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

Percentage Accurate: 98.9% → 98.9%

Time: 13.5s

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 99.5%

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

3. Final simplification 99.5%

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

Alternative 2: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-253}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-163}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* (- y z) t)))))
   (if (<= t -1.15e-168)
     t_1
     (if (<= t 2.8e-253)
       (+ 1.0 (/ x (* y z)))
       (if (<= t 3.5e-163) (- 1.0 (/ (/ x y) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / ((y - z) * t));
	double tmp;
	if (t <= -1.15e-168) {
		tmp = t_1;
	} else if (t <= 2.8e-253) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 3.5e-163) {
		tmp = 1.0 - ((x / y) / y);
	} 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 - z) * t))
    if (t <= (-1.15d-168)) then
        tmp = t_1
    else if (t <= 2.8d-253) then
        tmp = 1.0d0 + (x / (y * z))
    else if (t <= 3.5d-163) then
        tmp = 1.0d0 - ((x / y) / y)
    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 - z) * t));
	double tmp;
	if (t <= -1.15e-168) {
		tmp = t_1;
	} else if (t <= 2.8e-253) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 3.5e-163) {
		tmp = 1.0 - ((x / y) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + (x / ((y - z) * t))
	tmp = 0
	if t <= -1.15e-168:
		tmp = t_1
	elif t <= 2.8e-253:
		tmp = 1.0 + (x / (y * z))
	elif t <= 3.5e-163:
		tmp = 1.0 - ((x / y) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)))
	tmp = 0.0
	if (t <= -1.15e-168)
		tmp = t_1;
	elseif (t <= 2.8e-253)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif (t <= 3.5e-163)
		tmp = Float64(1.0 - Float64(Float64(x / y) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (x / ((y - z) * t));
	tmp = 0.0;
	if (t <= -1.15e-168)
		tmp = t_1;
	elseif (t <= 2.8e-253)
		tmp = 1.0 + (x / (y * z));
	elseif (t <= 3.5e-163)
		tmp = 1.0 - ((x / y) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-168], t$95$1, If[LessEqual[t, 2.8e-253], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-163], N[(1.0 - N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.14999999999999993e-168 or 3.50000000000000027e-163 < t

   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. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in t around inf 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

   7. Simplified 94.5%

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

   if -1.14999999999999993e-168 < t < 2.80000000000000006e-253

   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 96.2%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. associate-*r/ 73.2%

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

      2. mul-1-neg 73.2%

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

      3. *-commutative 73.2%

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

   6. Simplified 73.2%

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

   if 2.80000000000000006e-253 < t < 3.50000000000000027e-163

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 94.7%

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

      1. div-inv 94.7%

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

      2. *-commutative 94.7%

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

      3. associate-/r* 94.7%

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

   5. Applied egg-rr 94.7%

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

      1. associate-*r/ 97.3%

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

      2. associate-*r/ 97.3%

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

      3. associate-*l/ 97.3%

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

      4. *-rgt-identity 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in y around inf 89.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-168}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-253}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-163}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ x y) y))))
   (if (<= y -2.2e+22)
     t_1
     (if (<= y 3.05e-40)
       (- 1.0 (/ x (* z t)))
       (if (<= y 7.2e+20) (+ 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 <= -2.2e+22) {
		tmp = t_1;
	} else if (y <= 3.05e-40) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 7.2e+20) {
		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 <= (-2.2d+22)) then
        tmp = t_1
    else if (y <= 3.05d-40) then
        tmp = 1.0d0 - (x / (z * t))
    else if (y <= 7.2d+20) 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 <= -2.2e+22) {
		tmp = t_1;
	} else if (y <= 3.05e-40) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 7.2e+20) {
		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 <= -2.2e+22:
		tmp = t_1
	elif y <= 3.05e-40:
		tmp = 1.0 - (x / (z * t))
	elif y <= 7.2e+20:
		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 <= -2.2e+22)
		tmp = t_1;
	elseif (y <= 3.05e-40)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (y <= 7.2e+20)
		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 <= -2.2e+22)
		tmp = t_1;
	elseif (y <= 3.05e-40)
		tmp = 1.0 - (x / (z * t));
	elseif (y <= 7.2e+20)
		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, -2.2e+22], t$95$1, If[LessEqual[y, 3.05e-40], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+20], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e22 or 7.2e20 < 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 0 98.1%

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

      1. div-inv 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-/r* 98.1%

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

   5. Applied egg-rr 98.1%

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

      1. associate-*r/ 98.1%

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

      2. associate-*r/ 98.1%

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

      3. associate-*l/ 98.1%

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

      4. *-rgt-identity 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in y around inf 93.4%

