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

Percentage Accurate: 99.2% → 99.2%

Time: 9.7s

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: 99.2% 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: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

3. Final simplification 98.6%

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

Alternative 2: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-48} \lor \neg \left(y \leq 3400000\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.65e-48) (not (<= y 3400000.0)))
   (- 1.0 (/ x (* y (- y t))))
   (- 1.0 (/ (/ x t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.65e-48) || !(y <= 3400000.0)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - ((x / t) / 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 ((y <= (-1.65d-48)) .or. (.not. (y <= 3400000.0d0))) then
        tmp = 1.0d0 - (x / (y * (y - t)))
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.65e-48) || !(y <= 3400000.0)) {
		tmp = 1.0 - (x / (y * (y - t)));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.65e-48) or not (y <= 3400000.0):
		tmp = 1.0 - (x / (y * (y - t)))
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.65e-48) || !(y <= 3400000.0))
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.65e-48) || ~((y <= 3400000.0)))
		tmp = 1.0 - (x / (y * (y - t)));
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.65e-48], N[Not[LessEqual[y, 3400000.0]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-48 or 3.4e6 < 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 95.7%

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

   if -1.65e-48 < y < 3.4e6

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 72.9%

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

      1. associate-/r* 74.1%

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

      2. div-inv 74.1%

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

   5. Applied egg-rr 74.1%

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

      1. un-div-inv 74.1%

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

   7. Applied egg-rr 74.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-48} \lor \neg \left(y \leq 3400000\right):\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-110} \lor \neg \left(t \leq 6.8 \cdot 10^{-144}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e-110) (not (<= t 6.8e-144)))
   (- 1.0 (/ x (* t (- z y))))
   (+ 1.0 (/ (/ x (- z y)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-110) || !(t <= 6.8e-144)) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + ((x / (z - y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.8d-110)) .or. (.not. (t <= 6.8d-144))) then
        tmp = 1.0d0 - (x / (t * (z - y)))
    else
        tmp = 1.0d0 + ((x / (z - y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-110) || !(t <= 6.8e-144)) {
		tmp = 1.0 - (x / (t * (z - y)));
	} else {
		tmp = 1.0 + ((x / (z - y)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.8e-110) or not (t <= 6.8e-144):
		tmp = 1.0 - (x / (t * (z - y)))
	else:
		tmp = 1.0 + ((x / (z - y)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.8e-110) || !(t <= 6.8e-144))
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.8e-110) || ~((t <= 6.8e-144)))
		tmp = 1.0 - (x / (t * (z - y)));
	else
		tmp = 1.0 + ((x / (z - y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.8e-110], N[Not[LessEqual[t, 6.8e-144]], $MachinePrecision]], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e-110 or 6.80000000000000035e-144 < t

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. neg-mul-1 93.5%

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

   5. Simplified 93.5%

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

   if -2.8e-110 < t < 6.80000000000000035e-144

   1. Initial program 95.8%

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

      1. clear-num 95.7%

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

      2. associate-/r/ 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in t around 0 92.9%

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

      1. *-lft-identity 92.9%

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

      2. times-frac 92.8%

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

      3. associate-*l/ 92.9%

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

      4. *-lft-identity 92.9%

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

   7. Simplified 92.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-110} \lor \neg \left(t \leq 6.8 \cdot 10^{-144}\right):\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-206}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.5e-206)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.3e-143)
     (+ 1.0 (/ (/ x (- z y)) y))
     (- 1.0 (/ x (* t (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-206) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.3e-143) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.5d-206)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.3d-143) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    else
        tmp = 1.0d0 - (x / (t * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-206) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.3e-143) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.5e-206:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.3e-143:
		tmp = 1.0 + ((x / (z - y)) / y)
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.5e-206)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.3e-143)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.5e-206)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.3e-143)
		tmp = 1.0 + ((x / (z - y)) / y);
	else
		tmp = 1.0 - (x / (t * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.5e-206], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-143], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e-206

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. associate-/r* 76.5%

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

      3. distribute-neg-frac 76.5%

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

   5. Simplified 76.5%

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

   if -2.5e-206 < t < 1.29999999999999994e-143

   1. Initial program 97.8%

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

      1. clear-num 97.8%

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

      2. associate-/r/ 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in t around 0 95.6%

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

      1. *-lft-identity 95.6%

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

      2. times-frac 95.5%

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

      3. associate-*l/ 95.6%

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

      4. *-lft-identity 95.6%

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

   7. Simplified 95.6%

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

   if 1.29999999999999994e-143 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 95.1%

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

      1. associate-*r/ 95.1%

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

      2. neg-mul-1 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-206}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-205}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e-205)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 2.55e-61)
     (+ 1.0 (/ x (* y (- z y))))
     (- 1.0 (/ (/ x t) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e-205) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 2.55e-61) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 - ((x / t) / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.7d-205)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 2.55d-61) then
        tmp = 1.0d0 + (x / (y * (z - y)))
    else
        tmp = 1.0d0 - ((x / t) / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e-205) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 2.55e-61) {
		tmp = 1.0 + (x / (y * (z - y)));
	} else {
		tmp = 1.0 - ((x / t) / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.7e-205:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 2.55e-61:
		tmp = 1.0 + (x / (y * (z - y)))
	else:
		tmp = 1.0 - ((x / t) / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.7e-205)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 2.55e-61)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.7e-205)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 2.55e-61)
		tmp = 1.0 + (x / (y * (z - y)));
	else
		tmp = 1.0 - ((x / t) / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.7e-205], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-61], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000001e-205

