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

Percentage Accurate: 99.1% → 99.0%

Time: 10.3s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(y - t\right) \leq 2 \cdot 10^{-119}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \end{array} \end{array} \]

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 z) (- y t)) 2e-119)
   (+ 1.0 (/ (/ x (- y t)) (- z y)))
   (+ 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) {
	double tmp;
	if (((y - z) * (y - t)) <= 2e-119) {
		tmp = 1.0 + ((x / (y - t)) / (z - y));
	} else {
		tmp = 1.0 + (x / ((y - z) * (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 - z) * (y - t)) <= 2d-119) then
        tmp = 1.0d0 + ((x / (y - t)) / (z - y))
    else
        tmp = 1.0d0 + (x / ((y - z) * (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 - z) * (y - t)) <= 2e-119) {
		tmp = 1.0 + ((x / (y - t)) / (z - y));
	} else {
		tmp = 1.0 + (x / ((y - z) * (t - y)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((y - z) * (y - t)) <= 2e-119:
		tmp = 1.0 + ((x / (y - t)) / (z - y))
	else:
		tmp = 1.0 + (x / ((y - z) * (t - y)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(y - z) * Float64(y - t)) <= 2e-119)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / Float64(z - y)));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * 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 - z) * (y - t)) <= 2e-119)
		tmp = 1.0 + ((x / (y - t)) / (z - y));
	else
		tmp = 1.0 + (x / ((y - z) * (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[N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision], 2e-119], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 y t)) < 2.00000000000000003e-119

   1. Initial program 94.1%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

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

      3. associate-/l* 98.8%

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

   4. Applied egg-rr 98.8%

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

   5. Taylor expanded in x around 0 94.1%

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

      1. associate-/r* 98.0%

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

   7. Simplified 98.0%

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

   if 2.00000000000000003e-119 < (*.f64 (-.f64 y z) (-.f64 y t))

   1. Initial program 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(y - t\right) \leq 2 \cdot 10^{-119}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-46} \lor \neg \left(z \leq 3.2 \cdot 10^{-67}\right):\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \end{array} \end{array} \]

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 (<= z -1.55e-46) (not (<= z 3.2e-67)))
   (+ 1.0 (/ x (* z (- y t))))
   (+ 1.0 (/ (/ x (- t y)) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-46) || !(z <= 3.2e-67)) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0 + ((x / (t - y)) / 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 ((z <= (-1.55d-46)) .or. (.not. (z <= 3.2d-67))) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else
        tmp = 1.0d0 + ((x / (t - y)) / 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 ((z <= -1.55e-46) || !(z <= 3.2e-67)) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else {
		tmp = 1.0 + ((x / (t - y)) / y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55e-46) or not (z <= 3.2e-67):
		tmp = 1.0 + (x / (z * (y - t)))
	else:
		tmp = 1.0 + ((x / (t - y)) / y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55e-46) || !(z <= 3.2e-67))
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / Float64(t - y)) / 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 ((z <= -1.55e-46) || ~((z <= 3.2e-67)))
		tmp = 1.0 + (x / (z * (y - t)));
	else
		tmp = 1.0 + ((x / (t - y)) / 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[z, -1.55e-46], N[Not[LessEqual[z, 3.2e-67]], $MachinePrecision]], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e-46 or 3.20000000000000021e-67 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 96.6%

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

      1. associate-*r/ 96.6%

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

      2. neg-mul-1 96.6%

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

      3. *-commutative 96.6%

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

   5. Simplified 96.6%

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

   if -1.55e-46 < z < 3.20000000000000021e-67

   1. Initial program 93.8%

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

      1. *-un-lft-identity 93.8%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 85.2%

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

      1. associate-*l/ 85.2%

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

      2. *-un-lft-identity 85.2%

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

   7. Applied egg-rr 85.2%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-46} \lor \neg \left(z \leq 3.2 \cdot 10^{-67}\right):\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-142} \lor \neg \left(y \leq 5.5 \cdot 10^{-130}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{t \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

