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

Percentage Accurate: 99.0% → 99.0%

Time: 10.9s

Alternatives: 7

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 99.2%

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

3. Final simplification 99.2%

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

Alternative 2: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-91}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-14}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e-79)
   1.0
   (if (<= y 7.8e-91)
     (- 1.0 (/ x (* z t)))
     (if (<= y 6.4e-14) (+ 1.0 (/ x (* y t))) (- 1.0 (/ (/ x y) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-79) {
		tmp = 1.0;
	} else if (y <= 7.8e-91) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 6.4e-14) {
		tmp = 1.0 + (x / (y * t));
	} 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 <= (-8.5d-79)) then
        tmp = 1.0d0
    else if (y <= 7.8d-91) then
        tmp = 1.0d0 - (x / (z * t))
    else if (y <= 6.4d-14) then
        tmp = 1.0d0 + (x / (y * t))
    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 <= -8.5e-79) {
		tmp = 1.0;
	} else if (y <= 7.8e-91) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 6.4e-14) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e-79:
		tmp = 1.0
	elif y <= 7.8e-91:
		tmp = 1.0 - (x / (z * t))
	elif y <= 6.4e-14:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e-79)
		tmp = 1.0;
	elseif (y <= 7.8e-91)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (y <= 6.4e-14)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	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 <= -8.5e-79)
		tmp = 1.0;
	elseif (y <= 7.8e-91)
		tmp = 1.0 - (x / (z * t));
	elseif (y <= 6.4e-14)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 - ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e-79], 1.0, If[LessEqual[y, 7.8e-91], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-14], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.50000000000000029e-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 88.6%

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

   if -8.50000000000000029e-79 < y < 7.79999999999999987e-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 81.3%

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

   if 7.79999999999999987e-91 < y < 6.4000000000000005e-14

   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 73.0%

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

      1. +-commutative 73.0%

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

      2. associate-/r* 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in y around inf 57.2%

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

   if 6.4000000000000005e-14 < 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 98.2%

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

      1. associate-/r* 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in y around inf 96.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-91}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-14}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e-89)
   (+ 1.0 (/ -1.0 (* t (/ z x))))
   (if (<= t 1.15e-22)
     (+ 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 <= -7e-89) {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	} else if (t <= 1.15e-22) {
		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 <= (-7d-89)) then
        tmp = 1.0d0 + ((-1.0d0) / (t * (z / x)))
    else if (t <= 1.15d-22) 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 <= -7e-89) {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	} else if (t <= 1.15e-22) {
		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 <= -7e-89:
		tmp = 1.0 + (-1.0 / (t * (z / x)))
	elif t <= 1.15e-22:
		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 <= -7e-89)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(t * Float64(z / x))));
	elseif (t <= 1.15e-22)
		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 <= -7e-89)
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	elseif (t <= 1.15e-22)
		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, -7e-89], N[(1.0 + N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-22], 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 < -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 79.7%

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

      1. clear-num 79.8%

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

      2. inv-pow 79.8%

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

   5. Applied egg-rr 79.8%

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

      1. unpow-1 79.8%

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

      2. associate-/l* 78.5%

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

   7. Simplified 78.5%

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

   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 89.6%

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

   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 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-/r* 95.8%

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

   5. Simplified 95.8%

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

4. Final simplification 87.9%

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

Alternative 4: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-13}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e-11)
   1.0
   (if (<= y 1.72e-13) (+ 1.0 (/ (/ x t) (- y z))) (- 1.0 (/ (/ x y) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-11) {
		tmp = 1.0;
	} else if (y <= 1.72e-13) {
		tmp = 1.0 + ((x / t) / (y - z));
	} 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 <= (-6.5d-11)) then
        tmp = 1.0d0
    else if (y <= 1.72d-13) then
        tmp = 1.0d0 + ((x / t) / (y - z))
    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 <= -6.5e-11) {
		tmp = 1.0;
	} else if (y <= 1.72e-13) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else {
		tmp = 1.0 - ((x / y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e-11:
		tmp = 1.0
	elif y <= 1.72e-13:
		tmp = 1.0 + ((x / t) / (y - z))
	else:
		tmp = 1.0 - ((x / y) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e-11)
		tmp = 1.0;
	elseif (y <= 1.72e-13)
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	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 <= -6.5e-11)
		tmp = 1.0;
	elseif (y <= 1.72e-13)
		tmp = 1.0 + ((x / t) / (y - z));
	else
		tmp = 1.0 - ((x / y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e-11], 1.0, If[LessEqual[y, 1.72e-13], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.49999999999999953e-11

   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 95.0%

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

   if -6.49999999999999953e-11 < y < 1.71999999999999999e-13

   1. Initial program 98.6%

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

   3. Taylor expanded in t around inf 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-/r* 83.8%

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

   5. Simplified 83.8%

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

   if 1.71999999999999999e-13 < 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 98.2%

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

      1. associate-/r* 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in y around inf 96.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-13}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-73}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-77) 1.0 (if (<= y 2.25e-73) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-77) {
		tmp = 1.0;
	} else if (y <= 2.25e-73) {
		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 <= (-5.5d-77)) then
        tmp = 1.0d0
    else if (y <= 2.25d-73) 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 <= -5.5e-77) {
		tmp = 1.0;
	} else if (y <= 2.25e-73) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-77:
		tmp = 1.0
	elif y <= 2.25e-73:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-77)
		tmp = 1.0;
	elseif (y <= 2.25e-73)
		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 <= -5.5e-77)
		tmp = 1.0;
	elseif (y <= 2.25e-73)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-77], 1.0, If[LessEqual[y, 2.25e-73], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999998e-77 or 2.25e-73 < 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 85.6%

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

   if -5.49999999999999998e-77 < y < 2.25e-73

   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 79.4%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-73}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-247}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-194}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.25e-247) 1.0 (if (<= z 1.3e-194) (+ 1.0 (/ x (* y t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-247) {
		tmp = 1.0;
	} else if (z <= 1.3e-194) {
		tmp = 1.0 + (x / (y * 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 (z <= (-1.25d-247)) then
        tmp = 1.0d0
    else if (z <= 1.3d-194) then
        tmp = 1.0d0 + (x / (y * 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 (z <= -1.25e-247) {
		tmp = 1.0;
	} else if (z <= 1.3e-194) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e-247:
		tmp = 1.0
	elif z <= 1.3e-194:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e-247)
		tmp = 1.0;
	elseif (z <= 1.3e-194)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.25e-247)
		tmp = 1.0;
	elseif (z <= 1.3e-194)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e-247], 1.0, If[LessEqual[z, 1.3e-194], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999994e-247 or 1.30000000000000001e-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 75.9%

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

   if -1.24999999999999994e-247 < z < 1.30000000000000001e-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 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/r* 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in y around inf 72.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-247}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-194}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 72.8%

   \[\leadsto \color{blue}{1} \]
4. 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)))))