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. associate-/r* 76.5%

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

      3. distribute-neg-frac 76.5%

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

   5. Simplified 76.5%

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

   if -3.7000000000000001e-205 < t < 2.54999999999999984e-61

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 94.5%

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

   if 2.54999999999999984e-61 < t

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. *-un-lft-identity 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. mul-1-neg 96.8%

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

   9. Simplified 96.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-205}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-165}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-104}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e-165) 1.0 (if (<= z 5.3e-104) (+ 1.0 (/ x (* y t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e-165) {
		tmp = 1.0;
	} else if (z <= 5.3e-104) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0;
	}
	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 <= (-3.3d-165)) then
        tmp = 1.0d0
    else if (z <= 5.3d-104) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e-165) {
		tmp = 1.0;
	} else if (z <= 5.3e-104) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e-165:
		tmp = 1.0
	elif z <= 5.3e-104:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e-165)
		tmp = 1.0;
	elseif (z <= 5.3e-104)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.3e-165)
		tmp = 1.0;
	elseif (z <= 5.3e-104)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e-165], 1.0, If[LessEqual[z, 5.3e-104], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999998e-165 or 5.30000000000000018e-104 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 62.4%

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

   4. Taylor expanded in x around 0 79.5%

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

   if -3.2999999999999998e-165 < z < 5.30000000000000018e-104

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 86.6%

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

   4. Taylor expanded in t around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

   6. Simplified 71.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-165}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-104}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-164}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-99}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.1e-164) 1.0 (if (<= z 7.5e-99) (+ 1.0 (/ (/ x t) y)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.1e-164) {
		tmp = 1.0;
	} else if (z <= 7.5e-99) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.1d-164)) then
        tmp = 1.0d0
    else if (z <= 7.5d-99) then
        tmp = 1.0d0 + ((x / t) / y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.1e-164) {
		tmp = 1.0;
	} else if (z <= 7.5e-99) {
		tmp = 1.0 + ((x / t) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.1e-164:
		tmp = 1.0
	elif z <= 7.5e-99:
		tmp = 1.0 + ((x / t) / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.1e-164)
		tmp = 1.0;
	elseif (z <= 7.5e-99)
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.1e-164)
		tmp = 1.0;
	elseif (z <= 7.5e-99)
		tmp = 1.0 + ((x / t) / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.1e-164], 1.0, If[LessEqual[z, 7.5e-99], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000036e-164 or 7.4999999999999999e-99 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 62.4%

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

   4. Taylor expanded in x around 0 79.5%

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

   if -5.10000000000000036e-164 < z < 7.4999999999999999e-99

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 86.6%

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

   4. Taylor expanded in t around inf 71.8%

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

      1. +-commutative 71.8%

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

      2. *-commutative 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in x around 0 71.8%

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

      1. associate-/r* 73.2%

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

   9. Simplified 73.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-164}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-99}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-55}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.66e-99) 1.0 (if (<= y 1.8e-55) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.66e-99) {
		tmp = 1.0;
	} else if (y <= 1.8e-55) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	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 <= (-1.66d-99)) then
        tmp = 1.0d0
    else if (y <= 1.8d-55) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.66e-99) {
		tmp = 1.0;
	} else if (y <= 1.8e-55) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.66e-99:
		tmp = 1.0
	elif y <= 1.8e-55:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.66e-99)
		tmp = 1.0;
	elseif (y <= 1.8e-55)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.66e-99)
		tmp = 1.0;
	elseif (y <= 1.8e-55)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.66e-99], 1.0, If[LessEqual[y, 1.8e-55], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6599999999999999e-99 or 1.8e-55 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.8%

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

   4. Taylor expanded in x around 0 89.5%

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

   if -1.6599999999999999e-99 < y < 1.8e-55

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 74.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-55}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-54}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e-99) 1.0 (if (<= y 1.3e-54) (- 1.0 (/ (/ x t) z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e-99) {
		tmp = 1.0;
	} else if (y <= 1.3e-54) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	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 <= (-5.6d-99)) then
        tmp = 1.0d0
    else if (y <= 1.3d-54) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e-99) {
		tmp = 1.0;
	} else if (y <= 1.3e-54) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e-99:
		tmp = 1.0
	elif y <= 1.3e-54:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e-99)
		tmp = 1.0;
	elseif (y <= 1.3e-54)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e-99)
		tmp = 1.0;
	elseif (y <= 1.3e-54)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e-99], 1.0, If[LessEqual[y, 1.3e-54], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000001e-99 or 1.30000000000000001e-54 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.8%

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

   4. Taylor expanded in x around 0 89.5%

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

   if -5.6000000000000001e-99 < y < 1.30000000000000001e-54

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. associate-/r* 75.8%

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

      2. div-inv 75.8%

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

   5. Applied egg-rr 75.8%

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

      1. un-div-inv 75.8%

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

   7. Applied egg-rr 75.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-54}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 98.6%

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

3. Taylor expanded in z around 0 68.5%

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

4. Taylor expanded in x around 0 74.4%

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

5. Final simplification 74.4%

   \[\leadsto 1 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))))