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

Percentage Accurate: 99.1% → 99.1%

Time: 7.0s

Alternatives: 9

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: 99.1% 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: 99.1% 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]

Derivation

1. Initial program 99.5%

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

2. Final simplification 99.5%

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

Alternative 2: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-98} \lor \neg \left(y \leq 3.5 \cdot 10^{-78}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e-98) (not (<= y 3.5e-78)))
   (- 1.0 (/ x (* y (- y z))))
   (+ 1.0 (* x (/ (/ -1.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-98) || !(y <= 3.5e-78)) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y <= (-6d-98)) .or. (.not. (y <= 3.5d-78))) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else
        tmp = 1.0d0 + (x * (((-1.0d0) / t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-98) || !(y <= 3.5e-78)) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e-98) or not (y <= 3.5e-78):
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 + (x * ((-1.0 / t) / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e-98) || !(y <= 3.5e-78))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	else
		tmp = Float64(1.0 + Float64(x * Float64(Float64(-1.0 / t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6e-98) || ~((y <= 3.5e-78)))
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6e-98], N[Not[LessEqual[y, 3.5e-78]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e-98 or 3.4999999999999999e-78 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.1%

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

   if -6e-98 < y < 3.4999999999999999e-78

   1. Initial program 98.9%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-/r* 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in y around 0 80.8%

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

      1. associate-/r* 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-98} \lor \neg \left(y \leq 3.5 \cdot 10^{-78}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \end{array} \]

Alternative 3: 91.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{-126} \lor \neg \left(t \leq 1.36 \cdot 10^{-76}\right):\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.65e-126) (not (<= t 1.36e-76)))
   (+ 1.0 (/ x (* (- y z) t)))
   (- 1.0 (/ x (* y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.65e-126) || !(t <= 1.36e-76)) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((t <= (-2.65d-126)) .or. (.not. (t <= 1.36d-76))) then
        tmp = 1.0d0 + (x / ((y - z) * t))
    else
        tmp = 1.0d0 - (x / (y * (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.65e-126) || !(t <= 1.36e-76)) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.65e-126) or not (t <= 1.36e-76):
		tmp = 1.0 + (x / ((y - z) * t))
	else:
		tmp = 1.0 - (x / (y * (y - z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.65e-126) || !(t <= 1.36e-76))
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.65e-126) || ~((t <= 1.36e-76)))
		tmp = 1.0 + (x / ((y - z) * t));
	else
		tmp = 1.0 - (x / (y * (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.65e-126], N[Not[LessEqual[t, 1.36e-76]], $MachinePrecision]], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $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 < -2.64999999999999997e-126 or 1.35999999999999993e-76 < 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 95.7%

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

      1. associate-*r/ 95.7%

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

      2. neg-mul-1 95.7%

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

   4. Simplified 95.7%

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

   if -2.64999999999999997e-126 < t < 1.35999999999999993e-76

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 86.1%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{-126} \lor \neg \left(t \leq 1.36 \cdot 10^{-76}\right):\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 4: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-103}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e-38)
   (- 1.0 (/ x (* y y)))
   (if (<= y 8.8e-103) (+ 1.0 (* x (/ (/ -1.0 t) z))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-38) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 8.8e-103) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-4.1d-38)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 8.8d-103) then
        tmp = 1.0d0 + (x * (((-1.0d0) / t) / z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-38) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 8.8e-103) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e-38:
		tmp = 1.0 - (x / (y * y))
	elif y <= 8.8e-103:
		tmp = 1.0 + (x * ((-1.0 / t) / z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e-38)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 8.8e-103)
		tmp = Float64(1.0 + Float64(x * Float64(Float64(-1.0 / t) / z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.1e-38)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 8.8e-103)
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e-38], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-103], N[(1.0 + N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999998e-38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. unpow2 90.7%

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

   4. Simplified 90.7%

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

   if -4.0999999999999998e-38 < y < 8.7999999999999997e-103

   1. Initial program 98.9%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-/r* 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in y around 0 78.4%

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

      1. associate-/r* 78.4%

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

   6. Simplified 78.4%

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

   if 8.7999999999999997e-103 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.3%

