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

Percentage Accurate: 98.9% → 98.9%

Time: 10.0s

Alternatives: 10

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: 98.9% 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: 98.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (+ 1.0 (/ x (* (- y z) (- t y)))))

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + (x / ((y - z) * (t - y)))
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 + (x / ((y - z) * (t - y)));
end

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Final simplification 99.6%

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

Alternative 2: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-111}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 0.00132:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ x y) y))))
   (if (<= y -1.75e-68)
     t_1
     (if (<= y 9e-111)
       (- 1.0 (/ x (* z t)))
       (if (<= y 0.00132) (+ 1.0 (/ x (* y z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((x / y) / y);
	double tmp;
	if (y <= -1.75e-68) {
		tmp = t_1;
	} else if (y <= 9e-111) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 0.00132) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((x / y) / y)
    if (y <= (-1.75d-68)) then
        tmp = t_1
    else if (y <= 9d-111) then
        tmp = 1.0d0 - (x / (z * t))
    else if (y <= 0.00132d0) then
        tmp = 1.0d0 + (x / (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((x / y) / y);
	double tmp;
	if (y <= -1.75e-68) {
		tmp = t_1;
	} else if (y <= 9e-111) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 0.00132) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - ((x / y) / y)
	tmp = 0
	if y <= -1.75e-68:
		tmp = t_1
	elif y <= 9e-111:
		tmp = 1.0 - (x / (z * t))
	elif y <= 0.00132:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(Float64(x / y) / y))
	tmp = 0.0
	if (y <= -1.75e-68)
		tmp = t_1;
	elseif (y <= 9e-111)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (y <= 0.00132)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - ((x / y) / y);
	tmp = 0.0;
	if (y <= -1.75e-68)
		tmp = t_1;
	elseif (y <= 9e-111)
		tmp = 1.0 - (x / (z * t));
	elseif (y <= 0.00132)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-68], t$95$1, If[LessEqual[y, 9e-111], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00132], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75000000000000006e-68 or 0.00132 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/r* 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in y around inf 88.6%

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

   if -1.75000000000000006e-68 < y < 8.99999999999999987e-111

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 83.8%

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

   if 8.99999999999999987e-111 < y < 0.00132

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 83.0%

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

   4. Taylor expanded in y around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. neg-mul-1 59.9%

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

      3. *-commutative 59.9%

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

   6. Simplified 59.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-68}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-111}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 0.00132:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-22} \lor \neg \left(y \leq 1.8 \cdot 10^{+99}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e-22) (not (<= y 1.8e+99)))
   (- 1.0 (/ (/ x y) y))
   (- 1.0 (/ x (* t (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-22) || !(y <= 1.8e+99)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.1d-22)) .or. (.not. (y <= 1.8d+99))) then
        tmp = 1.0d0 - ((x / y) / y)
    else
        tmp = 1.0d0 - (x / (t * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-22) || !(y <= 1.8e+99)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e-22) or not (y <= 1.8e+99):
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e-22) || !(y <= 1.8e+99))
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.1e-22) || ~((y <= 1.8e+99)))
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = 1.0 - (x / (t * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e-22], N[Not[LessEqual[y, 1.8e+99]], $MachinePrecision]], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000008e-22 or 1.8000000000000001e99 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 96.7%

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

      1. *-commutative 96.7%

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

      2. associate-/r* 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in y around inf 93.8%

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

   if -2.10000000000000008e-22 < y < 1.8000000000000001e99

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 92.3%

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

      1. distribute-lft-out 92.3%

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

      2. mul-1-neg 92.3%

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

      3. distribute-rgt-neg-in 92.3%

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

      4. unsub-neg 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in t around inf 83.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-22} \lor \neg \left(y \leq 1.8 \cdot 10^{+99}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-24} \lor \neg \left(y \leq 9.5 \cdot 10^{-129}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e-24) (not (<= y 9.5e-129)))
   (+ 1.0 (/ x (* y (- t y))))
   (- 1.0 (/ x (* t (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-24) || !(y <= 9.5e-129)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.5d-24)) .or. (.not. (y <= 9.5d-129))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - (x / (t * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-24) || !(y <= 9.5e-129)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e-24) or not (y <= 9.5e-129):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e-24) || !(y <= 9.5e-129))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5e-24) || ~((y <= 9.5e-129)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - (x / (t * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e-24], N[Not[LessEqual[y, 9.5e-129]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999996e-24 or 9.5000000000000006e-129 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.7%