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

   if -2.2e22 < y < 3.0500000000000002e-40

   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 75.2%

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

   if 3.0500000000000002e-40 < y < 7.2e20

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 76.4%

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

   4. Taylor expanded in y around 0 66.1%

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

      1. associate-*r/ 66.1%

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

      2. mul-1-neg 66.1%

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

      3. *-commutative 66.1%

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

   6. Simplified 66.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+22}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-41}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ x y) y))))
   (if (<= y -2.8e+24)
     t_1
     (if (<= y 6.8e-41)
       (- 1.0 (/ x (* z t)))
       (if (<= y 7.2e+20) (+ 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 <= -2.8e+24) {
		tmp = t_1;
	} else if (y <= 6.8e-41) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 7.2e+20) {
		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 <= (-2.8d+24)) then
        tmp = t_1
    else if (y <= 6.8d-41) then
        tmp = 1.0d0 - (x / (z * t))
    else if (y <= 7.2d+20) 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 <= -2.8e+24) {
		tmp = t_1;
	} else if (y <= 6.8e-41) {
		tmp = 1.0 - (x / (z * t));
	} else if (y <= 7.2e+20) {
		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 <= -2.8e+24:
		tmp = t_1
	elif y <= 6.8e-41:
		tmp = 1.0 - (x / (z * t))
	elif y <= 7.2e+20:
		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 <= -2.8e+24)
		tmp = t_1;
	elseif (y <= 6.8e-41)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	elseif (y <= 7.2e+20)
		tmp = Float64(1.0 + Float64(Float64(x / 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 <= -2.8e+24)
		tmp = t_1;
	elseif (y <= 6.8e-41)
		tmp = 1.0 - (x / (z * t));
	elseif (y <= 7.2e+20)
		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, -2.8e+24], t$95$1, If[LessEqual[y, 6.8e-41], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+20], N[(1.0 + N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000002e24 or 7.2e20 < 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 0 98.1%

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

      1. div-inv 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-/r* 98.1%

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

   5. Applied egg-rr 98.1%

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

      1. associate-*r/ 98.1%

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

      2. associate-*r/ 98.1%

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

      3. associate-*l/ 98.1%

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

      4. *-rgt-identity 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in y around inf 93.4%

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

   if -2.8000000000000002e24 < y < 6.7999999999999997e-41

   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 75.2%

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

   if 6.7999999999999997e-41 < y < 7.2e20

   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 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

      3. *-commutative 78.3%

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

   5. Simplified 78.3%

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

      1. neg-mul-1 78.3%

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

      2. *-commutative 78.3%

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

      3. times-frac 78.4%

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

   7. Applied egg-rr 78.4%

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

      1. associate-*l/ 78.3%

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

      2. associate-*r/ 78.3%

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

      3. mul-1-neg 78.3%

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

   9. Simplified 78.3%

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

   10. Taylor expanded in y around inf 66.1%

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

       1. associate-*r/ 66.1%

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

       2. mul-1-neg 66.1%

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

   12. Simplified 66.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-41}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-59} \lor \neg \left(t \leq 6 \cdot 10^{-94}\right):\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e-59) (not (<= t 6e-94)))
   (+ 1.0 (/ x (* (- y z) t)))
   (+ 1.0 (/ x (* y (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e-59) || !(t <= 6e-94)) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0 + (x / (y * (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 ((t <= (-5d-59)) .or. (.not. (t <= 6d-94))) then
        tmp = 1.0d0 + (x / ((y - z) * t))
    else
        tmp = 1.0d0 + (x / (y * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e-59) || !(t <= 6e-94)) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0 + (x / (y * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e-59) or not (t <= 6e-94):
		tmp = 1.0 + (x / ((y - z) * t))
	else:
		tmp = 1.0 + (x / (y * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e-59) || !(t <= 6e-94))
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5e-59) || ~((t <= 6e-94)))
		tmp = 1.0 + (x / ((y - z) * t));
	else
		tmp = 1.0 + (x / (y * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e-59], N[Not[LessEqual[t, 6e-94]], $MachinePrecision]], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000001e-59 or 6.0000000000000003e-94 < t

   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. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 95.6%

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in t around inf 98.1%

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

      1. mul-1-neg 98.1%

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

      2. unsub-neg 98.1%

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

   7. Simplified 98.1%

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

   if -5.0000000000000001e-59 < t < 6.0000000000000003e-94

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 84.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-59} \lor \neg \left(t \leq 6 \cdot 10^{-94}\right):\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-183}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 10^{-91}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.22e-183)
   (+ 1.0 (/ x (* z (- y t))))
   (if (<= t 1e-91) (+ 1.0 (/ x (* y (- z y)))) (+ 1.0 (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.22e-183) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 1e-91) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + (x / ((y - 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 (t <= (-1.22d-183)) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else if (t <= 1d-91) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.22e-183) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 1e-91) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.22e-183:
		tmp = 1.0 + (x / (z * (y - t)))
	elif t <= 1e-91:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.22e-183)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	elseif (t <= 1e-91)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.22e-183)
		tmp = 1.0 + (x / (z * (y - t)));
	elseif (t <= 1e-91)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.22e-183], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-91], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.21999999999999992e-183

