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

Percentage Accurate: 99.2% → 98.6%

Time: 9.2s

Alternatives: 13

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: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 + \frac{1}{y - z} \cdot \frac{x}{t - y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (+ 1.0 (* (/ 1.0 (- y z)) (/ x (- t y)))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 + ((1.0d0 / (y - z)) * (x / (t - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 + ((1.0 / (y - z)) * (x / (t - y)));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 + N[(N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

   1. *-un-lft-identity 98.4%

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

   2. times-frac 97.7%

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

4. Applied egg-rr 97.7%

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

5. Final simplification 97.7%

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

Alternative 2: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2400:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-73} \lor \neg \left(z \leq -1.6 \cdot 10^{-124}\right) \land z \leq 2.6 \cdot 10^{-135}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2400.0)
   (- 1.0 (/ (/ x z) t))
   (if (or (<= z -4.7e-73) (and (not (<= z -1.6e-124)) (<= z 2.6e-135)))
     (+ 1.0 (/ x (* y t)))
     (- 1.0 (/ (/ x t) z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2400.0) {
		tmp = 1.0 - ((x / z) / t);
	} else if ((z <= -4.7e-73) || (!(z <= -1.6e-124) && (z <= 2.6e-135))) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2400.0d0)) then
        tmp = 1.0d0 - ((x / z) / t)
    else if ((z <= (-4.7d-73)) .or. (.not. (z <= (-1.6d-124))) .and. (z <= 2.6d-135)) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2400.0) {
		tmp = 1.0 - ((x / z) / t);
	} else if ((z <= -4.7e-73) || (!(z <= -1.6e-124) && (z <= 2.6e-135))) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2400.0:
		tmp = 1.0 - ((x / z) / t)
	elif (z <= -4.7e-73) or (not (z <= -1.6e-124) and (z <= 2.6e-135)):
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2400.0)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	elseif ((z <= -4.7e-73) || (!(z <= -1.6e-124) && (z <= 2.6e-135)))
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2400.0)
		tmp = 1.0 - ((x / z) / t);
	elseif ((z <= -4.7e-73) || (~((z <= -1.6e-124)) && (z <= 2.6e-135)))
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2400.0], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.7e-73], And[N[Not[LessEqual[z, -1.6e-124]], $MachinePrecision], LessEqual[z, 2.6e-135]]], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2400

   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 86.2%

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

      1. *-un-lft-identity 86.2%

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

      2. times-frac 86.2%

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

   5. Applied egg-rr 86.2%

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

      1. associate-*l/ 86.3%

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

      2. *-un-lft-identity 86.3%

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

   7. Applied egg-rr 86.3%

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

   if -2400 < z < -4.69999999999999994e-73 or -1.60000000000000002e-124 < z < 2.60000000000000004e-135

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 85.0%

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

      1. associate-/r* 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in y around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. distribute-neg-frac2 65.6%

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

      3. *-commutative 65.6%

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

      4. distribute-rgt-neg-out 65.6%

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

   8. Simplified 65.6%

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

   if -4.69999999999999994e-73 < z < -1.60000000000000002e-124 or 2.60000000000000004e-135 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 74.7%

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

      1. *-un-lft-identity 74.7%

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

      2. times-frac 75.6%

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

   5. Applied egg-rr 75.6%

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

      1. associate-*r/ 72.1%

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

      2. associate-*l/ 72.2%

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

      3. *-un-lft-identity 72.2%

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

   7. Applied egg-rr 72.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2400:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-73} \lor \neg \left(z \leq -1.6 \cdot 10^{-124}\right) \land z \leq 2.6 \cdot 10^{-135}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-275}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-45}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+214}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-275)
   (- 1.0 (/ (/ x z) t))
   (if (<= t 5.6e-45)
     (+ 1.0 (/ x (* y z)))
     (if (<= t 4.6e+214) (+ 1.0 (/ x (* y t))) (- 1.0 (/ x (* z t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-275) {
		tmp = 1.0 - ((x / z) / t);
	} else if (t <= 5.6e-45) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 4.6e+214) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-4.2d-275)) then
        tmp = 1.0d0 - ((x / z) / t)
    else if (t <= 5.6d-45) then
        tmp = 1.0d0 + (x / (y * z))
    else if (t <= 4.6d+214) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-275) {
		tmp = 1.0 - ((x / z) / t);
	} else if (t <= 5.6e-45) {
		tmp = 1.0 + (x / (y * z));
	} else if (t <= 4.6e+214) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e-275:
		tmp = 1.0 - ((x / z) / t)
	elif t <= 5.6e-45:
		tmp = 1.0 + (x / (y * z))
	elif t <= 4.6e+214:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-275)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	elseif (t <= 5.6e-45)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	elseif (t <= 4.6e+214)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.2e-275)
		tmp = 1.0 - ((x / z) / t);
	elseif (t <= 5.6e-45)
		tmp = 1.0 + (x / (y * z));
	elseif (t <= 4.6e+214)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-275], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-45], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+214], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.19999999999999976e-275

