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

Percentage Accurate: 99.1% → 98.4%

Time: 7.5s

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: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 - t)) * ((-1.0d0) / (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. *-un-lft-identity 99.2%

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

   2. times-frac 99.5%

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

3. Applied egg-rr 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-122}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-162} \lor \neg \left(y \leq 9.6 \cdot 10^{-45}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* y (- y t))))))
   (if (<= y -5.4e-14)
     t_1
     (if (<= y -1.5e-122)
       (+ 1.0 (/ x (* y z)))
       (if (or (<= y -3.7e-162) (not (<= y 9.6e-45)))
         t_1
         (- 1.0 (/ x (* z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / (y * (y - t)));
	double tmp;
	if (y <= -5.4e-14) {
		tmp = t_1;
	} else if (y <= -1.5e-122) {
		tmp = 1.0 + (x / (y * z));
	} else if ((y <= -3.7e-162) || !(y <= 9.6e-45)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - (x / (y * (y - t)))
    if (y <= (-5.4d-14)) then
        tmp = t_1
    else if (y <= (-1.5d-122)) then
        tmp = 1.0d0 + (x / (y * z))
    else if ((y <= (-3.7d-162)) .or. (.not. (y <= 9.6d-45))) then
        tmp = t_1
    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 t_1 = 1.0 - (x / (y * (y - t)));
	double tmp;
	if (y <= -5.4e-14) {
		tmp = t_1;
	} else if (y <= -1.5e-122) {
		tmp = 1.0 + (x / (y * z));
	} else if ((y <= -3.7e-162) || !(y <= 9.6e-45)) {
		tmp = t_1;
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / (y * (y - t)))
	tmp = 0
	if y <= -5.4e-14:
		tmp = t_1
	elif y <= -1.5e-122:
		tmp = 1.0 + (x / (y * z))
	elif (y <= -3.7e-162) or not (y <= 9.6e-45):
		tmp = t_1
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))))
	tmp = 0.0
	if (y <= -5.4e-14)
		tmp = t_1;
	elseif (y <= -1.5e-122)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif ((y <= -3.7e-162) || !(y <= 9.6e-45))
		tmp = t_1;
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / (y * (y - t)));
	tmp = 0.0;
	if (y <= -5.4e-14)
		tmp = t_1;
	elseif (y <= -1.5e-122)
		tmp = 1.0 + (x / (y * z));
	elseif ((y <= -3.7e-162) || ~((y <= 9.6e-45)))
		tmp = t_1;
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e-14], t$95$1, If[LessEqual[y, -1.5e-122], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.7e-162], N[Not[LessEqual[y, 9.6e-45]], $MachinePrecision]], t$95$1, N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3999999999999997e-14 or -1.50000000000000002e-122 < y < -3.7000000000000002e-162 or 9.5999999999999996e-45 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.5%

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

   if -5.3999999999999997e-14 < y < -1.50000000000000002e-122

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 62.2%

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

   3. Taylor expanded in y around 0 49.7%

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

      1. associate-*r/ 49.7%

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

      2. neg-mul-1 49.7%

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

      3. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   if -3.7000000000000002e-162 < y < 9.5999999999999996e-45

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 87.2%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-122}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-162} \lor \neg \left(y \leq 9.6 \cdot 10^{-45}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 3: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ x y) y))))
   (if (<= y -2.2e-13)
     t_1
     (if (<= y -1.25e-144)
       (+ 1.0 (/ x (* y z)))
       (if (<= y 2.9e-43) (- 1.0 (/ x (* z t))) 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-13) {
		tmp = t_1;
	} else if (y <= -1.25e-144) {
		tmp = 1.0 + (x / (y * z));
	} else if (y <= 2.9e-43) {
		tmp = 1.0 - (x / (z * t));
	} 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-13)) then
        tmp = t_1
    else if (y <= (-1.25d-144)) then
        tmp = 1.0d0 + (x / (y * z))
    else if (y <= 2.9d-43) then
        tmp = 1.0d0 - (x / (z * t))
    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-13) {
		tmp = t_1;
	} else if (y <= -1.25e-144) {
		tmp = 1.0 + (x / (y * z));
	} else if (y <= 2.9e-43) {
		tmp = 1.0 - (x / (z * t));
	} 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-13:
		tmp = t_1
	elif y <= -1.25e-144:
		tmp = 1.0 + (x / (y * z))
	elif y <= 2.9e-43:
		tmp = 1.0 - (x / (z * t))
	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-13)
		tmp = t_1;
	elseif (y <= -1.25e-144)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif (y <= 2.9e-43)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	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-13)
		tmp = t_1;
	elseif (y <= -1.25e-144)
		tmp = 1.0 + (x / (y * z));
	elseif (y <= 2.9e-43)
		tmp = 1.0 - (x / (z * t));
	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-13], t$95$1, If[LessEqual[y, -1.25e-144], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-43], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.19999999999999997e-13 or 2.9000000000000001e-43 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-/r* 90.8%

