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

Percentage Accurate: 99.1% → 98.4%

Time: 11.8s

Alternatives: 11

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: 99.1% 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: 98.4% accurate, 1.0× speedup

Math

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

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)) (- t y))))

C

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

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)) / (t - y))
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)) / (t - y));
}

Python

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

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 + Float64(Float64(x / Float64(y - z)) / Float64(t - y)))
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)) / (t - y));
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[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

3. Taylor expanded in x around 0 99.0%

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

   1. associate-/l/ 98.5%

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

   2. metadata-eval 98.5%

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

   3. cancel-sign-sub-inv 98.5%

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

   4. *-lft-identity 98.5%

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

5. Simplified 98.5%

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

6. Final simplification 98.5%

   \[\leadsto 1 + \frac{\frac{x}{y - z}}{t - y} \]
7. Add Preprocessing

Alternative 2: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-124}:\\ \;\;\;\;\frac{z + \frac{x}{y}}{z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+49}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 t) (- y z)))))
   (if (<= t -2.45e-147)
     t_1
     (if (<= t 9.2e-124)
       (/ (+ z (/ x y)) z)
       (if (<= t 1.75e+49) (- 1.0 (/ (/ x y) (- y t))) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((x / t) / (y - z));
	double tmp;
	if (t <= -2.45e-147) {
		tmp = t_1;
	} else if (t <= 9.2e-124) {
		tmp = (z + (x / y)) / z;
	} else if (t <= 1.75e+49) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = t_1;
	}
	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 / t) / (y - z))
    if (t <= (-2.45d-147)) then
        tmp = t_1
    else if (t <= 9.2d-124) then
        tmp = (z + (x / y)) / z
    else if (t <= 1.75d+49) then
        tmp = 1.0d0 - ((x / y) / (y - t))
    else
        tmp = t_1
    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 / t) / (y - z));
	double tmp;
	if (t <= -2.45e-147) {
		tmp = t_1;
	} else if (t <= 9.2e-124) {
		tmp = (z + (x / y)) / z;
	} else if (t <= 1.75e+49) {
		tmp = 1.0 - ((x / y) / (y - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + ((x / t) / (y - z))
	tmp = 0
	if t <= -2.45e-147:
		tmp = t_1
	elif t <= 9.2e-124:
		tmp = (z + (x / y)) / z
	elif t <= 1.75e+49:
		tmp = 1.0 - ((x / y) / (y - t))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)))
	tmp = 0.0
	if (t <= -2.45e-147)
		tmp = t_1;
	elseif (t <= 9.2e-124)
		tmp = Float64(Float64(z + Float64(x / y)) / z);
	elseif (t <= 1.75e+49)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	else
		tmp = t_1;
	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 / t) / (y - z));
	tmp = 0.0;
	if (t <= -2.45e-147)
		tmp = t_1;
	elseif (t <= 9.2e-124)
		tmp = (z + (x / y)) / z;
	elseif (t <= 1.75e+49)
		tmp = 1.0 - ((x / y) / (y - t));
	else
		tmp = t_1;
	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[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.45e-147], t$95$1, If[LessEqual[t, 9.2e-124], N[(N[(z + N[(x / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.75e+49], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.45000000000000002e-147 or 1.74999999999999987e49 < t

   1. Initial program 99.5%

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

   3. Taylor expanded in t around inf 94.7%

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

      1. associate-/r* 95.1%

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

   5. Simplified 95.1%

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

   if -2.45000000000000002e-147 < t < 9.20000000000000048e-124

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 81.5%

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

      1. associate-/r* 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in y around inf 73.7%

