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

Percentage Accurate: 99.3% → 99.3%

Time: 9.4s

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: 99.3% 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: 99.3% 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 98.9%

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

3. Final simplification 98.9%

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

Alternative 2: 84.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{z + \frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-115}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-186}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.3e-37)
   (/ (+ z (/ x (- y t))) z)
   (if (<= z -7.2e-115)
     (+ 1.0 (/ (/ x y) (- z y)))
     (if (<= z -6.5e-143)
       (/ (- z (/ x t)) z)
       (if (<= z 6.5e-186) (+ 1.0 (/ x (* y (- t y)))) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.3e-37) {
		tmp = (z + (x / (y - t))) / z;
	} else if (z <= -7.2e-115) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (z <= -6.5e-143) {
		tmp = (z - (x / t)) / z;
	} else if (z <= 6.5e-186) {
		tmp = 1.0 + (x / (y * (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 <= (-6.3d-37)) then
        tmp = (z + (x / (y - t))) / z
    else if (z <= (-7.2d-115)) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (z <= (-6.5d-143)) then
        tmp = (z - (x / t)) / z
    else if (z <= 6.5d-186) then
        tmp = 1.0d0 + (x / (y * (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 <= -6.3e-37) {
		tmp = (z + (x / (y - t))) / z;
	} else if (z <= -7.2e-115) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (z <= -6.5e-143) {
		tmp = (z - (x / t)) / z;
	} else if (z <= 6.5e-186) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.3e-37:
		tmp = (z + (x / (y - t))) / z
	elif z <= -7.2e-115:
		tmp = 1.0 + ((x / y) / (z - y))
	elif z <= -6.5e-143:
		tmp = (z - (x / t)) / z
	elif z <= 6.5e-186:
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.3e-37)
		tmp = Float64(Float64(z + Float64(x / Float64(y - t))) / z);
	elseif (z <= -7.2e-115)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (z <= -6.5e-143)
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	elseif (z <= 6.5e-186)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.3e-37)
		tmp = (z + (x / (y - t))) / z;
	elseif (z <= -7.2e-115)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (z <= -6.5e-143)
		tmp = (z - (x / t)) / z;
	elseif (z <= 6.5e-186)
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.3e-37], N[(N[(z + N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -7.2e-115], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-143], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 6.5e-186], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.30000000000000023e-37

   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 inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. associate-/r* 98.7%

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

      3. distribute-neg-frac 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in z around 0 97.4%

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

      1. sub-neg 97.4%

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

      2. mul-1-neg 97.4%

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

      3. remove-double-neg 97.4%

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

   8. Simplified 97.4%

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

   if -6.30000000000000023e-37 < z < -7.20000000000000018e-115

   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 84.9%

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

      1. associate-/r* 84.9%

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

   5. Simplified 84.9%

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

   if -7.20000000000000018e-115 < z < -6.4999999999999999e-143

   1. Initial program 77.9%

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

   3. Taylor expanded in y around 0 62.1%

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

   4. Taylor expanded in z around 0 84.2%

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

   if -6.4999999999999999e-143 < z < 6.49999999999999962e-186

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 90.7%

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

   if 6.49999999999999962e-186 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 60.1%

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

   4. Taylor expanded in x around 0 77.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{z + \frac{x}{y - t}}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-115}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-186}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-37}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-115}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-187}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e-37)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z -3e-115)
     (+ 1.0 (/ (/ x y) (- z y)))
     (if (<= z -6.5e-143)
       (/ (- z (/ x t)) z)
       (if (<= z 1.5e-187)
         (+ 1.0 (/ x (* y (- t y))))
         (- 1.0 (/ x (* t (- z y)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-37) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -3e-115) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (z <= -6.5e-143) {
		tmp = (z - (x / t)) / z;
	} else if (z <= 1.5e-187) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1d-37)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= (-3d-115)) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (z <= (-6.5d-143)) then
        tmp = (z - (x / t)) / z
    else if (z <= 1.5d-187) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - (x / (t * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-37) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -3e-115) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (z <= -6.5e-143) {
		tmp = (z - (x / t)) / z;
	} else if (z <= 1.5e-187) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e-37:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= -3e-115:
		tmp = 1.0 + ((x / y) / (z - y))
	elif z <= -6.5e-143:
		tmp = (z - (x / t)) / z
	elif z <= 1.5e-187:
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e-37)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= -3e-115)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (z <= -6.5e-143)
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	elseif (z <= 1.5e-187)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e-37)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= -3e-115)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (z <= -6.5e-143)
		tmp = (z - (x / t)) / z;
	elseif (z <= 1.5e-187)
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - (x / (t * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e-37], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-115], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-143], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.5e-187], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.00000000000000007e-37

