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

Percentage Accurate: 99.0% → 98.3%

Time: 6.6s

Alternatives: 12

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: 99.0% 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: 98.3% accurate, 0.2× speedup

Math

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

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 (* (pow (- y z) -1.0) (/ x (- y t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 - (pow((y - z), -1.0) * (x / (y - 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 - (((y - z) ** (-1.0d0)) * (x / (y - 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 - (Math.pow((y - z), -1.0) * (x / (y - t)));
}

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 - (((y - z) ^ -1.0) * (x / (y - 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[(N[Power[N[(y - z), $MachinePrecision], -1.0], $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

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

   1. lift-/.f64 N/A

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

   2. *-lft-identity N/A

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

   3. lift-*.f64 N/A

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

   4. times-frac N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 98.1

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

4. Applied rewrites 98.1%

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

5. Final simplification 98.1%

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

Alternative 2: 81.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+254}:\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{elif}\;t\_1 \leq -500000 \lor \neg \left(t\_1 \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -2e+254)
     (+ (/ x (* z y)) 1.0)
     (if (or (<= t_1 -500000.0) (not (<= t_1 5e-5)))
       (- 1.0 (/ x (* y y)))
       1.0))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -2e+254) {
		tmp = (x / (z * y)) + 1.0;
	} else if ((t_1 <= -500000.0) || !(t_1 <= 5e-5)) {
		tmp = 1.0 - (x / (y * y));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if (t_1 <= (-2d+254)) then
        tmp = (x / (z * y)) + 1.0d0
    else if ((t_1 <= (-500000.0d0)) .or. (.not. (t_1 <= 5d-5))) then
        tmp = 1.0d0 - (x / (y * y))
    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 t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -2e+254) {
		tmp = (x / (z * y)) + 1.0;
	} else if ((t_1 <= -500000.0) || !(t_1 <= 5e-5)) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -2e+254:
		tmp = (x / (z * y)) + 1.0
	elif (t_1 <= -500000.0) or not (t_1 <= 5e-5):
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -2e+254)
		tmp = Float64(Float64(x / Float64(z * y)) + 1.0);
	elseif ((t_1 <= -500000.0) || !(t_1 <= 5e-5))
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	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)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -2e+254)
		tmp = (x / (z * y)) + 1.0;
	elseif ((t_1 <= -500000.0) || ~((t_1 <= 5e-5)))
		tmp = 1.0 - (x / (y * y));
	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_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+254], N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[Or[LessEqual[t$95$1, -500000.0], N[Not[LessEqual[t$95$1, 5e-5]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1.9999999999999999e254

   1. Initial program 91.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 91.6

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

   4. Applied rewrites 91.6%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 55.4

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

   7. Applied rewrites 55.4%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 58.0%

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

   if -1.9999999999999999e254 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5e5 or 5.00000000000000024e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto 1 - \frac{x}{\color{blue}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. lower-*.f64 41.2

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

   5. Applied rewrites 41.2%

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

   if -5e5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.00000000000000024e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -2 \cdot 10^{+254}:\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -500000 \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(y - t\right)\\ t_2 := \frac{x}{t\_1}\\ \mathbf{if}\;t\_2 \leq -500000 \lor \neg \left(t\_2 \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{-x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- y t))) (t_2 (/ x t_1)))
   (if (or (<= t_2 -500000.0) (not (<= t_2 5e-5))) (/ (- x) t_1) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (y - t);
	double t_2 = x / t_1;
	double tmp;
	if ((t_2 <= -500000.0) || !(t_2 <= 5e-5)) {
		tmp = -x / t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * (y - t)
    t_2 = x / t_1
    if ((t_2 <= (-500000.0d0)) .or. (.not. (t_2 <= 5d-5))) then
        tmp = -x / t_1
    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 t_1 = (y - z) * (y - t);
	double t_2 = x / t_1;
	double tmp;
	if ((t_2 <= -500000.0) || !(t_2 <= 5e-5)) {
		tmp = -x / t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (y - z) * (y - t)
	t_2 = x / t_1
	tmp = 0
	if (t_2 <= -500000.0) or not (t_2 <= 5e-5):
		tmp = -x / t_1
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(y - t))
	t_2 = Float64(x / t_1)
	tmp = 0.0
	if ((t_2 <= -500000.0) || !(t_2 <= 5e-5))
		tmp = Float64(Float64(-x) / t_1);
	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)
	t_1 = (y - z) * (y - t);
	t_2 = x / t_1;
	tmp = 0.0;
	if ((t_2 <= -500000.0) || ~((t_2 <= 5e-5)))
		tmp = -x / t_1;
	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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -500000.0], N[Not[LessEqual[t$95$2, 5e-5]], $MachinePrecision]], N[((-x) / t$95$1), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5e5 or 5.00000000000000024e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower--.f64 91.4

