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

Percentage Accurate: 99.0% → 99.0%

Time: 9.6s

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: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (t - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

3. Final simplification 98.6%

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

Alternative 2: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-159}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.9e-117)
   1.0
   (if (<= t 1.5e-303)
     (+ 1.0 (/ (/ x z) y))
     (if (<= t 8.4e-159) (- 1.0 (/ x (* y y))) (+ 1.0 (/ (/ x t) (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.9e-117) {
		tmp = 1.0;
	} else if (t <= 1.5e-303) {
		tmp = 1.0 + ((x / z) / y);
	} else if (t <= 8.4e-159) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 + ((x / t) / (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 <= (-4.9d-117)) then
        tmp = 1.0d0
    else if (t <= 1.5d-303) then
        tmp = 1.0d0 + ((x / z) / y)
    else if (t <= 8.4d-159) then
        tmp = 1.0d0 - (x / (y * y))
    else
        tmp = 1.0d0 + ((x / t) / (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 <= -4.9e-117) {
		tmp = 1.0;
	} else if (t <= 1.5e-303) {
		tmp = 1.0 + ((x / z) / y);
	} else if (t <= 8.4e-159) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.9e-117:
		tmp = 1.0
	elif t <= 1.5e-303:
		tmp = 1.0 + ((x / z) / y)
	elif t <= 8.4e-159:
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.9e-117)
		tmp = 1.0;
	elseif (t <= 1.5e-303)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	elseif (t <= 8.4e-159)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.9e-117)
		tmp = 1.0;
	elseif (t <= 1.5e-303)
		tmp = 1.0 + ((x / z) / y);
	elseif (t <= 8.4e-159)
		tmp = 1.0 - (x / (y * y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.9e-117], 1.0, If[LessEqual[t, 1.5e-303], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e-159], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.8999999999999998e-117

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 89.5%

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

   if -4.8999999999999998e-117 < t < 1.50000000000000014e-303

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-/r* 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in y around inf 62.1%

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

   if 1.50000000000000014e-303 < t < 8.3999999999999997e-159

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.3%

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

   4. Taylor expanded in y around inf 81.2%

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

   if 8.3999999999999997e-159 < t

   1. Initial program 98.9%

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

   3. Taylor expanded in t around inf 95.7%

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

      1. +-commutative 95.7%

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

      2. associate-/r* 94.7%

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

   5. Simplified 94.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-159}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-90}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.45e-90)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 7e-144) (+ 1.0 (/ x (* y (- z y)))) (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e-90) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 7e-144) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (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 <= (-1.45d-90)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 7d-144) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + ((x / t) / (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 <= -1.45e-90) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 7e-144) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.45e-90:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 7e-144:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.45e-90)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 7e-144)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.45e-90)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 7e-144)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.45e-90], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-144], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.44999999999999992e-90

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. +-commutative 86.1%

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

      2. associate-/r* 86.1%

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

   5. Simplified 86.1%

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

   if -1.44999999999999992e-90 < t < 6.9999999999999997e-144

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf 91.9%

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

   if 6.9999999999999997e-144 < t

   1. Initial program 98.9%

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

   3. Taylor expanded in t around inf 96.7%

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

      1. +-commutative 96.7%

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

      2. associate-/r* 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-90}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-72}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-250}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-72)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 3.8e-250)
     (- 1.0 (/ x (* y (- y t))))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-72) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.8e-250) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / t) / (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 (z <= (-1.8d-72)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 3.8d-250) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-72) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.8e-250) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e-72:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 3.8e-250:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-72)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 3.8e-250)
		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

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e-72)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 3.8e-250)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-72], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-250], 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 3 regimes

