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

Percentage Accurate: 99.2% → 99.9%

Time: 10.7s

Alternatives: 12

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: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-13}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot \frac{-1}{y - t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e-13)
   (- 1.0 (/ x (* (- y z) (- y t))))
   (+ 1.0 (/ (* x (/ -1.0 (- y t))) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-13) {
		tmp = 1.0 - (x / ((y - z) * (y - t)));
	} else {
		tmp = 1.0 + ((x * (-1.0 / (y - t))) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1d-13)) then
        tmp = 1.0d0 - (x / ((y - z) * (y - t)))
    else
        tmp = 1.0d0 + ((x * ((-1.0d0) / (y - t))) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-13) {
		tmp = 1.0 - (x / ((y - z) * (y - t)));
	} else {
		tmp = 1.0 + ((x * (-1.0 / (y - t))) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1e-13:
		tmp = 1.0 - (x / ((y - z) * (y - t)))
	else:
		tmp = 1.0 + ((x * (-1.0 / (y - t))) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e-13)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(Float64(x * Float64(-1.0 / Float64(y - t))) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e-13)
		tmp = 1.0 - (x / ((y - z) * (y - t)));
	else
		tmp = 1.0 + ((x * (-1.0 / (y - t))) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1e-13], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x * N[(-1.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-13

   1. Initial program 100.0%

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

   if -1e-13 < z

   1. Initial program 97.2%

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

      1. clear-num 97.2%

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

      2. associate-/r/ 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-/r* 97.2%

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

   4. Applied egg-rr 97.2%

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

      1. frac-2neg 97.2%

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

      2. associate-*l/ 98.8%

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

      3. distribute-neg-frac 98.8%

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

      4. metadata-eval 98.8%

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

   6. Applied egg-rr 98.8%

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

4. Final simplification 99.1%

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

Alternative 2: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{x}{z \cdot y}\\ \mathbf{if}\;t \leq 6 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* z y)))))
   (if (<= t 6e-60)
     t_1
     (if (<= t 2.05e-40) (/ x (* z (- t))) (if (<= t 1.65e-22) t_1 1.0)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (z * y));
	double tmp;
	if (t <= 6e-60) {
		tmp = t_1;
	} else if (t <= 2.05e-40) {
		tmp = x / (z * -t);
	} else if (t <= 1.65e-22) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 / (z * y))
    if (t <= 6d-60) then
        tmp = t_1
    else if (t <= 2.05d-40) then
        tmp = x / (z * -t)
    else if (t <= 1.65d-22) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / (z * y));
	double tmp;
	if (t <= 6e-60) {
		tmp = t_1;
	} else if (t <= 2.05e-40) {
		tmp = x / (z * -t);
	} else if (t <= 1.65e-22) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + (x / (z * y))
	tmp = 0
	if t <= 6e-60:
		tmp = t_1
	elif t <= 2.05e-40:
		tmp = x / (z * -t)
	elif t <= 1.65e-22:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(z * y)))
	tmp = 0.0
	if (t <= 6e-60)
		tmp = t_1;
	elseif (t <= 2.05e-40)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t <= 1.65e-22)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (x / (z * y));
	tmp = 0.0;
	if (t <= 6e-60)
		tmp = t_1;
	elseif (t <= 2.05e-40)
		tmp = x / (z * -t);
	elseif (t <= 1.65e-22)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 6e-60], t$95$1, If[LessEqual[t, 2.05e-40], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-22], t$95$1, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if t < 6.00000000000000038e-60 or 2.04999999999999981e-40 < t < 1.65e-22

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-/r* 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in y around inf 61.7%

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

      1. *-commutative 61.7%

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

   8. Simplified 61.7%

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

   if 6.00000000000000038e-60 < t < 2.04999999999999981e-40

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. associate-/l/ 60.1%

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

      3. distribute-frac-neg 60.1%

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

      4. distribute-neg-frac2 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around 0 27.7%