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

   if -3.4999999999999996e-24 < y < 9.5000000000000006e-129

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 96.6%

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

      1. distribute-lft-out 96.6%

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

      2. mul-1-neg 96.6%

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

      3. distribute-rgt-neg-in 96.6%

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

      4. unsub-neg 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around inf 91.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-24} \lor \neg \left(y \leq 9.5 \cdot 10^{-129}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-25}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e-25)
   (- 1.0 (/ x (* y (- y z))))
   (if (<= y 4.1e-128)
     (- 1.0 (/ x (* t (- z y))))
     (+ 1.0 (/ x (* y (- t y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-25) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 4.1e-128) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1d-25)) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else if (y <= 4.1d-128) then
        tmp = 1.0d0 - (x / (t * (z - y)))
    else
        tmp = 1.0d0 + (x / (y * (t - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-25) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 4.1e-128) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1e-25:
		tmp = 1.0 - (x / (y * (y - z)))
	elif y <= 4.1e-128:
		tmp = 1.0 - (x / (t * (z - y)))
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e-25)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	elseif (y <= 4.1e-128)
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e-25)
		tmp = 1.0 - (x / (y * (y - z)));
	elseif (y <= 4.1e-128)
		tmp = 1.0 - (x / (t * (z - y)));
	else
		tmp = 1.0 + (x / (y * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e-25], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-128], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000004e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.5%

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

   if -1.00000000000000004e-25 < y < 4.1e-128

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 96.6%

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

      1. distribute-lft-out 96.6%

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

      2. mul-1-neg 96.6%

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

      3. distribute-rgt-neg-in 96.6%

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

      4. unsub-neg 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around inf 92.3%

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

   if 4.1e-128 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-25}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e-58)
   (- 1.0 (/ x (* y (- y z))))
   (if (<= y 4.1e-128)
     (- 1.0 (/ x (* t (- z y))))
     (+ 1.0 (/ (/ x (- t y)) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-58) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 4.1e-128) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + ((x / (t - y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.5d-58)) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else if (y <= 4.1d-128) then
        tmp = 1.0d0 - (x / (t * (z - y)))
    else
        tmp = 1.0d0 + ((x / (t - y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-58) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else if (y <= 4.1e-128) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + ((x / (t - y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e-58:
		tmp = 1.0 - (x / (y * (y - z)))
	elif y <= 4.1e-128:
		tmp = 1.0 - (x / (t * (z - y)))
	else:
		tmp = 1.0 + ((x / (t - y)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e-58)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	elseif (y <= 4.1e-128)
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / Float64(t - y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e-58)
		tmp = 1.0 - (x / (y * (y - z)));
	elseif (y <= 4.1e-128)
		tmp = 1.0 - (x / (t * (z - y)));
	else
		tmp = 1.0 + ((x / (t - y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e-58], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-128], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.49999999999999964e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 97.5%

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

   if -6.49999999999999964e-58 < y < 4.1e-128

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 96.6%

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

      1. distribute-lft-out 96.6%

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

      2. mul-1-neg 96.6%

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

      3. distribute-rgt-neg-in 96.6%

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

      4. unsub-neg 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around inf 92.3%

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

   if 4.1e-128 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-/r* 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-181}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.3e-61)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z 1.95e-181)
     (+ 1.0 (/ (/ x (- t y)) y))
     (- 1.0 (/ x (* t (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e-61) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 1.95e-181) {
		tmp = 1.0 + ((x / (t - y)) / y);
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.3d-61)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= 1.95d-181) then
        tmp = 1.0d0 + ((x / (t - y)) / y)
    else
        tmp = 1.0d0 - (x / (t * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e-61) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= 1.95e-181) {
		tmp = 1.0 + ((x / (t - y)) / y);
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.3e-61:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= 1.95e-181:
		tmp = 1.0 + ((x / (t - y)) / y)
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.3e-61)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 1.95e-181)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(t - y)) / y));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.3e-61)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= 1.95e-181)
		tmp = 1.0 + ((x / (t - y)) / y);
	else
		tmp = 1.0 - (x / (t * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.3e-61], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-181], N[(1.0 + N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3e-61

