0) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 2.35e-39) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -49000000000000.0:
		tmp = 1.0 - (x / (y * y))
	elif y <= 2.35e-39:
		tmp = 1.0 + ((x / t) / (y - z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -49000000000000.0)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 2.35e-39)
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - 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 <= -49000000000000.0)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 2.35e-39)
		tmp = 1.0 + ((x / t) / (y - 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, -49000000000000.0], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e-39], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9e13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.7%

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

      1. unpow2 93.7%

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

   4. Simplified 93.7%

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

   if -4.9e13 < y < 2.3500000000000001e-39

   1. Initial program 97.5%

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

   2. Taylor expanded in t around inf 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-/r* 83.5%

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

   4. Simplified 83.5%

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

   if 2.3500000000000001e-39 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -49000000000000:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-84}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t \leq 820:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.1e-84)
   (- 1.0 (/ x (* t z)))
   (if (<= t 820.0) (- 1.0 (/ (/ x y) (- y z))) (+ 1.0 (/ (/ x t) (- y z))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.1e-84) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 820.0) {
		tmp = 1.0 - ((x / y) / (y - z));
	} 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 (t <= (-1.1d-84)) then
        tmp = 1.0d0 - (x / (t * z))
    else if (t <= 820.0d0) then
        tmp = 1.0d0 - ((x / y) / (y - z))
    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 (t <= -1.1e-84) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 820.0) {
		tmp = 1.0 - ((x / y) / (y - z));
	} 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 t <= -1.1e-84:
		tmp = 1.0 - (x / (t * z))
	elif t <= 820.0:
		tmp = 1.0 - ((x / y) / (y - z))
	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 (t <= -1.1e-84)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (t <= 820.0)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - z)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / 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 (t <= -1.1e-84)
		tmp = 1.0 - (x / (t * z));
	elseif (t <= 820.0)
		tmp = 1.0 - ((x / y) / (y - z));
	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[t, -1.1e-84], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 820.0], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0999999999999999e-84

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.3%

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

   if -1.0999999999999999e-84 < t < 820

   1. Initial program 97.3%

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

   2. Taylor expanded in t around 0 83.4%

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

      1. associate-/r* 85.0%

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

   4. Simplified 85.0%

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

   if 820 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 98.4%

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

      1. +-commutative 98.4%

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

      2. associate-/r* 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-84}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t \leq 820:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-87}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-197}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.1e-87) 1.0 (if (<= t 9.6e-197) (+ 1.0 (/ x (* y z))) 1.0)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.1e-87) {
		tmp = 1.0;
	} else if (t <= 9.6e-197) {
		tmp = 1.0 + (x / (y * 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 (t <= (-3.1d-87)) then
        tmp = 1.0d0
    else if (t <= 9.6d-197) then
        tmp = 1.0d0 + (x / (y * 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 (t <= -3.1e-87) {
		tmp = 1.0;
	} else if (t <= 9.6e-197) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3.1e-87:
		tmp = 1.0
	elif t <= 9.6e-197:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.1e-87)
		tmp = 1.0;
	elseif (t <= 9.6e-197)
		tmp = Float64(1.0 + Float64(x / Float64(y * 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 (t <= -3.1e-87)
		tmp = 1.0;
	elseif (t <= 9.6e-197)
		tmp = 1.0 + (x / (y * 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[t, -3.1e-87], 1.0, If[LessEqual[t, 9.6e-197], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -3.09999999999999998e-87 or 9.6000000000000003e-197 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 81.3%

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

   if -3.09999999999999998e-87 < t < 9.6000000000000003e-197

   1. Initial program 95.8%

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

   2. Taylor expanded in t around 0 86.2%

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

      1. associate-/r* 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in z around inf 69.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-87}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-197}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 99.2% 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 98.8%

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

2. Final simplification 98.8%

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

Alternative 11: 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 98.8%

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

   1. associate-/l/ 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 12: 75.4% 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 98.8%

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

2. Taylor expanded in x around 0 75.8%

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

3. Final simplification 75.8%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023196 
(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)))))