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

      1. associate-*r/ 27.7%

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

      2. neg-mul-1 27.7%

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

      3. *-commutative 27.7%

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

   8. Simplified 27.7%

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

   if 1.65e-22 < t

   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 85.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{-60}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-206}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.35e-206)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= z 1.5e-303)
     (- 1.0 (/ x (* y (- y t))))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e-206) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.5e-303) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.35d-206)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (z <= 1.5d-303) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e-206) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.5e-303) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.35e-206:
		tmp = 1.0 - ((x / z) / (t - y))
	elif z <= 1.5e-303:
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.35e-206)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (z <= 1.5e-303)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.35e-206)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (z <= 1.5e-303)
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.35e-206], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-303], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3499999999999999e-206

   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 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-/r* 88.4%

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

   5. Simplified 88.4%

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

   if -2.3499999999999999e-206 < z < 1.50000000000000014e-303

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0 89.6%

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

   if 1.50000000000000014e-303 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/r* 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-206}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-206}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.35e-206)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= z 1.5e-303)
     (+ 1.0 (/ (/ x y) (- t y)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e-206) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.5e-303) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.35d-206)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (z <= 1.5d-303) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e-206) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (z <= 1.5e-303) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.35e-206:
		tmp = 1.0 - ((x / z) / (t - y))
	elif z <= 1.5e-303:
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.35e-206)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (z <= 1.5e-303)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.35e-206)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (z <= 1.5e-303)
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.35e-206], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-303], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3499999999999999e-206

   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 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-/r* 88.4%

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

   5. Simplified 88.4%

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

   if -2.3499999999999999e-206 < z < 1.50000000000000014e-303

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0 89.6%

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

      1. associate-/r* 99.7%

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

   5. Simplified 99.7%

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

   if 1.50000000000000014e-303 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/r* 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-206}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-206}:\\ \;\;\;\;1 + x \cdot \frac{-1}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.35e-206)
   (+ 1.0 (* x (/ -1.0 (* z (- t y)))))
   (if (<= z 1.5e-303)
     (+ 1.0 (/ (/ x y) (- t y)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e-206) {
		tmp = 1.0 + (x * (-1.0 / (z * (t - y))));
	} else if (z <= 1.5e-303) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.35d-206)) then
        tmp = 1.0d0 + (x * ((-1.0d0) / (z * (t - y))))
    else if (z <= 1.5d-303) then
        tmp = 1.0d0 + ((x / y) / (t - y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e-206) {
		tmp = 1.0 + (x * (-1.0 / (z * (t - y))));
	} else if (z <= 1.5e-303) {
		tmp = 1.0 + ((x / y) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.35e-206:
		tmp = 1.0 + (x * (-1.0 / (z * (t - y))))
	elif z <= 1.5e-303:
		tmp = 1.0 + ((x / y) / (t - y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.35e-206)
		tmp = Float64(1.0 + Float64(x * Float64(-1.0 / Float64(z * Float64(t - y)))));
	elseif (z <= 1.5e-303)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.35e-206)
		tmp = 1.0 + (x * (-1.0 / (z * (t - y))));
	elseif (z <= 1.5e-303)
		tmp = 1.0 + ((x / y) / (t - y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.35e-206], N[(1.0 + N[(x * N[(-1.0 / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-303], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3499999999999999e-206

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 91.6%

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

   if -2.3499999999999999e-206 < z < 1.50000000000000014e-303

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0 89.6%

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

      1. associate-/r* 99.7%

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

   5. Simplified 99.7%

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

   if 1.50000000000000014e-303 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-/r* 82.8%

