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

Percentage Accurate: 99.1% → 99.1%

Time: 10.9s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+94}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-81} \lor \neg \left(z \leq -1.45 \cdot 10^{-223}\right) \land z \leq -4.8 \cdot 10^{-235}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e+94)
   (+ 1.0 (/ x (* y z)))
   (if (or (<= z -9.5e-81) (and (not (<= z -1.45e-223)) (<= z -4.8e-235)))
     (- 1.0 (/ x (* z t)))
     (+ 1.0 (/ x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+94) {
		tmp = 1.0 + (x / (y * z));
	} else if ((z <= -9.5e-81) || (!(z <= -1.45e-223) && (z <= -4.8e-235))) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * 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 (z <= (-1.9d+94)) then
        tmp = 1.0d0 + (x / (y * z))
    else if ((z <= (-9.5d-81)) .or. (.not. (z <= (-1.45d-223))) .and. (z <= (-4.8d-235))) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 + (x / (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+94) {
		tmp = 1.0 + (x / (y * z));
	} else if ((z <= -9.5e-81) || (!(z <= -1.45e-223) && (z <= -4.8e-235))) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.9e+94:
		tmp = 1.0 + (x / (y * z))
	elif (z <= -9.5e-81) or (not (z <= -1.45e-223) and (z <= -4.8e-235)):
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e+94)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif ((z <= -9.5e-81) || (!(z <= -1.45e-223) && (z <= -4.8e-235)))
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.9e+94)
		tmp = 1.0 + (x / (y * z));
	elseif ((z <= -9.5e-81) || (~((z <= -1.45e-223)) && (z <= -4.8e-235)))
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 + (x / (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e+94], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -9.5e-81], And[N[Not[LessEqual[z, -1.45e-223]], $MachinePrecision], LessEqual[z, -4.8e-235]]], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999998e94

   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 95.3%

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

   4. Taylor expanded in y around 0 95.3%

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

      1. associate-*r/ 95.3%

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

      2. neg-mul-1 95.3%

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

      3. *-commutative 95.3%

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

   6. Simplified 95.3%

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

   if -1.8999999999999998e94 < z < -9.49999999999999917e-81 or -1.45e-223 < z < -4.80000000000000022e-235

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.9%

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

   if -9.49999999999999917e-81 < z < -1.45e-223 or -4.80000000000000022e-235 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 78.5%

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

   4. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. distribute-neg-frac2 58.6%

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

      3. distribute-rgt-neg-in 58.6%

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

   6. Simplified 58.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+94}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-81} \lor \neg \left(z \leq -1.45 \cdot 10^{-223}\right) \land z \leq -4.8 \cdot 10^{-235}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+94}:\\ \;\;\;\;1 - x \cdot \frac{-1}{y \cdot z}\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-81} \lor \neg \left(z \leq -1.45 \cdot 10^{-223}\right) \land z \leq -4.8 \cdot 10^{-235}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e+94)
   (- 1.0 (* x (/ -1.0 (* y z))))
   (if (or (<= z -7.9e-81) (and (not (<= z -1.45e-223)) (<= z -4.8e-235)))
     (- 1.0 (/ x (* z t)))
     (+ 1.0 (/ x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+94) {
		tmp = 1.0 - (x * (-1.0 / (y * z)));
	} else if ((z <= -7.9e-81) || (!(z <= -1.45e-223) && (z <= -4.8e-235))) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * 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 (z <= (-2.4d+94)) then
        tmp = 1.0d0 - (x * ((-1.0d0) / (y * z)))
    else if ((z <= (-7.9d-81)) .or. (.not. (z <= (-1.45d-223))) .and. (z <= (-4.8d-235))) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0 + (x / (y * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+94) {
		tmp = 1.0 - (x * (-1.0 / (y * z)));
	} else if ((z <= -7.9e-81) || (!(z <= -1.45e-223) && (z <= -4.8e-235))) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0 + (x / (y * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e+94:
		tmp = 1.0 - (x * (-1.0 / (y * z)))
	elif (z <= -7.9e-81) or (not (z <= -1.45e-223) and (z <= -4.8e-235)):
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0 + (x / (y * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e+94)
		tmp = Float64(1.0 - Float64(x * Float64(-1.0 / Float64(y * z))));
	elseif ((z <= -7.9e-81) || (!(z <= -1.45e-223) && (z <= -4.8e-235)))
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.4e+94)
		tmp = 1.0 - (x * (-1.0 / (y * z)));
	elseif ((z <= -7.9e-81) || (~((z <= -1.45e-223)) && (z <= -4.8e-235)))
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0 + (x / (y * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.4e+94], N[(1.0 - N[(x * N[(-1.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.9e-81], And[N[Not[LessEqual[z, -1.45e-223]], $MachinePrecision], LessEqual[z, -4.8e-235]]], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999983e94

   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 99.9%

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

      1. associate-/r* 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 95.4%

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

      1. *-commutative 95.4%

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

   10. Simplified 95.4%

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

   if -2.39999999999999983e94 < z < -7.90000000000000016e-81 or -1.45e-223 < z < -4.80000000000000022e-235

