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

Percentage Accurate: 99.2% → 99.2%

Time: 13.3s

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: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Final simplification 99.7%

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

Alternative 2: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{z}}{y - t} + 1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-167}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.6e-55)
   (+ (/ (/ x z) (- y t)) 1.0)
   (if (<= z 8.8e-167)
     (- 1.0 (/ (/ x y) (- y t)))
     (+ (/ (/ x t) (- y z)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e-55) {
		tmp = ((x / z) / (y - t)) + 1.0;
	} else if (z <= 8.8e-167) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = ((x / t) / (y - z)) + 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 (z <= (-5.6d-55)) then
        tmp = ((x / z) / (y - t)) + 1.0d0
    else if (z <= 8.8d-167) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else
        tmp = ((x / t) / (y - z)) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e-55) {
		tmp = ((x / z) / (y - t)) + 1.0;
	} else if (z <= 8.8e-167) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = ((x / t) / (y - z)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.6e-55:
		tmp = ((x / z) / (y - t)) + 1.0
	elif z <= 8.8e-167:
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = ((x / t) / (y - z)) + 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.6e-55)
		tmp = Float64(Float64(Float64(x / z) / Float64(y - t)) + 1.0);
	elseif (z <= 8.8e-167)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = Float64(Float64(Float64(x / t) / Float64(y - z)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.6e-55)
		tmp = ((x / z) / (y - t)) + 1.0;
	elseif (z <= 8.8e-167)
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = ((x / t) / (y - z)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.6e-55], N[(N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[z, 8.8e-167], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999968e-55

   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 inf 97.2%

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

      1. associate-/r* 97.3%

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

   5. Simplified 97.3%

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

   if -5.59999999999999968e-55 < z < 8.7999999999999999e-167

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 92.0%

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

      1. sub-neg 92.0%

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

      2. associate-/r* 89.2%

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

      3. distribute-neg-frac2 89.2%

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

      4. neg-sub0 89.2%

         \[\leadsto 1 + \frac{\frac{x}{y}}{\color{blue}{0 - \left(y - t\right)}} \]

      5. sub-neg 89.2%

         \[\leadsto 1 + \frac{\frac{x}{y}}{0 - \color{blue}{\left(y + \left(-t\right)\right)}} \]

      6. +-commutative 89.2%

         \[\leadsto 1 + \frac{\frac{x}{y}}{0 - \color{blue}{\left(\left(-t\right) + y\right)}} \]

      7. associate--r+ 89.2%

         \[\leadsto 1 + \frac{\frac{x}{y}}{\color{blue}{\left(0 - \left(-t\right)\right) - y}} \]

      8. neg-sub0 89.2%

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

      9. remove-double-neg 89.2%

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

   5. Simplified 89.2%

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

   if 8.7999999999999999e-167 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.4%

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

      1. associate-/r* 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{z}}{y - t} + 1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-167}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e-38)
   1.0
   (if (<= y 7.5e-81)
     (+ (/ (/ x t) (- y z)) 1.0)
     (- 1.0 (/ (/ x y) (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-38) {
		tmp = 1.0;
	} else if (y <= 7.5e-81) {
		tmp = ((x / t) / (y - z)) + 1.0;
	} else {
		tmp = 1.0 - ((x / y) / (y - 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 (y <= (-2.25d-38)) then
        tmp = 1.0d0
    else if (y <= 7.5d-81) then
        tmp = ((x / t) / (y - z)) + 1.0d0
    else
        tmp = 1.0d0 - ((x / y) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-38) {
		tmp = 1.0;
	} else if (y <= 7.5e-81) {
		tmp = ((x / t) / (y - z)) + 1.0;
	} else {
		tmp = 1.0 - ((x / y) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e-38:
		tmp = 1.0
	elif y <= 7.5e-81:
		tmp = ((x / t) / (y - z)) + 1.0
	else:
		tmp = 1.0 - ((x / y) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-38)
		tmp = 1.0;
	elseif (y <= 7.5e-81)
		tmp = Float64(Float64(Float64(x / t) / Float64(y - z)) + 1.0);
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-38)
		tmp = 1.0;
	elseif (y <= 7.5e-81)
		tmp = ((x / t) / (y - z)) + 1.0;
	else
		tmp = 1.0 - ((x / y) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e-38], 1.0, If[LessEqual[y, 7.5e-81], N[(N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25000000000000004e-38

   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 92.7%

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

   if -2.25000000000000004e-38 < y < 7.50000000000000018e-81

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 91.8%

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

      1. associate-/r* 89.9%

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

   5. Simplified 89.9%

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

   if 7.50000000000000018e-81 < 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 z around 0 90.3%