2. if z < -1.8e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-/r* 97.3%

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

   5. Simplified 97.3%

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

   if -1.8e-72 < z < 3.79999999999999971e-250

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 90.2%

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

   if 3.79999999999999971e-250 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/r* 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-72}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-250}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-158}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.85e-303)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 5.5e-158) (- 1.0 (/ x (* y y))) (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.85e-303) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 5.5e-158) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 + ((x / t) / (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 <= 1.85d-303) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 5.5d-158) then
        tmp = 1.0d0 - (x / (y * y))
    else
        tmp = 1.0d0 + ((x / t) / (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 <= 1.85e-303) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 5.5e-158) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.85e-303:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 5.5e-158:
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.85e-303)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 5.5e-158)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.85e-303)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 5.5e-158)
		tmp = 1.0 - (x / (y * y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.85e-303], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-158], N[(1.0 - N[(x / N[(y * y), $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 < 1.8500000000000001e-303

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 76.7%

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

      1. +-commutative 76.7%

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

      2. associate-/r* 76.6%

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

   5. Simplified 76.6%

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

   if 1.8500000000000001e-303 < t < 5.50000000000000025e-158

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.3%

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

   4. Taylor expanded in y around inf 81.2%

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

   if 5.50000000000000025e-158 < t

   1. Initial program 98.9%

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

   3. Taylor expanded in t around inf 95.7%

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

      1. +-commutative 95.7%

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

      2. associate-/r* 94.7%

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

   5. Simplified 94.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-158}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-44}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-162}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-44)
   (- 1.0 (/ x (* y y)))
   (if (<= y 4.3e-162) (/ (- z (/ x t)) z) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-44) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 4.3e-162) {
		tmp = (z - (x / 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 <= (-1.7d-44)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 4.3d-162) then
        tmp = (z - (x / 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 <= -1.7e-44) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 4.3e-162) {
		tmp = (z - (x / t)) / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-44:
		tmp = 1.0 - (x / (y * y))
	elif y <= 4.3e-162:
		tmp = (z - (x / t)) / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-44)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 4.3e-162)
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-44)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 4.3e-162)
		tmp = (z - (x / t)) / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-44], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-162], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000008e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.8%

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

   4. Taylor expanded in y around inf 86.9%

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

   if -1.70000000000000008e-44 < y < 4.29999999999999996e-162

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 80.8%

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

   4. Taylor expanded in z around 0 79.8%

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

   if 4.29999999999999996e-162 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.8%

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

Alternative 7: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-44}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e-44)
   (- 1.0 (/ x (* y y)))
   (if (<= y 4.3e-162) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e-44) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 4.3e-162) {
		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 <= (-2.05d-44)) then
        tmp = 1.0d0 - (x / (y * y))
    else if (y <= 4.3d-162) 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 <= -2.05e-44) {
		tmp = 1.0 - (x / (y * y));
	} else if (y <= 4.3e-162) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.05e-44:
		tmp = 1.0 - (x / (y * y))
	elif y <= 4.3e-162:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e-44)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	elseif (y <= 4.3e-162)
		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 <= -2.05e-44)
		tmp = 1.0 - (x / (y * y));
	elseif (y <= 4.3e-162)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e-44], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-162], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -2.04999999999999996e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 98.8%

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

   4. Taylor expanded in y around inf 86.9%

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

   if -2.04999999999999996e-44 < y < 4.29999999999999996e-162

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 80.8%

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

   if 4.29999999999999996e-162 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-44}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-166}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-50) 1.0 (if (<= y 2.7e-166) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-50) {
		tmp = 1.0;
	} else if (y <= 2.7e-166) {
		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 <= (-2.5d-50)) then
        tmp = 1.0d0
    else if (y <= 2.7d-166) 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 <= -2.5e-50) {
		tmp = 1.0;
	} else if (y <= 2.7e-166) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-50:
		tmp = 1.0
	elif y <= 2.7e-166:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-50)
		tmp = 1.0;
	elseif (y <= 2.7e-166)
		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 <= -2.5e-50)
		tmp = 1.0;
	elseif (y <= 2.7e-166)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-50], 1.0, If[LessEqual[y, 2.7e-166], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999984e-50 or 2.70000000000000006e-166 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.2%

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

   if -2.49999999999999984e-50 < y < 2.70000000000000006e-166

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 80.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-166}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% 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 98.6%

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

3. Taylor expanded in x around 0 77.9%

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

Reproduce

herbie shell --seed 2024137 
(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)))))