   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%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. associate-/r* 82.9%

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

      3. distribute-neg-frac2 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in x around 0 83.9%

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

   if -1.21999999999999992e-183 < t < 1.00000000000000002e-91

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 91.4%

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

   if 1.00000000000000002e-91 < t

   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. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 93.5%

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

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in t around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-183}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 10^{-91}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{-176}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-93}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.32e-176)
   (+ 1.0 (/ x (* z (- y t))))
   (if (<= t 7.2e-93)
     (+ 1.0 (/ x (* y (- z y))))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.32e-176) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 7.2e-93) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.32d-176)) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else if (t <= 7.2d-93) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.32e-176) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 7.2e-93) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.32e-176:
		tmp = 1.0 + (x / (z * (y - t)))
	elif t <= 7.2e-93:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.32e-176)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	elseif (t <= 7.2e-93)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.32e-176)
		tmp = 1.0 + (x / (z * (y - t)));
	elseif (t <= 7.2e-93)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.32e-176], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-93], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.32e-176

   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%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate-/r* 82.6%

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

      3. distribute-neg-frac2 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in x around 0 83.6%

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

   if -1.32e-176 < t < 7.2000000000000003e-93

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 91.7%

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

   if 7.2000000000000003e-93 < t

   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. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 93.5%

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

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in t around inf 98.5%

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

      1. associate-/r* 98.5%

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

      2. mul-1-neg 98.5%

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

      3. unsub-neg 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{-176}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-93}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-90}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.2e-179)
   (+ 1.0 (/ x (* z (- y t))))
   (if (<= t 5e-90) (+ 1.0 (/ (/ x (- z y)) y)) (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.2e-179) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 5e-90) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8.2d-179)) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else if (t <= 5d-90) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.2e-179) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (t <= 5e-90) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.2e-179:
		tmp = 1.0 + (x / (z * (y - t)))
	elif t <= 5e-90:
		tmp = 1.0 + ((x / (z - y)) / y)
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.2e-179)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	elseif (t <= 5e-90)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.2e-179)
		tmp = 1.0 + (x / (z * (y - t)));
	elseif (t <= 5e-90)
		tmp = 1.0 + ((x / (z - y)) / y);
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.2e-179], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-90], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2e-179

   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%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate-/r* 82.6%

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

      3. distribute-neg-frac2 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in x around 0 83.6%

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

   if -8.2e-179 < t < 5.00000000000000019e-90

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 91.7%

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

      1. div-inv 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-/r* 91.6%

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

   5. Applied egg-rr 91.6%

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

      1. associate-*r/ 92.3%

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

      2. associate-*r/ 92.3%

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

      3. associate-*l/ 92.3%

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

      4. *-rgt-identity 92.3%

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

   7. Simplified 92.3%

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

   if 5.00000000000000019e-90 < t

   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. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 93.5%

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

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in t around inf 98.5%

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

      1. associate-/r* 98.5%

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

      2. mul-1-neg 98.5%

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

      3. unsub-neg 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-179}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-90}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+26} \lor \neg \left(y \leq 0.032\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e+26) (not (<= y 0.032)))
   (- 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 <= -3.5e+26) || !(y <= 0.032)) {
		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 <= (-3.5d+26)) .or. (.not. (y <= 0.032d0))) 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 <= -3.5e+26) || !(y <= 0.032)) {
		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 <= -3.5e+26) or not (y <= 0.032):
		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 <= -3.5e+26) || !(y <= 0.032))
		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 <= -3.5e+26) || ~((y <= 0.032)))
		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, -3.5e+26], N[Not[LessEqual[y, 0.032]], $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 < -3.4999999999999999e26 or 0.032000000000000001 < 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 0 98.0%

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

      1. div-inv 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-/r* 98.0%

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

   5. Applied egg-rr 98.0%

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

      1. associate-*r/ 98.1%

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

      2. associate-*r/ 98.1%

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

      3. associate-*l/ 98.1%

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

      4. *-rgt-identity 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in y around inf 91.2%

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

   if -3.4999999999999999e26 < y < 0.032000000000000001

   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 73.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+26} \lor \neg \left(y \leq 0.032\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% 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 99.5%

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

3. Taylor expanded in y around 0 64.4%

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

4. Final simplification 64.4%

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

Reproduce

herbie shell --seed 2024053 
(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)))))