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

      1. sub-neg 90.3%

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

      2. associate-/r* 90.3%

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

      3. distribute-neg-frac2 90.3%

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

      4. neg-sub0 90.3%

         \[\leadsto 1 + \frac{\frac{x}{y}}{\color{blue}{0 - \left(y - t\right)}} \]

      5. sub-neg 90.3%

         \[\leadsto 1 + \frac{\frac{x}{y}}{0 - \color{blue}{\left(y + \left(-t\right)\right)}} \]

      6. +-commutative 90.3%

         \[\leadsto 1 + \frac{\frac{x}{y}}{0 - \color{blue}{\left(\left(-t\right) + y\right)}} \]

      7. associate--r+ 90.3%

         \[\leadsto 1 + \frac{\frac{x}{y}}{\color{blue}{\left(0 - \left(-t\right)\right) - y}} \]

      8. neg-sub0 90.3%

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

      9. remove-double-neg 90.3%

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

   5. Simplified 90.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e-18) 1.0 (if (<= y 2.6e-67) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e-18) {
		tmp = 1.0;
	} else if (y <= 2.6e-67) {
		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 <= (-1.85d-18)) then
        tmp = 1.0d0
    else if (y <= 2.6d-67) 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 <= -1.85e-18) {
		tmp = 1.0;
	} else if (y <= 2.6e-67) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e-18:
		tmp = 1.0
	elif y <= 2.6e-67:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e-18)
		tmp = 1.0;
	elseif (y <= 2.6e-67)
		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 <= -1.85e-18)
		tmp = 1.0;
	elseif (y <= 2.6e-67)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e-18], 1.0, If[LessEqual[y, 2.6e-67], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8500000000000002e-18 or 2.5999999999999999e-67 < 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 90.9%

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

   if -1.8500000000000002e-18 < y < 2.5999999999999999e-67

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 82.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.65 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.65e-165)
   (+ (* (/ x z) (/ 1.0 y)) 1.0)
   (+ (/ (/ x t) (- y z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.65e-165) {
		tmp = ((x / z) * (1.0 / y)) + 1.0;
	} else {
		tmp = ((x / t) / (y - z)) + 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 <= 1.65d-165) then
        tmp = ((x / z) * (1.0d0 / y)) + 1.0d0
    else
        tmp = ((x / t) / (y - z)) + 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 <= 1.65e-165) {
		tmp = ((x / z) * (1.0 / y)) + 1.0;
	} else {
		tmp = ((x / t) / (y - z)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.65e-165:
		tmp = ((x / z) * (1.0 / y)) + 1.0
	else:
		tmp = ((x / t) / (y - z)) + 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.65e-165)
		tmp = Float64(Float64(Float64(x / z) * Float64(1.0 / y)) + 1.0);
	else
		tmp = Float64(Float64(Float64(x / t) / Float64(y - z)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.65e-165)
		tmp = ((x / z) * (1.0 / y)) + 1.0;
	else
		tmp = ((x / t) / (y - z)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.65e-165], N[(N[(N[(x / z), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.6499999999999999e-165

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 78.9%

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

      1. associate-/r* 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in y around inf 59.2%

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

      1. *-un-lft-identity 59.2%

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

      2. times-frac 59.1%

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

   8. Applied egg-rr 59.1%

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

   if 1.6499999999999999e-165 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 89.4%

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

      1. associate-/r* 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.65 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{y \cdot z} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.3e-162) (+ (/ x (* y z)) 1.0) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.3e-162) {
		tmp = (x / (y * z)) + 1.0;
	} 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 <= 1.3d-162) then
        tmp = (x / (y * z)) + 1.0d0
    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 <= 1.3e-162) {
		tmp = (x / (y * z)) + 1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.3e-162:
		tmp = (x / (y * z)) + 1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.3e-162)
		tmp = Float64(Float64(x / Float64(y * z)) + 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.3e-162)
		tmp = (x / (y * z)) + 1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.3e-162], N[(N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < 1.3e-162

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. associate-/r* 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in y around inf 59.3%

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

   if 1.3e-162 < t

   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 81.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{y \cdot z} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.3e+220) (/ x (* z (- t))) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.3e+220) {
		tmp = 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 (x <= (-4.3d+220)) then
        tmp = 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 (x <= -4.3e+220) {
		tmp = x / (z * -t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.3e+220:
		tmp = x / (z * -t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.3e+220)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.3e+220)
		tmp = x / (z * -t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.3e+220], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e220

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.1%

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

      1. associate-/r* 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around inf 55.0%

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

   7. Taylor expanded in y around 0 47.0%

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

      1. associate-*r/ 47.0%

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

      2. neg-mul-1 47.0%

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

   9. Simplified 47.0%

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

   if -4.3e220 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 78.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% 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 99.7%

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

3. Taylor expanded in x around 0 73.8%

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

Reproduce

herbie shell --seed 2024185 
(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)))))