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

Percentage Accurate: 99.0% → 99.0%

Time: 11.0s

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: 99.0% 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

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

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 99.2%

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

Alternative 2: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-92}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e-79)
   1.0
   (if (<= y 3.6e-92)
     (- 1.0 (/ x (* t z)))
     (if (<= y 3.2e-7) (+ (/ x (* t y)) 1.0) (- 1.0 (/ (/ x y) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-79) {
		tmp = 1.0;
	} else if (y <= 3.6e-92) {
		tmp = 1.0 - (x / (t * z));
	} else if (y <= 3.2e-7) {
		tmp = (x / (t * y)) + 1.0;
	} else {
		tmp = 1.0 - ((x / y) / 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 <= (-8.2d-79)) then
        tmp = 1.0d0
    else if (y <= 3.6d-92) then
        tmp = 1.0d0 - (x / (t * z))
    else if (y <= 3.2d-7) then
        tmp = (x / (t * y)) + 1.0d0
    else
        tmp = 1.0d0 - ((x / y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-79) {
		tmp = 1.0;
	} else if (y <= 3.6e-92) {
		tmp = 1.0 - (x / (t * z));
	} else if (y <= 3.2e-7) {
		tmp = (x / (t * y)) + 1.0;
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e-79:
		tmp = 1.0
	elif y <= 3.6e-92:
		tmp = 1.0 - (x / (t * z))
	elif y <= 3.2e-7:
		tmp = (x / (t * y)) + 1.0
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e-79)
		tmp = 1.0;
	elseif (y <= 3.6e-92)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (y <= 3.2e-7)
		tmp = Float64(Float64(x / Float64(t * y)) + 1.0);
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e-79)
		tmp = 1.0;
	elseif (y <= 3.6e-92)
		tmp = 1.0 - (x / (t * z));
	elseif (y <= 3.2e-7)
		tmp = (x / (t * y)) + 1.0;
	else
		tmp = 1.0 - ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e-79], 1.0, If[LessEqual[y, 3.6e-92], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-7], N[(N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.19999999999999987e-79

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.19999999999999987e-79 < y < 3.60000000000000016e-92

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.60000000000000016e-92 < y < 3.2000000000000001e-7

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.2000000000000001e-7 < 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 y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-91}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.48e-77)
   1.0
   (if (<= y 2.35e-91)
     (- 1.0 (/ x (* t z)))
     (if (<= y 5e-6) (+ (/ x (* t y)) 1.0) (- 1.0 (/ x (* y y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.48e-77) {
		tmp = 1.0;
	} else if (y <= 2.35e-91) {
		tmp = 1.0 - (x / (t * z));
	} else if (y <= 5e-6) {
		tmp = (x / (t * y)) + 1.0;
	} else {
		tmp = 1.0 - (x / (y * 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 <= (-1.48d-77)) then
        tmp = 1.0d0
    else if (y <= 2.35d-91) then
        tmp = 1.0d0 - (x / (t * z))
    else if (y <= 5d-6) then
        tmp = (x / (t * y)) + 1.0d0
    else
        tmp = 1.0d0 - (x / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.48e-77) {
		tmp = 1.0;
	} else if (y <= 2.35e-91) {
		tmp = 1.0 - (x / (t * z));
	} else if (y <= 5e-6) {
		tmp = (x / (t * y)) + 1.0;
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.48e-77:
		tmp = 1.0
	elif y <= 2.35e-91:
		tmp = 1.0 - (x / (t * z))
	elif y <= 5e-6:
		tmp = (x / (t * y)) + 1.0
	else:
		tmp = 1.0 - (x / (y * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.48e-77)
		tmp = 1.0;
	elseif (y <= 2.35e-91)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (y <= 5e-6)
		tmp = Float64(Float64(x / Float64(t * y)) + 1.0);
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.48e-77)
		tmp = 1.0;
	elseif (y <= 2.35e-91)
		tmp = 1.0 - (x / (t * z));
	elseif (y <= 5e-6)
		tmp = (x / (t * y)) + 1.0;
	else
		tmp = 1.0 - (x / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.48e-77], 1.0, If[LessEqual[y, 2.35e-91], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-6], N[(N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.48000000000000002e-77

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.48000000000000002e-77 < y < 2.35000000000000003e-91

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.35000000000000003e-91 < y < 5.00000000000000041e-6

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 5.00000000000000041e-6 < 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 y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-89}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e-89)
   (- 1.0 (/ x (* t z)))
   (if (<= t 1.15e-22)
     (- 1.0 (/ x (* (- y z) y)))
     (- 1.0 (/ (/ x t) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-89) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 1.15e-22) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = 1.0 - ((x / t) / (z - 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 (t <= (-7d-89)) then
        tmp = 1.0d0 - (x / (t * z))
    else if (t <= 1.15d-22) then
        tmp = 1.0d0 - (x / ((y - z) * y))
    else
        tmp = 1.0d0 - ((x / t) / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-89) {
		tmp = 1.0 - (x / (t * z));
	} else if (t <= 1.15e-22) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = 1.0 - ((x / t) / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e-89:
		tmp = 1.0 - (x / (t * z))
	elif t <= 1.15e-22:
		tmp = 1.0 - (x / ((y - z) * y))
	else:
		tmp = 1.0 - ((x / t) / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e-89)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	elseif (t <= 1.15e-22)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e-89)
		tmp = 1.0 - (x / (t * z));
	elseif (t <= 1.15e-22)
		tmp = 1.0 - (x / ((y - z) * y));
	else
		tmp = 1.0 - ((x / t) / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e-89], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-22], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.9999999999999994e-89