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

   5. Applied rewrites 91.4%

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

   if -5e5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.00000000000000024e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -500000 \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{-x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-5} \lor \neg \left(t\_1 \leq 10^{-23}\right):\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -2e-5) (not (<= t_1 1e-23))) (+ (/ x (* z y)) 1.0) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -2e-5) || !(t_1 <= 1e-23)) {
		tmp = (x / (z * y)) + 1.0;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if ((t_1 <= (-2d-5)) .or. (.not. (t_1 <= 1d-23))) then
        tmp = (x / (z * y)) + 1.0d0
    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 t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -2e-5) || !(t_1 <= 1e-23)) {
		tmp = (x / (z * y)) + 1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -2e-5) or not (t_1 <= 1e-23):
		tmp = (x / (z * y)) + 1.0
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -2e-5) || !(t_1 <= 1e-23))
		tmp = Float64(Float64(x / Float64(z * y)) + 1.0);
	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)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -2e-5) || ~((t_1 <= 1e-23)))
		tmp = (x / (z * y)) + 1.0;
	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_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-5], N[Not[LessEqual[t$95$1, 1e-23]], $MachinePrecision]], N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2.00000000000000016e-5 or 9.9999999999999996e-24 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 94.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 95.2

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

   4. Applied rewrites 95.2%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 48.7

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

   7. Applied rewrites 48.7%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 26.8%

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

   if -2.00000000000000016e-5 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 9.9999999999999996e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -2 \cdot 10^{-5} \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 10^{-23}\right):\\ \;\;\;\;\frac{x}{z \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+36} \lor \neg \left(t\_1 \leq 10^{+75}\right):\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (or (<= t_1 -4e+36) (not (<= t_1 1e+75))) (+ (/ x (* t y)) 1.0) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -4e+36) || !(t_1 <= 1e+75)) {
		tmp = (x / (t * y)) + 1.0;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if ((t_1 <= (-4d+36)) .or. (.not. (t_1 <= 1d+75))) then
        tmp = (x / (t * y)) + 1.0d0
    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 t_1 = x / ((y - z) * (y - t));
	double tmp;
	if ((t_1 <= -4e+36) || !(t_1 <= 1e+75)) {
		tmp = (x / (t * y)) + 1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if (t_1 <= -4e+36) or not (t_1 <= 1e+75):
		tmp = (x / (t * y)) + 1.0
	else:
		tmp = 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if ((t_1 <= -4e+36) || !(t_1 <= 1e+75))
		tmp = Float64(Float64(x / Float64(t * y)) + 1.0);
	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)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if ((t_1 <= -4e+36) || ~((t_1 <= 1e+75)))
		tmp = (x / (t * y)) + 1.0;
	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_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+36], N[Not[LessEqual[t$95$1, 1e+75]], $MachinePrecision]], N[(N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -4.00000000000000017e36 or 9.99999999999999927e74 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 57.9

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

   5. Applied rewrites 57.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 30.0%

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

   if -4.00000000000000017e36 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 9.99999999999999927e74

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 92.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -4 \cdot 10^{+36} \lor \neg \left(\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 10^{+75}\right):\\ \;\;\;\;\frac{x}{t \cdot y} + 1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-70} \lor \neg \left(y \leq 1.95 \cdot 10^{+37}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \end{array} \end{array} \]

