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

Percentage Accurate: 99.2% → 99.2%

Time: 7.9s

Alternatives: 6

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

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

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 99.6%

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

3. Final simplification 99.6%

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

Alternative 2: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-88}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-160}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-15)
   1.0
   (if (<= y -9.4e-88)
     (+ 1.0 (/ x (* y t)))
     (if (<= y 3e-160) (+ 1.0 (* (/ x z) (/ -1.0 t))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-15) {
		tmp = 1.0;
	} else if (y <= -9.4e-88) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 3e-160) {
		tmp = 1.0 + ((x / z) * (-1.0 / t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.15d-15)) then
        tmp = 1.0d0
    else if (y <= (-9.4d-88)) then
        tmp = 1.0d0 + (x / (y * t))
    else if (y <= 3d-160) then
        tmp = 1.0d0 + ((x / z) * ((-1.0d0) / t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-15) {
		tmp = 1.0;
	} else if (y <= -9.4e-88) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 3e-160) {
		tmp = 1.0 + ((x / z) * (-1.0 / t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-15:
		tmp = 1.0
	elif y <= -9.4e-88:
		tmp = 1.0 + (x / (y * t))
	elif y <= 3e-160:
		tmp = 1.0 + ((x / z) * (-1.0 / t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-15)
		tmp = 1.0;
	elseif (y <= -9.4e-88)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	elseif (y <= 3e-160)
		tmp = Float64(1.0 + Float64(Float64(x / z) * Float64(-1.0 / t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e-15)
		tmp = 1.0;
	elseif (y <= -9.4e-88)
		tmp = 1.0 + (x / (y * t));
	elseif (y <= 3e-160)
		tmp = 1.0 + ((x / z) * (-1.0 / t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-15], 1.0, If[LessEqual[y, -9.4e-88], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e-160], N[(1.0 + N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.14999999999999995e-15 or 2.99999999999999997e-160 < 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 inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-/r* 66.7%

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

      3. distribute-neg-frac 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around 0 84.9%

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

   if -1.14999999999999995e-15 < y < -9.4e-88

   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 82.8%

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

      1. associate-*r/ 82.8%

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

      2. neg-mul-1 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in y around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. *-commutative 72.2%

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

   8. Simplified 72.2%

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

   if -9.4e-88 < y < 2.99999999999999997e-160

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 87.7%

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

      1. *-un-lft-identity 87.7%

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

      2. times-frac 87.8%

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

   5. Applied egg-rr 87.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-88}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-160}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-87}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-160}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e-13)
   1.0
   (if (<= y -8e-87)
     (+ 1.0 (/ x (* y t)))
     (if (<= y 2.8e-160) (- 1.0 (/ x (* z t))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-13) {
		tmp = 1.0;
	} else if (y <= -8e-87) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 2.8e-160) {
		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 <= (-6d-13)) then
        tmp = 1.0d0
    else if (y <= (-8d-87)) then
        tmp = 1.0d0 + (x / (y * t))
    else if (y <= 2.8d-160) 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 <= -6e-13) {
		tmp = 1.0;
	} else if (y <= -8e-87) {
		tmp = 1.0 + (x / (y * t));
	} else if (y <= 2.8e-160) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e-13:
		tmp = 1.0
	elif y <= -8e-87:
		tmp = 1.0 + (x / (y * t))
	elif y <= 2.8e-160:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e-13)
		tmp = 1.0;
	elseif (y <= -8e-87)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	elseif (y <= 2.8e-160)
		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 <= -6e-13)
		tmp = 1.0;
	elseif (y <= -8e-87)
		tmp = 1.0 + (x / (y * t));
	elseif (y <= 2.8e-160)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e-13], 1.0, If[LessEqual[y, -8e-87], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-160], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999968e-13 or 2.80000000000000016e-160 < 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 inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-/r* 66.7%

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

      3. distribute-neg-frac 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around 0 84.9%

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

   if -5.99999999999999968e-13 < y < -8.00000000000000014e-87

   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 82.8%

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

      1. associate-*r/ 82.8%

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

      2. neg-mul-1 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in y around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. *-commutative 72.2%

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

   8. Simplified 72.2%

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

   if -8.00000000000000014e-87 < y < 2.80000000000000016e-160

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 87.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-87}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-160}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-141} \lor \neg \left(y \leq 3.3 \cdot 10^{-104}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.9e-141) (not (<= y 3.3e-104)))
   (- 1.0 (/ x (* y (- y t))))
   (+ 1.0 (* (/ x z) (/ -1.0 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.9e-141) || !(y <= 3.3e-104)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / z) * (-1.0 / 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 <= (-4.9d-141)) .or. (.not. (y <= 3.3d-104))) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + ((x / z) * ((-1.0d0) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.9e-141) || !(y <= 3.3e-104)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / z) * (-1.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.9e-141) or not (y <= 3.3e-104):
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + ((x / z) * (-1.0 / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.9e-141) || !(y <= 3.3e-104))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / z) * Float64(-1.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.9e-141) || ~((y <= 3.3e-104)))
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + ((x / z) * (-1.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.9e-141], N[Not[LessEqual[y, 3.3e-104]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.90000000000000006e-141 or 3.30000000000000002e-104 < 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 89.0%

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

   if -4.90000000000000006e-141 < y < 3.30000000000000002e-104

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 87.5%

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

      1. *-un-lft-identity 87.5%

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

      2. times-frac 87.5%

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

   5. Applied egg-rr 87.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-141} \lor \neg \left(y \leq 3.3 \cdot 10^{-104}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.12:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;y \leq 0.03:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.12)
   (+ 1.0 (/ (/ x y) (- z y)))
   (if (<= y 0.03) (+ 1.0 (/ x (* (- y z) t))) (- 1.0 (/ x (* y (- y t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.12) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (y <= 0.03) {
		tmp = 1.0 + (x / ((y - z) * t));
	} 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 <= (-0.12d0)) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (y <= 0.03d0) then
        tmp = 1.0d0 + (x / ((y - z) * t))
    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 <= -0.12) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (y <= 0.03) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0 - (x / (y * (y - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.12:
		tmp = 1.0 + ((x / y) / (z - y))
	elif y <= 0.03:
		tmp = 1.0 + (x / ((y - z) * t))
	else:
		tmp = 1.0 - (x / (y * (y - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.12)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (y <= 0.03)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.12)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (y <= 0.03)
		tmp = 1.0 + (x / ((y - z) * t));
	else
		tmp = 1.0 - (x / (y * (y - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.12], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.03], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.12

   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 0 93.8%

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

      1. associate-/r* 93.7%

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

   5. Simplified 93.7%

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

   if -0.12 < y < 0.029999999999999999

   1. Initial program 99.2%

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

   3. Taylor expanded in t around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. neg-mul-1 87.8%

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

   5. Simplified 87.8%

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

   if 0.029999999999999999 < 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 96.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.12:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;y \leq 0.03:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% 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 99.6%

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

3. Taylor expanded in z around inf 76.0%

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

   1. mul-1-neg 76.0%

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

   2. associate-/r* 75.9%

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

   3. distribute-neg-frac 75.9%

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

5. Simplified 75.9%

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

6. Taylor expanded in x around 0 76.0%

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

Reproduce

herbie shell --seed 2024108 
(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)))))