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

   4. Simplified 90.8%

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

   5. Taylor expanded in y around inf 84.7%

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

   if -2.19999999999999997e-13 < y < -1.2499999999999999e-144

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 63.8%

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

   3. Taylor expanded in y around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. neg-mul-1 50.3%

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

      3. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   if -1.2499999999999999e-144 < y < 2.9000000000000001e-43

   1. Initial program 97.8%

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

   2. Taylor expanded in y around 0 86.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-13}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]

Alternative 4: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;y \leq -1.38 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ x y) y))))
   (if (<= y -1.38e-12)
     t_1
     (if (<= y -1.5e-144)
       (+ 1.0 (/ (/ x z) y))
       (if (<= y 1.7e-43) (- 1.0 (/ x (* z t))) 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 <= -1.38e-12) {
		tmp = t_1;
	} else if (y <= -1.5e-144) {
		tmp = 1.0 + ((x / z) / y);
	} else if (y <= 1.7e-43) {
		tmp = 1.0 - (x / (z * t));
	} 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 <= (-1.38d-12)) then
        tmp = t_1
    else if (y <= (-1.5d-144)) then
        tmp = 1.0d0 + ((x / z) / y)
    else if (y <= 1.7d-43) then
        tmp = 1.0d0 - (x / (z * t))
    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 <= -1.38e-12) {
		tmp = t_1;
	} else if (y <= -1.5e-144) {
		tmp = 1.0 + ((x / z) / y);
	} else if (y <= 1.7e-43) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - ((x / y) / y)
	tmp = 0
	if y <= -1.38e-12:
		tmp = t_1
	elif y <= -1.5e-144:
		tmp = 1.0 + ((x / z) / y)
	elif y <= 1.7e-43:
		tmp = 1.0 - (x / (z * t))
	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 <= -1.38e-12)
		tmp = t_1;
	elseif (y <= -1.5e-144)
		tmp = Float64(1.0 + Float64(Float64(x / z) / y));
	elseif (y <= 1.7e-43)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	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 <= -1.38e-12)
		tmp = t_1;
	elseif (y <= -1.5e-144)
		tmp = 1.0 + ((x / z) / y);
	elseif (y <= 1.7e-43)
		tmp = 1.0 - (x / (z * t));
	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, -1.38e-12], t$95$1, If[LessEqual[y, -1.5e-144], N[(1.0 + N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-43], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.37999999999999998e-12 or 1.7e-43 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-/r* 90.8%

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

   4. Simplified 90.8%

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

   5. Taylor expanded in y around inf 84.7%

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

   if -1.37999999999999998e-12 < y < -1.4999999999999999e-144

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 63.8%

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

   3. Taylor expanded in y around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. neg-mul-1 50.3%

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

      3. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. *-commutative 50.3%

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

      3. associate-/r* 50.3%

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

      4. neg-mul-1 50.3%

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

   8. Simplified 50.3%

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

   if -1.4999999999999999e-144 < y < 1.7e-43

   1. Initial program 97.8%

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

   2. Taylor expanded in y around 0 86.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-12}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-144}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-43}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \end{array} \]

Alternative 5: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-144} \lor \neg \left(y \leq 3.2 \cdot 10^{-45}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e-144) (not (<= y 3.2e-45)))
   (- 1.0 (/ x (* y (- y z))))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-144) || !(y <= 3.2e-45)) {
		tmp = 1.0 - (x / (y * (y - z)));
	} 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 <= (-2.5d-144)) .or. (.not. (y <= 3.2d-45))) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    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 <= -2.5e-144) || !(y <= 3.2e-45)) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e-144) or not (y <= 3.2e-45):
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e-144) || !(y <= 3.2e-45))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	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 <= -2.5e-144) || ~((y <= 3.2e-45)))
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e-144], N[Not[LessEqual[y, 3.2e-45]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4999999999999999e-144 or 3.20000000000000007e-45 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 89.3%