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 69.9%

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

      1. *-un-lft-identity 69.9%

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

      2. times-frac 70.0%

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

   5. Applied egg-rr 70.0%

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

      1. associate-*l/ 70.0%

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

      2. *-un-lft-identity 70.0%

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

   7. Applied egg-rr 70.0%

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

   if -4.19999999999999976e-275 < t < 5.6000000000000003e-45

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 87.5%

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

   4. Taylor expanded in y around 0 69.1%

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

      1. associate-*r/ 69.1%

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

      2. neg-mul-1 69.1%

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

      3. *-commutative 69.1%

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

   6. Simplified 69.1%

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

   if 5.6000000000000003e-45 < t < 4.5999999999999998e214

   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 71.9%

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

      1. associate-/r* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-neg-frac2 67.4%

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

      3. *-commutative 67.4%

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

      4. distribute-rgt-neg-out 67.4%

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

   8. Simplified 67.4%

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

   if 4.5999999999999998e214 < 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 y around 0 95.7%

      \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-275}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-45}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+214}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-275}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-45}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+212}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-275)
   (- 1.0 (/ (/ x z) t))
   (if (<= t 6e-45)
     (+ 1.0 (/ (/ x y) z))
     (if (<= t 2.5e+212) (+ 1.0 (/ x (* y t))) (- 1.0 (/ x (* z t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-275) {
		tmp = 1.0 - ((x / z) / t);
	} else if (t <= 6e-45) {
		tmp = 1.0 + ((x / y) / z);
	} else if (t <= 2.5e+212) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-4.2d-275)) then
        tmp = 1.0d0 - ((x / z) / t)
    else if (t <= 6d-45) then
        tmp = 1.0d0 + ((x / y) / z)
    else if (t <= 2.5d+212) then
        tmp = 1.0d0 + (x / (y * t))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-275) {
		tmp = 1.0 - ((x / z) / t);
	} else if (t <= 6e-45) {
		tmp = 1.0 + ((x / y) / z);
	} else if (t <= 2.5e+212) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e-275:
		tmp = 1.0 - ((x / z) / t)
	elif t <= 6e-45:
		tmp = 1.0 + ((x / y) / z)
	elif t <= 2.5e+212:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-275)
		tmp = Float64(1.0 - Float64(Float64(x / z) / t));
	elseif (t <= 6e-45)
		tmp = Float64(1.0 + Float64(Float64(x / y) / z));
	elseif (t <= 2.5e+212)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.2e-275)
		tmp = 1.0 - ((x / z) / t);
	elseif (t <= 6e-45)
		tmp = 1.0 + ((x / y) / z);
	elseif (t <= 2.5e+212)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-275], N[(1.0 - N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-45], N[(1.0 + N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+212], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.19999999999999976e-275

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 69.9%

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

      1. *-un-lft-identity 69.9%

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

      2. times-frac 70.0%

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

   5. Applied egg-rr 70.0%

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

      1. associate-*l/ 70.0%

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

      2. *-un-lft-identity 70.0%

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

   7. Applied egg-rr 70.0%

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

   if -4.19999999999999976e-275 < t < 6.00000000000000022e-45

   1. Initial program 96.5%

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

   3. Taylor expanded in t around 0 87.5%

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

   4. Taylor expanded in y around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. associate-/r* 69.2%

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

      3. distribute-neg-frac2 69.2%

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

   6. Simplified 69.2%

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

   if 6.00000000000000022e-45 < t < 2.49999999999999996e212

   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 71.9%

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

      1. associate-/r* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-neg-frac2 67.4%