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.9%

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

   if -7.90000000000000016e-81 < z < -1.45e-223 or -4.80000000000000022e-235 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 78.5%

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

   4. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. distribute-neg-frac2 58.6%

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

      3. distribute-rgt-neg-in 58.6%

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

   6. Simplified 58.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+94}:\\ \;\;\;\;1 - x \cdot \frac{-1}{y \cdot z}\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-81} \lor \neg \left(z \leq -1.45 \cdot 10^{-223}\right) \land z \leq -4.8 \cdot 10^{-235}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{x}{y \cdot t}\\ \mathbf{if}\;y \leq -2200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* y t)))))
   (if (<= y -2200000000000.0)
     t_1
     (if (<= y -6.2e-68)
       (- 1.0 (/ x (* y z)))
       (if (<= y 3.2e-7) (- 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 * t));
	double tmp;
	if (y <= -2200000000000.0) {
		tmp = t_1;
	} else if (y <= -6.2e-68) {
		tmp = 1.0 - (x / (y * z));
	} else if (y <= 3.2e-7) {
		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 * t))
    if (y <= (-2200000000000.0d0)) then
        tmp = t_1
    else if (y <= (-6.2d-68)) then
        tmp = 1.0d0 - (x / (y * z))
    else if (y <= 3.2d-7) 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 * t));
	double tmp;
	if (y <= -2200000000000.0) {
		tmp = t_1;
	} else if (y <= -6.2e-68) {
		tmp = 1.0 - (x / (y * z));
	} else if (y <= 3.2e-7) {
		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 * t))
	tmp = 0
	if y <= -2200000000000.0:
		tmp = t_1
	elif y <= -6.2e-68:
		tmp = 1.0 - (x / (y * z))
	elif y <= 3.2e-7:
		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(x / Float64(y * t)))
	tmp = 0.0
	if (y <= -2200000000000.0)
		tmp = t_1;
	elseif (y <= -6.2e-68)
		tmp = Float64(1.0 - Float64(x / Float64(y * z)));
	elseif (y <= 3.2e-7)
		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 * t));
	tmp = 0.0;
	if (y <= -2200000000000.0)
		tmp = t_1;
	elseif (y <= -6.2e-68)
		tmp = 1.0 - (x / (y * z));
	elseif (y <= 3.2e-7)
		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[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2200000000000.0], t$95$1, If[LessEqual[y, -6.2e-68], N[(1.0 - N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-7], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e12 or 3.2000000000000001e-7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.4%

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

   4. Taylor expanded in y around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-neg-frac2 72.9%

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

      3. distribute-rgt-neg-in 72.9%

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

   6. Simplified 72.9%

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

   if -2.2e12 < y < -6.1999999999999999e-68

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. 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 65.2%

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

      1. associate-/r* 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in y around inf 57.5%

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

      1. *-commutative 57.5%

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

   10. Simplified 57.5%

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

       1. associate-*l/ 57.5%

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

       2. neg-mul-1 57.5%

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

       3. add-sqr-sqrt 35.9%

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

       4. sqrt-unprod 53.2%

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

       5. sqr-neg 53.2%

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

       6. sqrt-unprod 21.4%

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

       7. *-commutative 21.4%

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

       8. add-sqr-sqrt 57.7%

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

   12. Applied egg-rr 57.7%

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

   if -6.1999999999999999e-68 < y < 3.2000000000000001e-7

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 76.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2200000000000:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-74} \lor \neg \left(y \leq 2.9 \cdot 10^{-101}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.2e-74) (not (<= y 2.9e-101)))
   (+ 1.0 (/ x (* y (- t y))))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.2e-74) || !(y <= 2.9e-101)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.2d-74)) .or. (.not. (y <= 2.9d-101))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.2e-74) || !(y <= 2.9e-101)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.2e-74) or not (y <= 2.9e-101):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.2e-74) || !(y <= 2.9e-101))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.2e-74) || ~((y <= 2.9e-101)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.2e-74], N[Not[LessEqual[y, 2.9e-101]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $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 < -9.19999999999999922e-74 or 2.9e-101 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 88.4%

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

   if -9.19999999999999922e-74 < y < 2.9e-101

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 84.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-74} \lor \neg \left(y \leq 2.9 \cdot 10^{-101}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-142} \lor \neg \left(y \leq 5.2 \cdot 10^{-130}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e-142) (not (<= y 5.2e-130)))
   (+ 1.0 (/ x (* y (- z y))))
   (- 1.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e-142) || !(y <= 5.2e-130)) {
		tmp = 1.0 + (x / (y * (z - 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 <= (-1.8d-142)) .or. (.not. (y <= 5.2d-130))) then
        tmp = 1.0d0 + (x / (y * (z - 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 <= -1.8e-142) || !(y <= 5.2e-130)) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e-142) or not (y <= 5.2e-130):
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e-142) || !(y <= 5.2e-130))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - 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 <= -1.8e-142) || ~((y <= 5.2e-130)))
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e-142], N[Not[LessEqual[y, 5.2e-130]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(z - y), $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 < -1.8e-142 or 5.2000000000000001e-130 < 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 89.4%