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 (or (<= y -1.05e-70) (not (<= y 1.95e+37)))
   (- 1.0 (/ x (* y y)))
   (+ (/ x (* (- y t) z)) 1.0)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-70) || !(y <= 1.95e+37)) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = (x / ((y - t) * z)) + 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 <= (-1.05d-70)) .or. (.not. (y <= 1.95d+37))) then
        tmp = 1.0d0 - (x / (y * y))
    else
        tmp = (x / ((y - t) * z)) + 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 <= -1.05e-70) || !(y <= 1.95e+37)) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = (x / ((y - t) * z)) + 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-70) or not (y <= 1.95e+37):
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = (x / ((y - t) * z)) + 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 <= -1.05e-70) || !(y <= 1.95e+37))
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	else
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 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 <= -1.05e-70) || ~((y <= 1.95e+37)))
		tmp = 1.0 - (x / (y * y));
	else
		tmp = (x / ((y - t) * z)) + 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[Or[LessEqual[y, -1.05e-70], N[Not[LessEqual[y, 1.95e+37]], $MachinePrecision]], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0500000000000001e-70 or 1.9499999999999999e37 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto 1 - \frac{x}{\color{blue}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. lower-*.f64 91.3

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

   5. Applied rewrites 91.3%

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

   if -1.0500000000000001e-70 < y < 1.9499999999999999e37

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 81.7

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

   5. Applied rewrites 81.7%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-70} \lor \neg \left(y \leq 1.95 \cdot 10^{+37}\right):\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

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 (<= t -1.05e-242)
   (+ (/ x (* (- y t) z)) 1.0)
   (if (<= t 1.05e-60)
     (- 1.0 (/ x (* (- y z) y)))
     (+ (/ x (* (- y 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 (t <= -1.05e-242) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (t <= 1.05e-60) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 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 (t <= (-1.05d-242)) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else if (t <= 1.05d-60) then
        tmp = 1.0d0 - (x / ((y - z) * y))
    else
        tmp = (x / ((y - z) * t)) + 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 (t <= -1.05e-242) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (t <= 1.05e-60) {
		tmp = 1.0 - (x / ((y - z) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e-242:
		tmp = (x / ((y - t) * z)) + 1.0
	elif t <= 1.05e-60:
		tmp = 1.0 - (x / ((y - z) * y))
	else:
		tmp = (x / ((y - z) * t)) + 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e-242)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	elseif (t <= 1.05e-60)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - z) * y)));
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 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 (t <= -1.05e-242)
		tmp = (x / ((y - t) * z)) + 1.0;
	elseif (t <= 1.05e-60)
		tmp = 1.0 - (x / ((y - z) * y));
	else
		tmp = (x / ((y - z) * t)) + 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[t, -1.05e-242], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t, 1.05e-60], N[(1.0 - N[(x / N[(N[(y - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000009e-242

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 73.5

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

   5. Applied rewrites 73.5%

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

   if -1.05000000000000009e-242 < t < 1.04999999999999996e-60

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 93.5

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

   5. Applied rewrites 93.5%

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

   if 1.04999999999999996e-60 < t

   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 inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 98.7

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

   5. Applied rewrites 98.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;1 - \frac{x}{\left(y - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-141}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

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 (<= z -6.5e-100)
   (+ (/ x (* (- y t) z)) 1.0)
   (if (<= z 1.5e-141)
     (- 1.0 (/ x (* (- y t) y)))
     (+ (/ x (* (- y 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 (z <= -6.5e-100) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 1.5e-141) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 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 (z <= (-6.5d-100)) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else if (z <= 1.5d-141) then
        tmp = 1.0d0 - (x / ((y - t) * y))
    else
        tmp = (x / ((y - z) * t)) + 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 (z <= -6.5e-100) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (z <= 1.5e-141) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e-100:
		tmp = (x / ((y - t) * z)) + 1.0
	elif z <= 1.5e-141:
		tmp = 1.0 - (x / ((y - t) * y))
	else:
		tmp = (x / ((y - z) * t)) + 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e-100)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	elseif (z <= 1.5e-141)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 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 (z <= -6.5e-100)
		tmp = (x / ((y - t) * z)) + 1.0;
	elseif (z <= 1.5e-141)
		tmp = 1.0 - (x / ((y - t) * y));
	else
		tmp = (x / ((y - z) * t)) + 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[z, -6.5e-100], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[z, 1.5e-141], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.50000000000000013e-100