   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 inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. associate-/r* 98.7%

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

      3. distribute-neg-frac 98.7%

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

   5. Simplified 98.7%

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

   if -1.00000000000000007e-37 < z < -3.0000000000000002e-115

   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 84.9%

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

      1. associate-/r* 84.9%

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

   5. Simplified 84.9%

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

   if -3.0000000000000002e-115 < z < -6.4999999999999999e-143

   1. Initial program 77.9%

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

   3. Taylor expanded in y around 0 62.1%

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

   4. Taylor expanded in z around 0 84.2%

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

   if -6.4999999999999999e-143 < z < 1.50000000000000002e-187

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 90.3%

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

   if 1.50000000000000002e-187 < 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 t around inf 71.9%

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

      1. associate-*r/ 71.9%

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

      2. neg-mul-1 71.9%

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

   5. Simplified 71.9%

      \[\leadsto 1 - \color{blue}{\frac{-x}{t \cdot \left(y - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-37}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-115}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-187}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-38}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-115}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-187}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e-38)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= z -2.7e-115)
     (+ 1.0 (/ (/ x y) (- z y)))
     (if (<= z -3.5e-143)
       (+ 1.0 (/ (/ x t) (- y z)))
       (if (<= z 2.35e-187)
         (+ 1.0 (/ x (* y (- t y))))
         (- 1.0 (/ x (* t (- z y)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-38) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -2.7e-115) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (z <= -3.5e-143) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else if (z <= 2.35e-187) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.75d-38)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (z <= (-2.7d-115)) then
        tmp = 1.0d0 + ((x / y) / (z - y))
    else if (z <= (-3.5d-143)) then
        tmp = 1.0d0 + ((x / t) / (y - z))
    else if (z <= 2.35d-187) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - (x / (t * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-38) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (z <= -2.7e-115) {
		tmp = 1.0 + ((x / y) / (z - y));
	} else if (z <= -3.5e-143) {
		tmp = 1.0 + ((x / t) / (y - z));
	} else if (z <= 2.35e-187) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - (x / (t * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e-38:
		tmp = 1.0 + ((x / z) / (y - t))
	elif z <= -2.7e-115:
		tmp = 1.0 + ((x / y) / (z - y))
	elif z <= -3.5e-143:
		tmp = 1.0 + ((x / t) / (y - z))
	elif z <= 2.35e-187:
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - (x / (t * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e-38)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= -2.7e-115)
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	elseif (z <= -3.5e-143)
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	elseif (z <= 2.35e-187)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(t * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.75e-38)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (z <= -2.7e-115)
		tmp = 1.0 + ((x / y) / (z - y));
	elseif (z <= -3.5e-143)
		tmp = 1.0 + ((x / t) / (y - z));
	elseif (z <= 2.35e-187)
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - (x / (t * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e-38], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-115], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-143], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-187], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7500000000000001e-38

   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 inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. associate-/r* 98.7%

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

      3. distribute-neg-frac 98.7%

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

   5. Simplified 98.7%

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

   if -1.7500000000000001e-38 < z < -2.7e-115

   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 84.9%

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

      1. associate-/r* 84.9%

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

   5. Simplified 84.9%

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

   if -2.7e-115 < z < -3.50000000000000005e-143

   1. Initial program 77.9%

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

      1. clear-num 77.7%

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

      2. associate-/r/ 68.3%

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

   4. Applied egg-rr 68.3%

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

      1. associate-*l/ 77.9%

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

      2. *-un-lft-identity 77.9%

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

      3. associate-/r* 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in t around inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

   9. Simplified 100.0%

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

   if -3.50000000000000005e-143 < z < 2.3500000000000001e-187

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 90.5%

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

   if 2.3500000000000001e-187 < 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 t around inf 72.5%

