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

Percentage Accurate: 99.1% → 99.1%

Time: 8.2s

Alternatives: 8

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-71}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-116}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e-71)
   (- 1.0 (/ x (* y (- y z))))
   (if (<= y 6.8e-116) (- 1.0 (/ x (* z t))) (- 1.0 (/ (/ x (- y t)) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e-71) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 6.8e-116) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	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 <= (-8d-71)) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else if (y <= 6.8d-116) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 - ((x / (y - t)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e-71) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 6.8e-116) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e-71:
		tmp = 1.0 - (x / (y * (y - z)))
	elif y <= 6.8e-116:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 - ((x / (y - t)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e-71)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	elseif (y <= 6.8e-116)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e-71)
		tmp = 1.0 - (x / (y * (y - z)));
	elseif (y <= 6.8e-116)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 - ((x / (y - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e-71], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-116], N[(1.0 - N[(x / N[(z * t), $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 < -7.9999999999999993e-71

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 88.0%

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

   if -7.9999999999999993e-71 < y < 6.79999999999999985e-116

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 86.0%

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

   if 6.79999999999999985e-116 < 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 86.3%

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

      1. *-commutative 86.3%

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

      2. associate-/r* 86.3%

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

   4. Simplified 86.3%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-71}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-116}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 3: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-23}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{elif}\;y \leq 460000000:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-23)
   (- 1.0 (/ (/ x y) (- y z)))
   (if (<= y 460000000.0)
     (+ 1.0 (/ (/ x z) (- y t)))
     (- 1.0 (/ (/ x (- y t)) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-23) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else if (y <= 460000000.0) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	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 <= (-5.5d-23)) then
        tmp = 1.0d0 - ((x / y) / (y - z))
    else if (y <= 460000000.0d0) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 - ((x / (y - t)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-23) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else if (y <= 460000000.0) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-23:
		tmp = 1.0 - ((x / y) / (y - z))
	elif y <= 460000000.0:
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 - ((x / (y - t)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-23)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - z)));
	elseif (y <= 460000000.0)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-23)
		tmp = 1.0 - ((x / y) / (y - z));
	elseif (y <= 460000000.0)
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 - ((x / (y - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-23], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 460000000.0], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $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 < -5.5000000000000001e-23

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 90.6%

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

      1. associate-/r* 90.7%

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

   4. Simplified 90.7%

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

   if -5.5000000000000001e-23 < y < 4.6e8

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/r* 84.4%

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

   4. Simplified 84.4%

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

   if 4.6e8 < 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 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-/r* 93.1%

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

   4. Simplified 93.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-23}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{elif}\;y \leq 460000000:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]

Alternative 4: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-68}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.8e-178)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.25e-68)
     (- 1.0 (/ (/ x (- y z)) y))
     (+ 1.0 (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e-178) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.25e-68) {
		tmp = 1.0 - ((x / (y - z)) / y);
	} 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 <= (-3.8d-178)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.25d-68) then
        tmp = 1.0d0 - ((x / (y - z)) / y)
    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 <= -3.8e-178) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.25e-68) {
		tmp = 1.0 - ((x / (y - z)) / y);
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.8e-178:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.25e-68:
		tmp = 1.0 - ((x / (y - z)) / y)
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.8e-178)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.25e-68)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - z)) / y));
	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 <= -3.8e-178)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.25e-68)
		tmp = 1.0 - ((x / (y - z)) / y);
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.8e-178], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-68], N[(1.0 - N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $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 < -3.80000000000000015e-178

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. associate-/r* 77.6%

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

   4. Simplified 77.6%

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

   if -3.80000000000000015e-178 < t < 1.24999999999999993e-68

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-/r* 96.5%

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

   4. Simplified 96.5%

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

   if 1.24999999999999993e-68 < 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 91.2%

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

      1. associate-*r/ 91.2%

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

      2. neg-mul-1 91.2%

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

   4. Simplified 91.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-178}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-68}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 5: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-41}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-79) 1.0 (if (<= y 6.8e-41) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-79) {
		tmp = 1.0;
	} else if (y <= 6.8e-41) {
		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 <= (-1.15d-79)) then
        tmp = 1.0d0
    else if (y <= 6.8d-41) 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 <= -1.15e-79) {
		tmp = 1.0;
	} else if (y <= 6.8e-41) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-79:
		tmp = 1.0
	elif y <= 6.8e-41:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-79)
		tmp = 1.0;
	elseif (y <= 6.8e-41)
		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 <= -1.15e-79)
		tmp = 1.0;
	elseif (y <= 6.8e-41)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-79], 1.0, If[LessEqual[y, 6.8e-41], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000006e-79 or 6.7999999999999997e-41 < 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 91.1%

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

      1. associate-/r* 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in x around 0 89.8%

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

   if -1.15000000000000006e-79 < y < 6.7999999999999997e-41

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 81.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-41}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-69}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-37}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e-69)
   (- 1.0 (/ x (* y (- y z))))
   (if (<= y 3.6e-37) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e-69) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 3.6e-37) {
		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 <= (-7d-69)) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else if (y <= 3.6d-37) 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 <= -7e-69) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 3.6e-37) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e-69:
		tmp = 1.0 - (x / (y * (y - z)))
	elif y <= 3.6e-37:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e-69)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	elseif (y <= 3.6e-37)
		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 <= -7e-69)
		tmp = 1.0 - (x / (y * (y - z)));
	elseif (y <= 3.6e-37)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e-69], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-37], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000003e-69

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 88.0%

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

   if -7.0000000000000003e-69 < y < 3.60000000000000007e-37

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.1%

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

   if 3.60000000000000007e-37 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.8%

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

      1. associate-/r* 94.8%

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

   4. Simplified 94.8%

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

   5. Taylor expanded in x around 0 91.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-69}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-37}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.5e-191) (+ 1.0 (/ (/ x z) y)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.5e-191) {
		tmp = 1.0 + ((x / z) / y);
	} 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 (t <= 6.5d-191) then
        tmp = 1.0d0 + ((x / z) / y)
    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 (t <= 6.5e-191) {
		tmp = 1.0 + ((x / z) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 6.5e-191:
		tmp = 1.0 + ((x / z) / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6.5e-191)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6.5e-191)
		tmp = 1.0 + ((x / z) / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 6.5e-191], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < 6.4999999999999995e-191

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 76.1%

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

      1. associate-/r* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in z around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-/r* 66.8%

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

   7. Simplified 66.8%

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

   if 6.4999999999999995e-191 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 67.9%

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

      1. associate-/r* 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in x around 0 77.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-191}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 75.5% 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 99.9%

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

2. Taylor expanded in t around 0 72.9%

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

   1. associate-/r* 71.8%

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

4. Simplified 71.8%

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

5. Taylor expanded in x around 0 77.5%

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

6. Final simplification 77.5%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023301 
(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)))))