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

      3. *-commutative 67.4%

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

      4. distribute-rgt-neg-out 67.4%

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

   8. Simplified 67.4%

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

   if 2.49999999999999996e212 < 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 y around 0 95.7%

      \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-275}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-45}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+212}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-101} \lor \neg \left(y \leq 1.8 \cdot 10^{-58}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e-101) (not (<= y 1.8e-58)))
   (+ 1.0 (/ x (* y (- t y))))
   (- 1.0 (/ (/ x t) z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-101) || !(y <= 1.8e-58)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.5d-101)) .or. (.not. (y <= 1.8d-58))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-101) || !(y <= 1.8e-58)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e-101) or not (y <= 1.8e-58):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e-101) || !(y <= 1.8e-58))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5e-101) || ~((y <= 1.8e-58)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e-101], N[Not[LessEqual[y, 1.8e-58]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $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 < -3.49999999999999994e-101 or 1.80000000000000005e-58 < y

   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 89.7%

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

   if -3.49999999999999994e-101 < y < 1.80000000000000005e-58

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. *-un-lft-identity 80.7%

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

      2. times-frac 79.8%

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

   5. Applied egg-rr 79.8%

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

      1. associate-*r/ 78.0%

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

      2. associate-*l/ 78.1%

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

      3. *-un-lft-identity 78.1%

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

   7. Applied egg-rr 78.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-101} \lor \neg \left(y \leq 1.8 \cdot 10^{-58}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-185} \lor \neg \left(t \leq 1.7 \cdot 10^{-95}\right):\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.1e-185) (not (<= t 1.7e-95)))
   (+ 1.0 (/ x (* (- y z) t)))
   (+ 1.0 (/ (/ x y) (- z y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.1e-185) || !(t <= 1.7e-95)) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0 + ((x / y) / (z - y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-5.1d-185)) .or. (.not. (t <= 1.7d-95))) then
        tmp = 1.0d0 + (x / ((y - z) * t))
    else
        tmp = 1.0d0 + ((x / y) / (z - y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.1e-185) || !(t <= 1.7e-95)) {
		tmp = 1.0 + (x / ((y - z) * t));
	} else {
		tmp = 1.0 + ((x / y) / (z - y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -5.1e-185) or not (t <= 1.7e-95):
		tmp = 1.0 + (x / ((y - z) * t))
	else:
		tmp = 1.0 + ((x / y) / (z - y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.1e-185) || !(t <= 1.7e-95))
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(z - y)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.1e-185) || ~((t <= 1.7e-95)))
		tmp = 1.0 + (x / ((y - z) * t));
	else
		tmp = 1.0 + ((x / y) / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.1e-185], N[Not[LessEqual[t, 1.7e-95]], $MachinePrecision]], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1000000000000003e-185 or 1.69999999999999997e-95 < t

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf 91.8%

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

      1. associate-*r/ 91.8%

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

      2. neg-mul-1 91.8%

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

   5. Simplified 91.8%

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

   if -5.1000000000000003e-185 < t < 1.69999999999999997e-95

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 88.8%

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

      1. associate-/r* 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-185} \lor \neg \left(t \leq 1.7 \cdot 10^{-95}\right):\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{-106}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.06e-106)
   (+ 1.0 (/ x (* y (- t y))))
   (if (<= y 3.2e-56) (- 1.0 (/ (/ x t) z)) (+ 1.0 (/ (/ x y) (- t y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e-106) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (y <= 3.2e-56) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / y) / (t - y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.06d-106)) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else if (y <= 3.2d-56) then
        tmp = 1.0d0 - ((x / t) / z)
    else
        tmp = 1.0d0 + ((x / y) / (t - y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e-106) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (y <= 3.2e-56) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0 + ((x / y) / (t - y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.06e-106:
		tmp = 1.0 + (x / (y * (t - y)))
	elif y <= 3.2e-56:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0 + ((x / y) / (t - y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.06e-106)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	elseif (y <= 3.2e-56)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = Float64(1.0 + Float64(Float64(x / y) / Float64(t - y)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.06e-106)
		tmp = 1.0 + (x / (y * (t - y)));
	elseif (y <= 3.2e-56)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0 + ((x / y) / (t - y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.06e-106], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-56], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / y), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.06000000000000007e-106