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

   5. Simplified 82.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-206}:\\ \;\;\;\;1 + x \cdot \frac{-1}{z \cdot \left(t - y\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-114) 1.0 (if (<= y 2e-162) (- 1.0 (/ x (* z t))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-114) {
		tmp = 1.0;
	} else if (y <= 2e-162) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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-114)) then
        tmp = 1.0d0
    else if (y <= 2d-162) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-114) {
		tmp = 1.0;
	} else if (y <= 2e-162) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-114:
		tmp = 1.0
	elif y <= 2e-162:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-114)
		tmp = 1.0;
	elseif (y <= 2e-162)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e-114)
		tmp = 1.0;
	elseif (y <= 2e-162)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-114], 1.0, If[LessEqual[y, 2e-162], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-114 or 1.99999999999999991e-162 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.5%

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

   if -1.15e-114 < y < 1.99999999999999991e-162

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0 77.7%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-162}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-181}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.4e-181) 1.0 (if (<= y 1.5e-245) (/ x (* z (- t))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e-181) {
		tmp = 1.0;
	} else if (y <= 1.5e-245) {
		tmp = x / (z * -t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-5.4d-181)) then
        tmp = 1.0d0
    else if (y <= 1.5d-245) then
        tmp = x / (z * -t)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e-181) {
		tmp = 1.0;
	} else if (y <= 1.5e-245) {
		tmp = x / (z * -t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.4e-181:
		tmp = 1.0
	elif y <= 1.5e-245:
		tmp = x / (z * -t)
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.4e-181)
		tmp = 1.0;
	elseif (y <= 1.5e-245)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.4e-181)
		tmp = 1.0;
	elseif (y <= 1.5e-245)
		tmp = x / (z * -t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5.4e-181], 1.0, If[LessEqual[y, 1.5e-245], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.3999999999999999e-181 or 1.5000000000000001e-245 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 79.9%

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

   if -5.3999999999999999e-181 < y < 1.5000000000000001e-245

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-/l/ 65.3%

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

      3. distribute-frac-neg 65.3%

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

      4. distribute-neg-frac2 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around 0 55.1%

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

      1. associate-*r/ 55.1%

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

      2. neg-mul-1 55.1%

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

      3. *-commutative 55.1%

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

   8. Simplified 55.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-181}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.2e-169) (+ 1.0 (/ x (* z y))) (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.2e-169) {
		tmp = 1.0 + (x / (z * y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= 6.2d-169) then
        tmp = 1.0d0 + (x / (z * y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.2e-169) {
		tmp = 1.0 + (x / (z * y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 6.2e-169:
		tmp = 1.0 + (x / (z * y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6.2e-169)
		tmp = Float64(1.0 + Float64(x / Float64(z * y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6.2e-169)
		tmp = 1.0 + (x / (z * y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 6.2e-169], N[(1.0 + N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.2000000000000004e-169

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 79.2%

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

      1. +-commutative 79.2%

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

      2. associate-/r* 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

   8. Simplified 60.5%

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

   if 6.2000000000000004e-169 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-/r* 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;1 + \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-158}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.25e-158)
   (- 1.0 (/ (/ x z) (- t y)))
   (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-158) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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-158)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e-158) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e-158:
		tmp = 1.0 - ((x / z) / (t - y))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e-158)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.25e-158)
		tmp = 1.0 - ((x / z) / (t - y));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e-158], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999993e-158

   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 93.9%

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

      1. +-commutative 93.9%

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

      2. associate-/r* 92.1%

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

   5. Simplified 92.1%

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

   if -1.24999999999999993e-158 < z

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/r* 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-158}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.2e-169) (+ 1.0 (/ x (* y (- z y)))) (+ 1.0 (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.2e-169) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= 6.2d-169) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.2e-169) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 6.2e-169:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6.2e-169)
		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

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6.2e-169)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 6.2e-169], 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 2 regimes

2. if t < 6.2000000000000004e-169

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 73.6%

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

   if 6.2000000000000004e-169 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-/r* 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.2% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / ((y - z) * (y - t)));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 98.1%

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

3. Final simplification 98.1%

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

Alternative 12: 75.5% accurate, 11.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 1.0)

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return 1.0
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 98.1%

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

3. Taylor expanded in x around 0 72.1%

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

4. Final simplification 72.1%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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)))))