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 -1.8e-142) (not (<= y 5.5e-130)))
   (+ 1.0 (/ x (* y (- t y))))
   (+ 1.0 (/ -1.0 (* t (/ z x))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e-142) || !(y <= 5.5e-130)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	}
	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 <= (-1.8d-142)) .or. (.not. (y <= 5.5d-130))) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else
        tmp = 1.0d0 + ((-1.0d0) / (t * (z / x)))
    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 <= -1.8e-142) || !(y <= 5.5e-130)) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e-142) or not (y <= 5.5e-130):
		tmp = 1.0 + (x / (y * (t - y)))
	else:
		tmp = 1.0 + (-1.0 / (t * (z / x)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e-142) || !(y <= 5.5e-130))
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	else
		tmp = Float64(1.0 + Float64(-1.0 / Float64(t * Float64(z / x))));
	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 <= -1.8e-142) || ~((y <= 5.5e-130)))
		tmp = 1.0 + (x / (y * (t - y)));
	else
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	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, -1.8e-142], N[Not[LessEqual[y, 5.5e-130]], $MachinePrecision]], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-142 or 5.50000000000000007e-130 < 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 84.7%

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

   if -1.8e-142 < y < 5.50000000000000007e-130

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 81.4%

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

      1. clear-num 81.4%

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

      2. inv-pow 81.4%

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

      3. *-commutative 81.4%

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

   5. Applied egg-rr 81.4%

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

      1. unpow-1 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-142} \lor \neg \left(y \leq 5.5 \cdot 10^{-130}\right):\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{t \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-266}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-37}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -8.6e-266)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 6.2e-37)
     (+ 1.0 (/ (/ x (- z y)) y))
     (+ 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 <= -8.6e-266) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 6.2e-37) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} 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 <= (-8.6d-266)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 6.2d-37) then
        tmp = 1.0d0 + ((x / (z - y)) / y)
    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 <= -8.6e-266) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 6.2e-37) {
		tmp = 1.0 + ((x / (z - y)) / y);
	} 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 <= -8.6e-266:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 6.2e-37:
		tmp = 1.0 + ((x / (z - y)) / y)
	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 <= -8.6e-266)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 6.2e-37)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(z - y)) / y));
	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 <= -8.6e-266)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 6.2e-37)
		tmp = 1.0 + ((x / (z - y)) / y);
	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, -8.6e-266], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-37], N[(1.0 + N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / y), $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 < -8.60000000000000056e-266

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-/r* 79.7%

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

      3. distribute-neg-frac 79.7%

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

   5. Simplified 79.7%

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

   if -8.60000000000000056e-266 < t < 6.19999999999999987e-37

   1. Initial program 95.6%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

      3. associate-/l* 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in x around 0 95.6%

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

      1. associate-/r* 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in t around 0 86.9%

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

      1. associate-/l/ 88.3%

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

   10. Simplified 88.3%

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

   if 6.19999999999999987e-37 < t

   1. Initial program 99.8%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. associate-/r* 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 98.6%

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

      1. associate-*r/ 98.6%

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

      2. mul-1-neg 98.6%

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

   10. Simplified 98.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-266}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-37}:\\ \;\;\;\;1 + \frac{\frac{x}{z - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-46}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-72}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

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 (<= z -1.6e-46)
   (+ 1.0 (/ x (* z (- y t))))
   (if (<= z 3.5e-72)
     (+ 1.0 (/ (/ x (- t y)) y))
     (+ 1.0 (/ (/ x z) (- y t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-46) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (z <= 3.5e-72) {
		tmp = 1.0 + ((x / (t - y)) / y);
	} else {
		tmp = 1.0 + ((x / z) / (y - 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 (z <= (-1.6d-46)) then
        tmp = 1.0d0 + (x / (z * (y - t)))
    else if (z <= 3.5d-72) then
        tmp = 1.0d0 + ((x / (t - y)) / y)
    else
        tmp = 1.0d0 + ((x / z) / (y - 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 (z <= -1.6e-46) {
		tmp = 1.0 + (x / (z * (y - t)));
	} else if (z <= 3.5e-72) {
		tmp = 1.0 + ((x / (t - y)) / y);
	} else {
		tmp = 1.0 + ((x / z) / (y - t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-46:
		tmp = 1.0 + (x / (z * (y - t)))
	elif z <= 3.5e-72:
		tmp = 1.0 + ((x / (t - y)) / y)
	else:
		tmp = 1.0 + ((x / z) / (y - t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-46)
		tmp = Float64(1.0 + Float64(x / Float64(z * Float64(y - t))));
	elseif (z <= 3.5e-72)
		tmp = Float64(1.0 + Float64(Float64(x / Float64(t - y)) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - 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 (z <= -1.6e-46)
		tmp = 1.0 + (x / (z * (y - t)));
	elseif (z <= 3.5e-72)
		tmp = 1.0 + ((x / (t - y)) / y);
	else
		tmp = 1.0 + ((x / z) / (y - 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[z, -1.6e-46], N[(1.0 + N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-72], N[(1.0 + N[(N[(x / N[(t - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e-46