   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 87.9%

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

   if -2.06000000000000007e-106 < y < 3.19999999999999986e-56

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. *-un-lft-identity 80.7%

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

      2. times-frac 79.8%

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

   5. Applied egg-rr 79.8%

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

      1. associate-*r/ 78.0%

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

      2. associate-*l/ 78.1%

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

      3. *-un-lft-identity 78.1%

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

   7. Applied egg-rr 78.1%

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

   if 3.19999999999999986e-56 < y

   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 91.6%

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

      1. associate-/r* 91.6%

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

   5. Simplified 91.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{-106}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y}}{t - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-185}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-95}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.5e-185)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= t 6.5e-95)
     (- 1.0 (/ (/ x y) (- y z)))
     (+ 1.0 (/ x (* (- y z) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e-185) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (t <= 6.5e-95) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-4.5d-185)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (t <= 6.5d-95) then
        tmp = 1.0d0 - ((x / y) / (y - z))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e-185) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (t <= 6.5e-95) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.5e-185:
		tmp = 1.0 - ((x / z) / (t - y))
	elif t <= 6.5e-95:
		tmp = 1.0 - ((x / y) / (y - z))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.5e-185)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (t <= 6.5e-95)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - z)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.5e-185)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (t <= 6.5e-95)
		tmp = 1.0 - ((x / y) / (y - z));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.5e-185], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-95], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5000000000000001e-185

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. associate-/r* 84.7%

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

      3. distribute-neg-frac 84.7%

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

   5. Simplified 84.7%

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

   if -4.5000000000000001e-185 < t < 6.49999999999999985e-95

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 88.8%

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

      1. associate-/r* 88.8%

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

   5. Simplified 88.8%

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

   if 6.49999999999999985e-95 < 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 96.7%

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

      1. associate-*r/ 96.7%

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

      2. neg-mul-1 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-185}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-95}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-188}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.4e-188)
   (- 1.0 (/ (/ x z) (- t y)))
   (if (<= t 1.9e-95)
     (- 1.0 (/ (/ x y) (- y z)))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-188) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (t <= 1.9e-95) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.4d-188)) then
        tmp = 1.0d0 - ((x / z) / (t - y))
    else if (t <= 1.9d-95) then
        tmp = 1.0d0 - ((x / y) / (y - z))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-188) {
		tmp = 1.0 - ((x / z) / (t - y));
	} else if (t <= 1.9e-95) {
		tmp = 1.0 - ((x / y) / (y - z));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.4e-188:
		tmp = 1.0 - ((x / z) / (t - y))
	elif t <= 1.9e-95:
		tmp = 1.0 - ((x / y) / (y - z))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.4e-188)
		tmp = Float64(1.0 - Float64(Float64(x / z) / Float64(t - y)));
	elseif (t <= 1.9e-95)
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - z)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e-188)
		tmp = 1.0 - ((x / z) / (t - y));
	elseif (t <= 1.9e-95)
		tmp = 1.0 - ((x / y) / (y - z));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.4e-188], N[(1.0 - N[(N[(x / z), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-95], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4000000000000001e-188

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. associate-/r* 84.7%

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

      3. distribute-neg-frac 84.7%

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

   5. Simplified 84.7%

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

   if -1.4000000000000001e-188 < t < 1.8999999999999999e-95

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 88.8%

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

      1. associate-/r* 88.8%

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

   5. Simplified 88.8%

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

   if 1.8999999999999999e-95 < t

   1. Initial program 99.9%

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

      1. *-un-lft-identity 99.9%

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

      2. times-frac 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. associate-/r* 96.8%