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 93.2

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

   5. Applied rewrites 93.2%

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

   if -6.50000000000000013e-100 < z < 1.49999999999999992e-141

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 88.3

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

   5. Applied rewrites 88.3%

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

   if 1.49999999999999992e-141 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 80.8

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

   5. Applied rewrites 80.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-141}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \end{array} \]

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 (<= t 2.9e-305)
   (+ (/ x (* (- y t) z)) 1.0)
   (if (<= t 1.75e-63) (- 1.0 (/ x (* y y))) (+ (/ x (* (- y 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 (t <= 2.9e-305) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (t <= 1.75e-63) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = (x / ((y - z) * t)) + 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 (t <= 2.9d-305) then
        tmp = (x / ((y - t) * z)) + 1.0d0
    else if (t <= 1.75d-63) then
        tmp = 1.0d0 - (x / (y * y))
    else
        tmp = (x / ((y - z) * t)) + 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 (t <= 2.9e-305) {
		tmp = (x / ((y - t) * z)) + 1.0;
	} else if (t <= 1.75e-63) {
		tmp = 1.0 - (x / (y * y));
	} else {
		tmp = (x / ((y - z) * t)) + 1.0;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 2.9e-305:
		tmp = (x / ((y - t) * z)) + 1.0
	elif t <= 1.75e-63:
		tmp = 1.0 - (x / (y * y))
	else:
		tmp = (x / ((y - z) * t)) + 1.0
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.9e-305)
		tmp = Float64(Float64(x / Float64(Float64(y - t) * z)) + 1.0);
	elseif (t <= 1.75e-63)
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	else
		tmp = Float64(Float64(x / Float64(Float64(y - z) * t)) + 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 (t <= 2.9e-305)
		tmp = (x / ((y - t) * z)) + 1.0;
	elseif (t <= 1.75e-63)
		tmp = 1.0 - (x / (y * y));
	else
		tmp = (x / ((y - z) * t)) + 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[t, 2.9e-305], N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t, 1.75e-63], N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.89999999999999988e-305

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 72.2

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

   5. Applied rewrites 72.2%

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

   if 2.89999999999999988e-305 < t < 1.75000000000000002e-63

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto 1 - \frac{x}{\color{blue}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. lower-*.f64 80.4

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

   5. Applied rewrites 80.4%

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

   if 1.75000000000000002e-63 < t

   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 inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 97.5

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

   5. Applied rewrites 97.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} + 1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-63}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t} + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-76} \lor \neg \left(y \leq 8.4 \cdot 10^{-106}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \end{array} \]

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 -3.4e-76) (not (<= y 8.4e-106))) 1.0 (- 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 <= -3.4e-76) || !(y <= 8.4e-106)) {
		tmp = 1.0;
	} 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 <= (-3.4d-76)) .or. (.not. (y <= 8.4d-106))) then
        tmp = 1.0d0
    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 <= -3.4e-76) || !(y <= 8.4e-106)) {
		tmp = 1.0;
	} 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 <= -3.4e-76) or not (y <= 8.4e-106):
		tmp = 1.0
	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 <= -3.4e-76) || !(y <= 8.4e-106))
		tmp = 1.0;
	else
		tmp = Float64(1.0 - Float64(x / Float64(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 <= -3.4e-76) || ~((y <= 8.4e-106)))
		tmp = 1.0;
	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, -3.4e-76], N[Not[LessEqual[y, 8.4e-106]], $MachinePrecision]], 1.0, N[(1.0 - N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3999999999999999e-76 or 8.40000000000000013e-106 < 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 x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.0%

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

   if -3.3999999999999999e-76 < y < 8.40000000000000013e-106

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 82.6

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

   5. Applied rewrites 82.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-76} \lor \neg \left(y \leq 8.4 \cdot 10^{-106}\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.0% accurate, 1.0× speedup

Math

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

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) (- y t)))))

C

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

Python

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

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(y - t))))
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) * (y - 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[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

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

Alternative 12: 75.2% accurate, 26.0× 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 98.5%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 76.3%

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

6. Final simplification 76.3%

   \[\leadsto 1 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024320 
(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)))))