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

   if -1.8e-142 < y < 5.2000000000000001e-130

   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 89.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-142} \lor \neg \left(y \leq 5.2 \cdot 10^{-130}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-66} \lor \neg \left(y \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e-66) (not (<= y 1.1e-16)))
   (- 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 <= -4e-66) || !(y <= 1.1e-16)) {
		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 <= (-4d-66)) .or. (.not. (y <= 1.1d-16))) 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 <= -4e-66) || !(y <= 1.1e-16)) {
		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 <= -4e-66) or not (y <= 1.1e-16):
		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 <= -4e-66) || !(y <= 1.1e-16))
		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 <= -4e-66) || ~((y <= 1.1e-16)))
		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, -4e-66], N[Not[LessEqual[y, 1.1e-16]], $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 < -3.9999999999999999e-66 or 1.1e-16 < y

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 73.9%

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

      1. associate-/r* 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in y around inf 69.6%

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

      1. *-commutative 69.6%

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

   10. Simplified 69.6%

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

       1. associate-*l/ 69.6%

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

       2. neg-mul-1 69.6%

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

       3. add-sqr-sqrt 29.8%

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

       4. sqrt-unprod 57.9%

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

       5. sqr-neg 57.9%

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

       6. sqrt-unprod 39.0%

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

       7. *-commutative 39.0%

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

       8. add-sqr-sqrt 69.0%

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

   12. Applied egg-rr 69.0%

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

   if -3.9999999999999999e-66 < y < 1.1e-16

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 77.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-66} \lor \neg \left(y \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e-44)
   (+ 1.0 (* x (/ (/ -1.0 z) (- t y))))
   (- 1.0 (/ (/ x (- y t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e-44) {
		tmp = 1.0 + (x * ((-1.0 / z) / (t - y)));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9.5d-44)) then
        tmp = 1.0d0 + (x * (((-1.0d0) / z) / (t - y)))
    else
        tmp = 1.0d0 - ((x / (y - t)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e-44) {
		tmp = 1.0 + (x * ((-1.0 / z) / (t - y)));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e-44:
		tmp = 1.0 + (x * ((-1.0 / z) / (t - y)))
	else:
		tmp = 1.0 - ((x / (y - t)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e-44)
		tmp = Float64(1.0 + Float64(x * Float64(Float64(-1.0 / z) / Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e-44)
		tmp = 1.0 + (x * ((-1.0 / z) / (t - y)));
	else
		tmp = 1.0 - ((x / (y - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e-44], N[(1.0 + N[(x * N[(N[(-1.0 / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999924e-44

   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 95.9%

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

      1. associate-/r* 95.9%

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

   7. Simplified 95.9%

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

   if -9.49999999999999924e-44 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.6%

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

      1. *-un-lft-identity 77.6%

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

      2. times-frac 77.7%

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

   5. Applied egg-rr 77.7%

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

      1. associate-*l/ 77.7%

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

      2. *-lft-identity 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;1 + x \cdot \frac{\frac{-1}{z}}{t - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-42}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-42) (+ 1.0 (/ (/ x z) (- y t))) (+ 1.0 (/ x (* y (- t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-42) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.5d-42)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 + (x / (y * (t - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-42) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + (x / (y * (t - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-42:
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 + (x / (y * (t - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-42)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-42)
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 + (x / (y * (t - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-42], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999972e-42

   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. sub-neg 99.9%

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

      2. distribute-lft-in 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in z around inf 95.9%

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

      1. associate-/r* 95.9%

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

      2. neg-mul-1 95.9%

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

      3. unsub-neg 95.9%

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

   7. Simplified 95.9%

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

   if -7.49999999999999972e-42 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-42}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-43}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.6e-43) (+ 1.0 (/ (/ x z) (- y t))) (- 1.0 (/ (/ x (- y t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e-43) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.6d-43)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 - ((x / (y - t)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e-43) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / (y - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.6e-43:
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 - ((x / (y - t)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.6e-43)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / Float64(y - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.6e-43)
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 - ((x / (y - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.6e-43], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999998e-43

   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. sub-neg 99.9%

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

      2. distribute-lft-in 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in z around inf 95.9%

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

      1. associate-/r* 95.9%

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

      2. neg-mul-1 95.9%

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

      3. unsub-neg 95.9%

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

   7. Simplified 95.9%

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

   if -4.5999999999999998e-43 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.6%

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

      1. *-un-lft-identity 77.6%

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

      2. times-frac 77.7%

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

   5. Applied egg-rr 77.7%

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

      1. associate-*l/ 77.7%

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

      2. *-lft-identity 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-43}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y - t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.1% 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 99.9%

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

3. Taylor expanded in y around 0 60.2%

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

4. Final simplification 60.2%

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

Reproduce

herbie shell --seed 2024071 
(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)))))