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

      1. associate-*r/ 72.5%

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

      2. neg-mul-1 72.5%

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

   5. Simplified 72.5%

      \[\leadsto 1 - \color{blue}{\frac{-x}{t \cdot \left(y - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-38}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-115}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-143}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-187}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-103} \lor \neg \left(y \leq 1.35 \cdot 10^{-164}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.3e-103) (not (<= y 1.35e-164)))
   (+ 1.0 (/ x (* y (- t y))))
   (/ (- z (/ x t)) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.3e-103) || !(y <= 1.35e-164)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = (z - (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 <= (-2.3d-103)) .or. (.not. (y <= 1.35d-164))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = (z - (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 <= -2.3e-103) || !(y <= 1.35e-164)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = (z - (x / t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.3e-103) or not (y <= 1.35e-164):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = (z - (x / t)) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.3e-103) || !(y <= 1.35e-164))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(Float64(z - Float64(x / t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.3e-103) || ~((y <= 1.35e-164)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = (z - (x / t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.3e-103], N[Not[LessEqual[y, 1.35e-164]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3000000000000001e-103 or 1.3500000000000001e-164 < 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 84.1%

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

   if -2.3000000000000001e-103 < y < 1.3500000000000001e-164

   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 80.1%

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

   4. Taylor expanded in z around 0 80.7%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-103} \lor \neg \left(y \leq 1.35 \cdot 10^{-164}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-154}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e-154) 1.0 (if (<= y 2.1e-108) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-154) {
		tmp = 1.0;
	} else if (y <= 2.1e-108) {
		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 <= (-3.3d-154)) then
        tmp = 1.0d0
    else if (y <= 2.1d-108) 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 <= -3.3e-154) {
		tmp = 1.0;
	} else if (y <= 2.1e-108) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e-154:
		tmp = 1.0
	elif y <= 2.1e-108:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e-154)
		tmp = 1.0;
	elseif (y <= 2.1e-108)
		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 <= -3.3e-154)
		tmp = 1.0;
	elseif (y <= 2.1e-108)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e-154], 1.0, If[LessEqual[y, 2.1e-108], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000027e-154 or 2.0999999999999999e-108 < 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 y around 0 44.8%

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

   4. Taylor expanded in x around 0 84.5%

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

   if -3.30000000000000027e-154 < y < 2.0999999999999999e-108

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 74.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-154}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-156}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-108}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e-156) 1.0 (if (<= y 1.65e-108) (/ (- z (/ x t)) z) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e-156) {
		tmp = 1.0;
	} else if (y <= 1.65e-108) {
		tmp = (z - (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 <= (-3.6d-156)) then
        tmp = 1.0d0
    else if (y <= 1.65d-108) then
        tmp = (z - (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 <= -3.6e-156) {
		tmp = 1.0;
	} else if (y <= 1.65e-108) {
		tmp = (z - (x / t)) / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e-156:
		tmp = 1.0
	elif y <= 1.65e-108:
		tmp = (z - (x / t)) / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e-156)
		tmp = 1.0;
	elseif (y <= 1.65e-108)
		tmp = Float64(Float64(z - 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 <= -3.6e-156)
		tmp = 1.0;
	elseif (y <= 1.65e-108)
		tmp = (z - (x / t)) / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e-156], 1.0, If[LessEqual[y, 1.65e-108], N[(N[(z - N[(x / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999999e-156 or 1.6500000000000001e-108 < 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 y around 0 44.8%

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

   4. Taylor expanded in x around 0 84.5%

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

   if -3.59999999999999999e-156 < y < 1.6500000000000001e-108

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 74.2%

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

   4. Taylor expanded in z around 0 74.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-156}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-108}:\\ \;\;\;\;\frac{z - \frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-74}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 5.6e-74) (+ 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 <= 5.6e-74) {
		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 <= 5.6d-74) 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 <= 5.6e-74) {
		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 <= 5.6e-74:
		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 <= 5.6e-74)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - 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 <= 5.6e-74)
		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, 5.6e-74], N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.59999999999999976e-74

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 80.5%

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

   if 5.59999999999999976e-74 < 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 98.5%

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

      1. associate-*r/ 98.5%

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

      2. neg-mul-1 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-74}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+71}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+71) (+ 1.0 (/ x (* y z))) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+71) {
		tmp = 1.0 + (x / (y * 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 (z <= (-5.2d+71)) then
        tmp = 1.0d0 + (x / (y * 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 (z <= -5.2e+71) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+71:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+71)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+71)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+71], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999983e71

   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 inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. associate-/r* 99.9%

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

      3. distribute-neg-frac 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 88.4%

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

      1. *-commutative 88.4%

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

   8. Simplified 88.4%

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

   if -5.19999999999999983e71 < z

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 50.2%

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

   4. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+71}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.4% 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 98.9%

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

3. Taylor expanded in y around 0 53.9%

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

4. Taylor expanded in x around 0 71.8%

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

5. Final simplification 71.8%

   \[\leadsto 1 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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)))))