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

   7. Taylor expanded in z around 0 75.3%

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

   if 9.20000000000000048e-124 < t < 1.74999999999999987e49

   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 86.0%

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

      1. sub-neg 86.0%

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

      2. associate-/r* 86.1%

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

      3. distribute-neg-frac2 86.1%

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

      4. neg-sub0 86.1%

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

      5. sub-neg 86.1%

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

      6. +-commutative 86.1%

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

      7. associate--r+ 86.1%

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

      8. neg-sub0 86.1%

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

      9. remove-double-neg 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-147}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-124}:\\ \;\;\;\;\frac{z + \frac{x}{y}}{z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+49}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-121}:\\ \;\;\;\;\frac{z + \frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-103}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -5000000.0)
   1.0
   (if (<= y -5.4e-121)
     (/ (+ z (/ x y)) z)
     (if (<= y 6.2e-103) (- 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 <= -5000000.0) {
		tmp = 1.0;
	} else if (y <= -5.4e-121) {
		tmp = (z + (x / y)) / z;
	} else if (y <= 6.2e-103) {
		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 <= (-5000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-5.4d-121)) then
        tmp = (z + (x / y)) / z
    else if (y <= 6.2d-103) 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 <= -5000000.0) {
		tmp = 1.0;
	} else if (y <= -5.4e-121) {
		tmp = (z + (x / y)) / z;
	} else if (y <= 6.2e-103) {
		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 <= -5000000.0:
		tmp = 1.0
	elif y <= -5.4e-121:
		tmp = (z + (x / y)) / z
	elif y <= 6.2e-103:
		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 <= -5000000.0)
		tmp = 1.0;
	elseif (y <= -5.4e-121)
		tmp = Float64(Float64(z + Float64(x / y)) / z);
	elseif (y <= 6.2e-103)
		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 <= -5000000.0)
		tmp = 1.0;
	elseif (y <= -5.4e-121)
		tmp = (z + (x / y)) / z;
	elseif (y <= 6.2e-103)
		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, -5000000.0], 1.0, If[LessEqual[y, -5.4e-121], N[(N[(z + N[(x / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.2e-103], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e6 or 6.2000000000000003e-103 < 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 89.9%

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

   if -5e6 < y < -5.4000000000000004e-121

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 72.7%

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

      1. associate-/r* 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around inf 64.9%

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

   7. Taylor expanded in z around 0 65.2%

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

   if -5.4000000000000004e-121 < y < 6.2000000000000003e-103

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 81.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-121}:\\ \;\;\;\;\frac{z + \frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-103}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5500000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-121}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-102}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -5500000.0)
   1.0
   (if (<= y -5.8e-121)
     (+ 1.0 (/ x (* y z)))
     (if (<= y 1.4e-102) (- 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 <= -5500000.0) {
		tmp = 1.0;
	} else if (y <= -5.8e-121) {
		tmp = 1.0 + (x / (y * z));
	} else if (y <= 1.4e-102) {
		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 <= (-5500000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-5.8d-121)) then
        tmp = 1.0d0 + (x / (y * z))
    else if (y <= 1.4d-102) 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 <= -5500000.0) {
		tmp = 1.0;
	} else if (y <= -5.8e-121) {
		tmp = 1.0 + (x / (y * z));
	} else if (y <= 1.4e-102) {
		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 <= -5500000.0:
		tmp = 1.0
	elif y <= -5.8e-121:
		tmp = 1.0 + (x / (y * z))
	elif y <= 1.4e-102:
		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 <= -5500000.0)
		tmp = 1.0;
	elseif (y <= -5.8e-121)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif (y <= 1.4e-102)
		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 <= -5500000.0)
		tmp = 1.0;
	elseif (y <= -5.8e-121)
		tmp = 1.0 + (x / (y * z));
	elseif (y <= 1.4e-102)
		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, -5500000.0], 1.0, If[LessEqual[y, -5.8e-121], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-102], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e6 or 1.40000000000000006e-102 < 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 89.9%

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

   if -5.5e6 < y < -5.8e-121

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 72.7%

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

      1. associate-/r* 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around inf 64.9%