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

      3. distribute-neg-frac2 96.8%

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

      4. sub-neg 96.8%

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

      5. neg-mul-1 96.8%

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

      6. +-commutative 96.8%

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

      7. distribute-neg-in 96.8%

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

      8. neg-mul-1 96.8%

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

      9. remove-double-neg 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-188}:\\ \;\;\;\;1 - \frac{\frac{x}{z}}{t - y}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+18} \lor \neg \left(y \leq 2.5 \cdot 10^{-28}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.6e+18) (not (<= y 2.5e-28)))
   (- 1.0 (/ x (* y z)))
   (- 1.0 (/ x (* z t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+18) || !(y <= 2.5e-28)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.6d+18)) .or. (.not. (y <= 2.5d-28))) then
        tmp = 1.0d0 - (x / (y * z))
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+18) || !(y <= 2.5e-28)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.6e+18) or not (y <= 2.5e-28):
		tmp = 1.0 - (x / (y * z))
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.6e+18) || !(y <= 2.5e-28))
		tmp = Float64(1.0 - Float64(x / Float64(y * z)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.6e+18) || ~((y <= 2.5e-28)))
		tmp = 1.0 - (x / (y * z));
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.6e+18], N[Not[LessEqual[y, 2.5e-28]], $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 < -1.6e18 or 2.5000000000000001e-28 < 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 97.5%

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

   4. Taylor expanded in y around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

      3. *-commutative 74.0%

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

   6. Simplified 74.0%

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

      1. add-sqr-sqrt 36.6%

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

      2. sqrt-unprod 67.7%

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

      3. sqr-neg 67.7%

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

      4. sqrt-unprod 37.5%

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

      5. add-sqr-sqrt 73.3%

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

      6. *-un-lft-identity 73.3%

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

      7. *-commutative 73.3%

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

   8. Applied egg-rr 73.3%

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

      1. *-lft-identity 73.3%

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

      2. *-commutative 73.3%

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

   10. Simplified 73.3%

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

   if -1.6e18 < y < 2.5000000000000001e-28

   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 74.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+18} \lor \neg \left(y \leq 2.5 \cdot 10^{-28}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+17} \lor \neg \left(y \leq 7.5 \cdot 10^{-28}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.6e+17) (not (<= y 7.5e-28)))
   (- 1.0 (/ x (* y z)))
   (- 1.0 (/ (/ x t) z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.6e+17) || !(y <= 7.5e-28)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-7.6d+17)) .or. (.not. (y <= 7.5d-28))) then
        tmp = 1.0d0 - (x / (y * z))
    else
        tmp = 1.0d0 - ((x / t) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.6e+17) || !(y <= 7.5e-28)) {
		tmp = 1.0 - (x / (y * z));
	} else {
		tmp = 1.0 - ((x / t) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -7.6e+17) or not (y <= 7.5e-28):
		tmp = 1.0 - (x / (y * z))
	else:
		tmp = 1.0 - ((x / t) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.6e+17) || !(y <= 7.5e-28))
		tmp = Float64(1.0 - Float64(x / Float64(y * z)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.6e+17) || ~((y <= 7.5e-28)))
		tmp = 1.0 - (x / (y * z));
	else
		tmp = 1.0 - ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.6e+17], N[Not[LessEqual[y, 7.5e-28]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.6e17 or 7.5000000000000003e-28 < 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 97.5%

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

   4. Taylor expanded in y around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

      3. *-commutative 74.0%

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

   6. Simplified 74.0%

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

      1. add-sqr-sqrt 36.6%

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

      2. sqrt-unprod 67.7%

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

      3. sqr-neg 67.7%

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

      4. sqrt-unprod 37.5%

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

      5. add-sqr-sqrt 73.3%

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

      6. *-un-lft-identity 73.3%

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

      7. *-commutative 73.3%

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

   8. Applied egg-rr 73.3%

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

      1. *-lft-identity 73.3%

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

      2. *-commutative 73.3%

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

   10. Simplified 73.3%

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

   if -7.6e17 < y < 7.5000000000000003e-28

   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 74.8%

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

      1. *-un-lft-identity 74.8%

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

      2. times-frac 74.1%

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

   5. Applied egg-rr 74.1%

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

      1. associate-*r/ 72.7%

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

      2. associate-*l/ 72.8%

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

      3. *-un-lft-identity 72.8%

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

   7. Applied egg-rr 72.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+17} \lor \neg \left(y \leq 7.5 \cdot 10^{-28}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.2% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (+ 1.0 (/ x (* (- y z) (- t y)))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 + (x / ((y - z) * (t - y)));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 98.4%

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

3. Final simplification 98.4%

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

Alternative 13: 61.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 - \frac{x}{z \cdot t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* z t))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 - (x / (z * t))

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - (x / (z * t));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in y around 0 64.4%

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

4. Final simplification 64.4%

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

Reproduce

herbie shell --seed 2024079 
(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)))))