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

      1. unpow2 86.3%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in x around 0 90.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-103}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;1 + \frac{-1}{y \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-103}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e-39)
   (+ 1.0 (/ -1.0 (* y (/ y x))))
   (if (<= y 4e-103) (+ 1.0 (* x (/ (/ -1.0 t) z))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-39) {
		tmp = 1.0 + (-1.0 / (y * (y / x)));
	} else if (y <= 4e-103) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-6.5d-39)) then
        tmp = 1.0d0 + ((-1.0d0) / (y * (y / x)))
    else if (y <= 4d-103) then
        tmp = 1.0d0 + (x * (((-1.0d0) / t) / z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-39) {
		tmp = 1.0 + (-1.0 / (y * (y / x)));
	} else if (y <= 4e-103) {
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e-39:
		tmp = 1.0 + (-1.0 / (y * (y / x)))
	elif y <= 4e-103:
		tmp = 1.0 + (x * ((-1.0 / t) / z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e-39)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(y * Float64(y / x))));
	elseif (y <= 4e-103)
		tmp = Float64(1.0 + Float64(x * Float64(Float64(-1.0 / t) / z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e-39)
		tmp = 1.0 + (-1.0 / (y * (y / x)));
	elseif (y <= 4e-103)
		tmp = 1.0 + (x * ((-1.0 / t) / z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e-39], N[(1.0 + N[(-1.0 / N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-103], N[(1.0 + N[(x * N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000027e-39

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. unpow2 90.7%

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

      2. associate-/r* 90.7%

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

   4. Simplified 90.7%

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

      1. clear-num 90.6%

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

      2. inv-pow 90.6%

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

      3. div-inv 90.7%

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

      4. clear-num 90.7%

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

   6. Applied egg-rr 90.7%

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

      1. unpow-1 90.7%

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

   8. Simplified 90.7%

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

   if -6.50000000000000027e-39 < y < 3.99999999999999983e-103

   1. Initial program 98.9%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-/r* 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in y around 0 78.4%

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

      1. associate-/r* 78.4%

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

   6. Simplified 78.4%

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

   if 3.99999999999999983e-103 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.3%

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

      1. unpow2 86.3%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in x around 0 90.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-39}:\\ \;\;\;\;1 + \frac{-1}{y \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-103}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-188}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-76}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.6e-188)
   (+ 1.0 (/ x (* z (- y t))))
   (if (<= t 1.08e-76)
     (- 1.0 (/ x (* y (- y z))))
     (+ 1.0 (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-188) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 1.08e-76) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (t <= (-3.6d-188)) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else if (t <= 1.08d-76) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-188) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 1.08e-76) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.6e-188:
		tmp = 1.0 + (x / (z * (y - t)))
	elif t <= 1.08e-76:
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.6e-188)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	elseif (t <= 1.08e-76)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.6e-188)
		tmp = 1.0 + (x / (z * (y - t)));
	elseif (t <= 1.08e-76)
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.6e-188], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e-76], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999997e-188

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.5%

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

      1. associate-*r/ 81.5%

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

      2. neg-mul-1 81.5%

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

   4. Simplified 81.5%

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

   if -3.5999999999999997e-188 < t < 1.08e-76

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 88.0%

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

   if 1.08e-76 < 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 95.2%

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

      1. associate-*r/ 95.2%

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

      2. neg-mul-1 95.2%

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

   4. Simplified 95.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-188}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-76}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 7: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-103}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-60) 1.0 (if (<= y 8.5e-103) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-60) {
		tmp = 1.0;
	} else if (y <= 8.5e-103) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-1.35d-60)) then
        tmp = 1.0d0
    else if (y <= 8.5d-103) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-60) {
		tmp = 1.0;
	} else if (y <= 8.5e-103) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-60:
		tmp = 1.0
	elif y <= 8.5e-103:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-60)
		tmp = 1.0;
	elseif (y <= 8.5e-103)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-60)
		tmp = 1.0;
	elseif (y <= 8.5e-103)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-60], 1.0, If[LessEqual[y, 8.5e-103], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-60 or 8.50000000000000032e-103 < 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 87.2%

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

      1. unpow2 87.2%

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

      2. associate-/r* 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in x around 0 87.8%

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

   if -1.35e-60 < y < 8.50000000000000032e-103

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 79.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-103}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-37}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-103}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e-37)
   (- 1.0 (/ x (* y y)))
   (if (<= y 7.2e-103) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e-37) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 7.2e-103) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-3.1d-37)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 7.2d-103) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e-37) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 7.2e-103) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.1e-37:
		tmp = 1.0 - (x / (y * y))
	elif y <= 7.2e-103:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.1e-37)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 7.2e-103)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.1e-37)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 7.2e-103)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.1e-37], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-103], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -3.09999999999999993e-37

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. unpow2 90.7%

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

   4. Simplified 90.7%

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

   if -3.09999999999999993e-37 < y < 7.1999999999999996e-103

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 78.5%

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

   if 7.1999999999999996e-103 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.3%

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

      1. unpow2 86.3%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in x around 0 90.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-37}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-103}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 75.8% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in y around inf 57.5%

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

   1. unpow2 57.5%

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

   2. associate-/r* 57.5%

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

4. Simplified 57.5%

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

5. Taylor expanded in x around 0 76.4%

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

6. Final simplification 76.4%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023230 
(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)))))