   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 97.8%

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

      1. associate-*r/ 97.8%

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

      2. neg-mul-1 97.8%

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

      3. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   if -1.6e-46 < z < 3.5e-72

   1. Initial program 93.8%

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

      1. *-un-lft-identity 93.8%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 85.2%

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

      1. associate-*l/ 85.2%

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

      2. *-un-lft-identity 85.2%

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

   7. Applied egg-rr 85.2%

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

   if 3.5e-72 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. associate-/r* 95.6%

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

      3. distribute-neg-frac 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-46}:\\ \;\;\;\;1 + \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-72}:\\ \;\;\;\;1 + \frac{\frac{x}{t - y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{-142}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-112}:\\ \;\;\;\;1 + \frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 -1.24e-142)
   (+ 1.0 (/ x (* y (- t y))))
   (if (<= y 7e-112)
     (+ 1.0 (/ -1.0 (* t (/ z x))))
     (- 1.0 (/ x (* y (- y z)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.24e-142) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (y <= 7e-112) {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	} else {
		tmp = 1.0 - (x / (y * (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 (y <= (-1.24d-142)) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else if (y <= 7d-112) then
        tmp = 1.0d0 + ((-1.0d0) / (t * (z / x)))
    else
        tmp = 1.0d0 - (x / (y * (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 (y <= -1.24e-142) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (y <= 7e-112) {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	} else {
		tmp = 1.0 - (x / (y * (y - z)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.24e-142:
		tmp = 1.0 + (x / (y * (t - y)))
	elif y <= 7e-112:
		tmp = 1.0 + (-1.0 / (t * (z / x)))
	else:
		tmp = 1.0 - (x / (y * (y - z)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.24e-142)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	elseif (y <= 7e-112)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(t * Float64(z / x))));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * 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 (y <= -1.24e-142)
		tmp = 1.0 + (x / (y * (t - y)));
	elseif (y <= 7e-112)
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	else
		tmp = 1.0 - (x / (y * (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[y, -1.24e-142], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-112], N[(1.0 + N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24000000000000003e-142

   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 83.6%

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

   if -1.24000000000000003e-142 < y < 6.99999999999999988e-112

   1. Initial program 93.2%

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

   3. Taylor expanded in y around 0 81.0%

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

      1. clear-num 81.0%

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

      2. inv-pow 81.0%

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

      3. *-commutative 81.0%

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

   5. Applied egg-rr 81.0%

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

      1. unpow-1 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-/l* 81.3%

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

   7. Simplified 81.3%

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

   if 6.99999999999999988e-112 < 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 t around 0 89.1%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{-142}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-112}:\\ \;\;\;\;1 + \frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-134}:\\ \;\;\;\;1 + \frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -2.4e-153)
   1.0
   (if (<= y 1.5e-134) (+ 1.0 (/ -1.0 (* t (/ z x)))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-153) {
		tmp = 1.0;
	} else if (y <= 1.5e-134) {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	} else {
		tmp = 1.0;
	}
	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 <= (-2.4d-153)) then
        tmp = 1.0d0
    else if (y <= 1.5d-134) then
        tmp = 1.0d0 + ((-1.0d0) / (t * (z / x)))
    else
        tmp = 1.0d0
    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 <= -2.4e-153) {
		tmp = 1.0;
	} else if (y <= 1.5e-134) {
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-153:
		tmp = 1.0
	elif y <= 1.5e-134:
		tmp = 1.0 + (-1.0 / (t * (z / x)))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-153)
		tmp = 1.0;
	elseif (y <= 1.5e-134)
		tmp = Float64(1.0 + Float64(-1.0 / Float64(t * Float64(z / x))));
	else
		tmp = 1.0;
	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 <= -2.4e-153)
		tmp = 1.0;
	elseif (y <= 1.5e-134)
		tmp = 1.0 + (-1.0 / (t * (z / x)));
	else
		tmp = 1.0;
	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, -2.4e-153], 1.0, If[LessEqual[y, 1.5e-134], N[(1.0 + N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000002e-153 or 1.5e-134 < 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 y around 0 49.1%