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6.9999999999999994e-89 < t < 1.1499999999999999e-22

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.1499999999999999e-22 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-79}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-69}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.8e-79)
   (- 1.0 (/ x (* (- y z) y)))
   (if (<= y 7.2e-69) (- 1.0 (/ x (* t z))) (+ 1.0 (/ (/ x y) (- t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.8e-79) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else if (y <= 7.2e-69) {
		tmp = 1.0 - (x / (t * z));
	} 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 <= (-9.8d-79)) then
        tmp = 1.0d0 - (x / ((y - z) * y))
    else if (y <= 7.2d-69) then
        tmp = 1.0d0 - (x / (t * z))
    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 <= -9.8e-79) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else if (y <= 7.2e-69) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0 + ((x / y) / (t - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.8e-79:
		tmp = 1.0 - (x / ((y - z) * y))
	elif y <= 7.2e-69:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0 + ((x / y) / (t - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.8e-79)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	elseif (y <= 7.2e-69)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.8e-79)
		tmp = 1.0 - (x / ((y - z) * y));
	elseif (y <= 7.2e-69)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0 + ((x / y) / (t - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.8e-79], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-69], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.8000000000000001e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.8000000000000001e-79 < y < 7.20000000000000035e-69

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 7.20000000000000035e-69 < 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 z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-69}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (/ x y) (- t y)))))
   (if (<= y -1.25e-82) t_1 (if (<= y 4.2e-69) (- 1.0 (/ x (* t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / y) / (t - y));
	double tmp;
	if (y <= -1.25e-82) {
		tmp = t_1;
	} else if (y <= 4.2e-69) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + ((x / y) / (t - y))
    if (y <= (-1.25d-82)) then
        tmp = t_1
    else if (y <= 4.2d-69) then
        tmp = 1.0d0 - (x / (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / y) / (t - y));
	double tmp;
	if (y <= -1.25e-82) {
		tmp = t_1;
	} else if (y <= 4.2e-69) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + ((x / y) / (t - y))
	tmp = 0
	if y <= -1.25e-82:
		tmp = t_1
	elif y <= 4.2e-69:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)))
	tmp = 0.0
	if (y <= -1.25e-82)
		tmp = t_1;
	elseif (y <= 4.2e-69)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((x / y) / (t - y));
	tmp = 0.0;
	if (y <= -1.25e-82)
		tmp = t_1;
	elseif (y <= 4.2e-69)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e-82], t$95$1, If[LessEqual[y, 4.2e-69], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e-82 or 4.1999999999999999e-69 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.25e-82 < y < 4.1999999999999999e-69

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-72}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.22e-77) 1.0 (if (<= y 8.2e-72) (- 1.0 (/ x (* t z))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e-77) {
		tmp = 1.0;
	} else if (y <= 8.2e-72) {
		tmp = 1.0 - (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 <= (-1.22d-77)) then
        tmp = 1.0d0
    else if (y <= 8.2d-72) then
        tmp = 1.0d0 - (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 <= -1.22e-77) {
		tmp = 1.0;
	} else if (y <= 8.2e-72) {
		tmp = 1.0 - (x / (t * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.22e-77:
		tmp = 1.0
	elif y <= 8.2e-72:
		tmp = 1.0 - (x / (t * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.22e-77)
		tmp = 1.0;
	elseif (y <= 8.2e-72)
		tmp = Float64(1.0 - Float64(x / Float64(t * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.22e-77)
		tmp = 1.0;
	elseif (y <= 8.2e-72)
		tmp = 1.0 - (x / (t * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.22e-77], 1.0, If[LessEqual[y, 8.2e-72], N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22000000000000001e-77 or 8.20000000000000007e-72 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.22000000000000001e-77 < y < 8.20000000000000007e-72

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-248}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.6e-248) 1.0 (if (<= z 2.55e-194) (+ (/ x (* t y)) 1.0) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e-248) {
		tmp = 1.0;
	} else if (z <= 2.55e-194) {
		tmp = (x / (t * y)) + 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 (z <= (-5.6d-248)) then
        tmp = 1.0d0
    else if (z <= 2.55d-194) then
        tmp = (x / (t * y)) + 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 (z <= -5.6e-248) {
		tmp = 1.0;
	} else if (z <= 2.55e-194) {
		tmp = (x / (t * y)) + 1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.6e-248:
		tmp = 1.0
	elif z <= 2.55e-194:
		tmp = (x / (t * y)) + 1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.6e-248)
		tmp = 1.0;
	elseif (z <= 2.55e-194)
		tmp = Float64(Float64(x / Float64(t * y)) + 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.6e-248)
		tmp = 1.0;
	elseif (z <= 2.55e-194)
		tmp = (x / (t * y)) + 1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.6e-248], 1.0, If[LessEqual[z, 2.55e-194], N[(N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6000000000000002e-248 or 2.5499999999999999e-194 < z

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.6000000000000002e-248 < z < 2.5499999999999999e-194

   1. Initial program 93.9%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 74.5% 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 99.2%

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

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))))