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

   if -5.8e-121 < y < 1.40000000000000006e-102

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 81.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5500000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-121}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-102}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-30}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-273}:\\ \;\;\;\;1 + \frac{-1}{\frac{y}{\frac{x}{y - t}}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -6.3e-30)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 3.6e-273)
     (+ 1.0 (/ -1.0 (/ y (/ x (- 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 <= -6.3e-30) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.6e-273) {
		tmp = 1.0 + (-1.0 / (y / (x / (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 <= (-6.3d-30)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 3.6d-273) then
        tmp = 1.0d0 + ((-1.0d0) / (y / (x / (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 <= -6.3e-30) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.6e-273) {
		tmp = 1.0 + (-1.0 / (y / (x / (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 <= -6.3e-30:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 3.6e-273:
		tmp = 1.0 + (-1.0 / (y / (x / (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 <= -6.3e-30)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 3.6e-273)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(y / Float64(x / 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 <= -6.3e-30)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 3.6e-273)
		tmp = 1.0 + (-1.0 / (y / (x / (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, -6.3e-30], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-273], N[(1.0 + N[(-1.0 / N[(y / N[(x / N[(y - t), $MachinePrecision]), $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 < -6.29999999999999982e-30

   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 98.0%

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

      1. associate-/r* 98.0%

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

   5. Simplified 98.0%

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

   if -6.29999999999999982e-30 < z < 3.59999999999999993e-273

   1. Initial program 97.7%

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

      1. *-un-lft-identity 97.7%

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

      2. times-frac 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. associate-*l/ 99.9%

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

      2. *-un-lft-identity 99.9%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 90.2%

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

   if 3.59999999999999993e-273 < z

   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 82.5%

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

      1. associate-/r* 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-30}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-273}:\\ \;\;\;\;1 + \frac{-1}{\frac{y}{\frac{x}{y - t}}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-145} \lor \neg \left(t \leq 3.8 \cdot 10^{-97}\right):\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x}{y}}{z}\\ \end{array} \end{array} \]

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 (or (<= t -1.5e-145) (not (<= t 3.8e-97)))
   (+ 1.0 (/ (/ x t) (- y z)))
   (/ (+ z (/ x y)) z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e-145) || !(t <= 3.8e-97)) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else {
		tmp = (z + (x / 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 <= (-1.5d-145)) .or. (.not. (t <= 3.8d-97))) then
        tmp = 1.0d0 + ((x / t) / (y - z))
    else
        tmp = (z + (x / 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 <= -1.5e-145) || !(t <= 3.8e-97)) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else {
		tmp = (z + (x / y)) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e-145) or not (t <= 3.8e-97):
		tmp = 1.0 + ((x / t) / (y - z))
	else:
		tmp = (z + (x / 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 <= -1.5e-145) || !(t <= 3.8e-97))
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	else
		tmp = Float64(Float64(z + Float64(x / 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 <= -1.5e-145) || ~((t <= 3.8e-97)))
		tmp = 1.0 + ((x / t) / (y - z));
	else
		tmp = (z + (x / 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[Or[LessEqual[t, -1.5e-145], N[Not[LessEqual[t, 3.8e-97]], $MachinePrecision]], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999996e-145 or 3.8000000000000001e-97 < t

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 91.3%

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

      1. associate-/r* 91.6%

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

   5. Simplified 91.6%

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

   if -1.49999999999999996e-145 < t < 3.8000000000000001e-97

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 81.0%

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

      1. associate-/r* 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in y around inf 73.5%

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

   7. Taylor expanded in z around 0 75.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-145} \lor \neg \left(t \leq 3.8 \cdot 10^{-97}\right):\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-30}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-273}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -7.2e-30)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 3.6e-273)
     (- 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 <= -7.2e-30) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.6e-273) {
		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 <= (-7.2d-30)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 3.6d-273) 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 <= -7.2e-30) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 3.6e-273) {
		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 <= -7.2e-30:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 3.6e-273:
		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 <= -7.2e-30)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 3.6e-273)
		tmp = Float64(1.0 - Float64(Float64(x / 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 <= -7.2e-30)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 3.6e-273)
		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, -7.2e-30], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-273], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $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 < -7.2000000000000006e-30