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

      1. *-un-lft-identity 49.1%

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

      2. times-frac 49.1%

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

      3. frac-2neg 49.1%

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

      4. metadata-eval 49.1%

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

      5. add-sqr-sqrt 25.2%

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

      6. sqrt-unprod 48.8%

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

      7. sqr-neg 48.8%

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

      8. sqrt-unprod 23.9%

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

      9. add-sqr-sqrt 48.5%

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

   5. Applied egg-rr 48.5%

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

      1. associate-*l/ 48.5%

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

      2. associate-*r/ 48.5%

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

      3. neg-mul-1 48.5%

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

   7. Simplified 48.5%

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

   8. Taylor expanded in x around 0 80.1%

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

   if -2.4000000000000002e-153 < y < 1.5e-134

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. clear-num 82.2%

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

      2. inv-pow 82.2%

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

      3. *-commutative 82.2%

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

   5. Applied egg-rr 82.2%

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

      1. unpow-1 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-/l* 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-134}:\\ \;\;\;\;1 + \frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-135}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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 -2.4e-153) 1.0 (if (<= y 4.6e-135) (- 1.0 (/ x (* z t))) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-153) {
		tmp = 1.0;
	} else if (y <= 4.6e-135) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	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 <= (-2.4d-153)) then
        tmp = 1.0d0
    else if (y <= 4.6d-135) then
        tmp = 1.0d0 - (x / (z * t))
    else
        tmp = 1.0d0
    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 <= -2.4e-153) {
		tmp = 1.0;
	} else if (y <= 4.6e-135) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-153:
		tmp = 1.0
	elif y <= 4.6e-135:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-153)
		tmp = 1.0;
	elseif (y <= 4.6e-135)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	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 <= -2.4e-153)
		tmp = 1.0;
	elseif (y <= 4.6e-135)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	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, -2.4e-153], 1.0, If[LessEqual[y, 4.6e-135], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000002e-153 or 4.5999999999999998e-135 < 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 y around 0 49.1%

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

      1. *-un-lft-identity 49.1%

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

      2. times-frac 49.1%

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

      3. frac-2neg 49.1%

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

      4. metadata-eval 49.1%

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

      5. add-sqr-sqrt 25.2%

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

      6. sqrt-unprod 48.8%

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

      7. sqr-neg 48.8%

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

      8. sqrt-unprod 23.9%

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

      9. add-sqr-sqrt 48.5%

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

   5. Applied egg-rr 48.5%

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

      1. associate-*l/ 48.5%

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

      2. associate-*r/ 48.5%

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

      3. neg-mul-1 48.5%

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

   7. Simplified 48.5%

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

   8. Taylor expanded in x around 0 80.1%

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

   if -2.4000000000000002e-153 < y < 4.5999999999999998e-135

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0 82.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-153}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-135}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.1% 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 97.7%

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

3. Final simplification 97.7%

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

Alternative 10: 74.9% accurate, 11.0× speedup

Math

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

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)

C

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

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
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;
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 97.7%

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

3. Taylor expanded in y around 0 58.9%

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

   1. *-un-lft-identity 58.9%

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

   2. times-frac 58.6%

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

   3. frac-2neg 58.6%

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

   4. metadata-eval 58.6%

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

   5. add-sqr-sqrt 30.2%

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

   6. sqrt-unprod 51.1%

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

   7. sqr-neg 51.1%

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

   8. sqrt-unprod 22.1%

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

   9. add-sqr-sqrt 47.3%

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

5. Applied egg-rr 47.3%

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

   1. associate-*l/ 47.3%

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

   2. associate-*r/ 47.3%

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

   3. neg-mul-1 47.3%

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

7. Simplified 47.3%

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

8. Taylor expanded in x around 0 70.3%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024087 
(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)))))