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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. inv-pow 99.9%

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

      3. associate-/l* 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in z around inf 98.2%

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

      1. mul-1-neg 98.2%

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

      2. associate-/r* 98.1%

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

      3. distribute-neg-frac2 98.1%

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

   7. Simplified 98.1%

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

   if -5.3e-61 < z < 1.95e-181

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-/r* 88.0%

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

   5. Simplified 88.0%

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

   if 1.95e-181 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. distribute-lft-out 84.8%

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

      2. mul-1-neg 84.8%

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

      3. distribute-rgt-neg-in 84.8%

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

      4. unsub-neg 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in t around inf 73.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-181}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+68} \lor \neg \left(y \leq 2.65 \cdot 10^{-67}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e+68) (not (<= y 2.65e-67)))
   (- 1.0 (/ x (* y t)))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e+68) || !(y <= 2.65e-67)) {
		tmp = 1.0 - (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.2d+68)) .or. (.not. (y <= 2.65d-67))) then
        tmp = 1.0d0 - (x / (y * t))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e+68) || !(y <= 2.65e-67)) {
		tmp = 1.0 - (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.2e+68) or not (y <= 2.65e-67):
		tmp = 1.0 - (x / (y * t))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.2e+68) || !(y <= 2.65e-67))
		tmp = Float64(1.0 - Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.2e+68) || ~((y <= 2.65e-67)))
		tmp = 1.0 - (x / (y * t));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.2e+68], N[Not[LessEqual[y, 2.65e-67]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.20000000000000004e68 or 2.64999999999999986e-67 < 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 t around inf 69.2%

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

      1. associate-*r/ 69.2%

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

      2. neg-mul-1 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in y around inf 65.8%

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

      1. div-inv 65.8%

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

      2. add-sqr-sqrt 34.1%

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

      3. sqrt-unprod 54.7%

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

      4. sqr-neg 54.7%

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

      5. sqrt-unprod 30.4%

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

      6. add-sqr-sqrt 63.7%

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

      7. *-commutative 63.7%

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

      8. associate-/r* 63.7%

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

   8. Applied egg-rr 63.7%

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

      1. associate-*r/ 63.7%

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

      2. associate-*r/ 63.7%

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

      3. *-rgt-identity 63.7%

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

      4. associate-/r* 63.7%

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

   10. Simplified 63.7%

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

   if -1.20000000000000004e68 < y < 2.64999999999999986e-67

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 73.5%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+68} \lor \neg \left(y \leq 2.65 \cdot 10^{-67}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-70} \lor \neg \left(y \leq 1.22 \cdot 10^{-64}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.8e-70) (not (<= y 1.22e-64)))
   (- 1.0 (/ (/ x y) y))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.8e-70) || !(y <= 1.22e-64)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.8d-70)) .or. (.not. (y <= 1.22d-64))) then
        tmp = 1.0d0 - ((x / y) / y)
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.8e-70) || !(y <= 1.22e-64)) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.8e-70) or not (y <= 1.22e-64):
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.8e-70) || !(y <= 1.22e-64))
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.8e-70) || ~((y <= 1.22e-64)))
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.8e-70], N[Not[LessEqual[y, 1.22e-64]], $MachinePrecision]], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.8000000000000001e-70 or 1.22000000000000003e-64 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-/r* 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around inf 84.7%

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

   if -9.8000000000000001e-70 < y < 1.22000000000000003e-64

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 78.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-70} \lor \neg \left(y \leq 1.22 \cdot 10^{-64}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{x}{z \cdot t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* z t))))

C

double code(double x, double y, double z, double t) {
	return 1.0 - (x / (z * 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 / (z * t))
end function

Java

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

Python

def code(x, y, z, t):
	return 1.0 - (x / (z * t))

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / (z * t));
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in y around 0 59.4%

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

4. Final simplification 59.4%

   \[\leadsto 1 - \frac{x}{z \cdot t} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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)))))