   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 98.0%

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

      1. associate-/r* 98.0%

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

   5. Simplified 98.0%

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

   if -7.2000000000000006e-30 < z < 3.59999999999999993e-273

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 89.3%

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

      1. sub-neg 89.3%

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

      2. associate-/r* 89.6%

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

      3. distribute-neg-frac2 89.6%

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

      4. neg-sub0 89.6%

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

      5. sub-neg 89.6%

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

      6. +-commutative 89.6%

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

      7. associate--r+ 89.6%

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

      8. neg-sub0 89.6%

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

      9. remove-double-neg 89.6%

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

   5. Simplified 89.6%

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

   if 3.59999999999999993e-273 < z

   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 82.5%

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

      1. associate-/r* 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-30}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-273}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-97}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-95}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 (<= t -6e-97) 1.0 (if (<= t 2.6e-95) (+ 1.0 (/ x (* y z))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e-97) {
		tmp = 1.0;
	} else if (t <= 2.6e-95) {
		tmp = 1.0 + (x / (y * z));
	} 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 (t <= (-6d-97)) then
        tmp = 1.0d0
    else if (t <= 2.6d-95) then
        tmp = 1.0d0 + (x / (y * z))
    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 (t <= -6e-97) {
		tmp = 1.0;
	} else if (t <= 2.6e-95) {
		tmp = 1.0 + (x / (y * z));
	} 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 t <= -6e-97:
		tmp = 1.0
	elif t <= 2.6e-95:
		tmp = 1.0 + (x / (y * z))
	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 (t <= -6e-97)
		tmp = 1.0;
	elseif (t <= 2.6e-95)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	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 (t <= -6e-97)
		tmp = 1.0;
	elseif (t <= 2.6e-95)
		tmp = 1.0 + (x / (y * z));
	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[t, -6e-97], 1.0, If[LessEqual[t, 2.6e-95], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000048e-97 or 2.60000000000000001e-95 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.0%

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

   if -6.00000000000000048e-97 < t < 2.60000000000000001e-95

   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 80.2%

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

      1. associate-/r* 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in y around inf 71.3%

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

Alternative 9: 73.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 4.9 \cdot 10^{+249}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

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 (<= x 4.9e+249) 1.0 (/ (- x) (* z t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 4.9e+249) {
		tmp = 1.0;
	} else {
		tmp = -x / (z * t);
	}
	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 (x <= 4.9d+249) then
        tmp = 1.0d0
    else
        tmp = -x / (z * t)
    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 (x <= 4.9e+249) {
		tmp = 1.0;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if x <= 4.9e+249:
		tmp = 1.0
	else:
		tmp = -x / (z * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= 4.9e+249)
		tmp = 1.0;
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	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 (x <= 4.9e+249)
		tmp = 1.0;
	else
		tmp = -x / (z * t);
	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[x, 4.9e+249], 1.0, N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.8999999999999996e249

   1. Initial program 98.9%

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

   3. Taylor expanded in x around 0 77.5%

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

   if 4.8999999999999996e249 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 70.3%

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

      1. associate-/r* 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in x around inf 60.6%

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

   7. Taylor expanded in y around 0 64.4%

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

      1. associate-*r/ 64.4%

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

      2. neg-mul-1 64.4%

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

   9. Simplified 64.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.9 \cdot 10^{+249}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.1% accurate, 1.0× speedup

Math

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

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) (- t y)))))

C

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

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) * (t - y)))
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) * (t - y)));
}

Python

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

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(t - y))))
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) * (t - y)));
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[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

3. Final simplification 99.0%

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

Alternative 11: 74.1% 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 99.0%

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

3. Taylor expanded in x around 0 74.9%

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

Reproduce

herbie shell --seed 2024186 
(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)))))