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

   if -2.4999999999999999e-144 < y < 3.20000000000000007e-45

   1. Initial program 97.8%

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

   2. Taylor expanded in y around 0 86.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-144} \lor \neg \left(y \leq 3.2 \cdot 10^{-45}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 6: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-106}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.25e-7)
   (- 1.0 (/ (/ x t) z))
   (if (<= t 3.7e-106)
     (- 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 <= -2.25e-7) {
		tmp = 1.0 - ((x / t) / z);
	} else if (t <= 3.7e-106) {
		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 <= (-2.25d-7)) then
        tmp = 1.0d0 - ((x / t) / z)
    else if (t <= 3.7d-106) 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 <= -2.25e-7) {
		tmp = 1.0 - ((x / t) / z);
	} else if (t <= 3.7e-106) {
		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 <= -2.25e-7:
		tmp = 1.0 - ((x / t) / z)
	elif t <= 3.7e-106:
		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 <= -2.25e-7)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	elseif (t <= 3.7e-106)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - 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 <= -2.25e-7)
		tmp = 1.0 - ((x / t) / z);
	elseif (t <= 3.7e-106)
		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, -2.25e-7], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-106], N[(1.0 - N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $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 < -2.2499999999999999e-7

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 96.2%

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

      1. associate-*r/ 96.2%

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

      2. neg-mul-1 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in y around 0 72.5%

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

      1. associate-/r* 72.5%

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

   7. Simplified 72.5%

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

   if -2.2499999999999999e-7 < t < 3.69999999999999979e-106

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/r* 84.6%

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

   4. Simplified 84.6%

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

   if 3.69999999999999979e-106 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 94.9%

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

      1. associate-*r/ 94.9%

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

      2. neg-mul-1 94.9%

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

   4. Simplified 94.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-106}:\\ \;\;\;\;1 - \frac{\frac{x}{y - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 7: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+52} \lor \neg \left(y \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e+52) (not (<= y 2e+85)))
   (- 1.0 (/ x (* y z)))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e+52) || !(y <= 2e+85)) {
		tmp = 1.0 - (x / (y * z));
	} 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 <= (-4.2d+52)) .or. (.not. (y <= 2d+85))) then
        tmp = 1.0d0 - (x / (y * z))
    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 <= -4.2e+52) || !(y <= 2e+85)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e+52) or not (y <= 2e+85):
		tmp = 1.0 - (x / (y * z))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e+52) || !(y <= 2e+85))
		tmp = Float64(1.0 - Float64(x / Float64(y * z)));
	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 <= -4.2e+52) || ~((y <= 2e+85)))
		tmp = 1.0 - (x / (y * z));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e+52], N[Not[LessEqual[y, 2e+85]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e52 or 2e85 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 99.4%

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

   3. Taylor expanded in y around 0 72.4%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

      3. *-commutative 72.4%

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

   5. Simplified 72.4%

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

      1. expm1-log1p-u 71.6%

         \[\leadsto 1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-x}{z \cdot y}\right)\right)} \]

      2. expm1-udef 71.6%

         \[\leadsto 1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{-x}{z \cdot y}\right)} - 1\right)} \]

      3. add-sqr-sqrt 37.5%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot y}\right)} - 1\right) \]

      4. sqrt-unprod 57.9%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot y}\right)} - 1\right) \]

      5. sqr-neg 57.9%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot y}\right)} - 1\right) \]

      6. sqrt-unprod 34.3%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot y}\right)} - 1\right) \]

      7. add-sqr-sqrt 71.8%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot y}\right)} - 1\right) \]

      8. associate-/r* 71.8%

         \[\leadsto 1 - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{\frac{x}{z}}{y}}\right)} - 1\right) \]

   7. Applied egg-rr 71.8%

      \[\leadsto 1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\frac{x}{z}}{y}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 71.8%

         \[\leadsto 1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{x}{z}}{y}\right)\right)} \]

      2. expm1-log1p 72.3%

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

      3. associate-/l/ 72.4%

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

   9. Simplified 72.4%

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

   if -4.2e52 < y < 2e85

   1. Initial program 98.7%

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

   2. Taylor expanded in y around 0 71.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+52} \lor \neg \left(y \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 8: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-101} \lor \neg \left(y \leq 6 \cdot 10^{-44}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e-101) (not (<= y 6e-44)))
   (- 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 <= -3.8e-101) || !(y <= 6e-44)) {
		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 <= (-3.8d-101)) .or. (.not. (y <= 6d-44))) 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 <= -3.8e-101) || !(y <= 6e-44)) {
		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 <= -3.8e-101) or not (y <= 6e-44):
		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 <= -3.8e-101) || !(y <= 6e-44))
		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 <= -3.8e-101) || ~((y <= 6e-44)))
		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, -3.8e-101], N[Not[LessEqual[y, 6e-44]], $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 < -3.8000000000000001e-101 or 6.0000000000000005e-44 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-/r* 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in y around inf 82.6%

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

   if -3.8000000000000001e-101 < y < 6.0000000000000005e-44

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 79.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-101} \lor \neg \left(y \leq 6 \cdot 10^{-44}\right):\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 9: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 10: 61.7% 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 99.2%

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

2. Taylor expanded in y around 0 60.8%

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

3. Final simplification 60.8%

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

Reproduce

herbie shell --seed 2023320 
(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)))))