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

Percentage Accurate: 99.1% → 98.5%

Time: 10.5s

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: 98.5% accurate, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (+ 1.0 (/ (/ 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(Float64(x / 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[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.1%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
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 99.5

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

4. Applied rewrites 99.5%

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

5. Final simplification 99.5%

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

Alternative 2: 85.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{z \cdot \left(-t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.001:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ x (* z (- t)))))
   (if (<= t_1 -1e+15)
     t_2
     (if (<= t_1 0.001) 1.0 (if (<= t_1 5e+164) t_2 (/ x (* y (- z y))))))))

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 t_2 = x / (z * -t);
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else if (t_1 <= 5e+164) {
		tmp = t_2;
	} else {
		tmp = x / (y * (z - y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    t_2 = x / (z * -t)
    if (t_1 <= (-1d+15)) then
        tmp = t_2
    else if (t_1 <= 0.001d0) then
        tmp = 1.0d0
    else if (t_1 <= 5d+164) then
        tmp = t_2
    else
        tmp = x / (y * (z - y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / (z * -t);
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else if (t_1 <= 5e+164) {
		tmp = t_2;
	} else {
		tmp = x / (y * (z - y));
	}
	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))
	t_2 = x / (z * -t)
	tmp = 0
	if t_1 <= -1e+15:
		tmp = t_2
	elif t_1 <= 0.001:
		tmp = 1.0
	elif t_1 <= 5e+164:
		tmp = t_2
	else:
		tmp = x / (y * (z - y))
	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)))
	t_2 = Float64(x / Float64(z * Float64(-t)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	elseif (t_1 <= 5e+164)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(y * Float64(z - y)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = x / (z * -t);
	tmp = 0.0;
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	elseif (t_1 <= 5e+164)
		tmp = t_2;
	else
		tmp = x / (y * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.001], 1.0, If[LessEqual[t$95$1, 5e+164], t$95$2, N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e15 or 1e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.9999999999999995e164

   1. Initial program 89.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 89.7

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.5%

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

   if -1e15 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e-3

   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 99.6%

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

   if 4.9999999999999995e164 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 95.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 55.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 0.001:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)))) (t_2 (/ x (* (- y z) (- t y)))))
   (if (<= t_1 -1e+15) t_2 (if (<= t_1 0.001) 1.0 t_2))))

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 t_2 = x / ((y - z) * (t - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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 = x / ((y - z) * (y - t))
    t_2 = x / ((y - z) * (t - y))
    if (t_1 <= (-1d+15)) then
        tmp = t_2
    else if (t_1 <= 0.001d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    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 t_2 = x / ((y - z) * (t - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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))
	t_2 = x / ((y - z) * (t - y))
	tmp = 0
	if t_1 <= -1e+15:
		tmp = t_2
	elif t_1 <= 0.001:
		tmp = 1.0
	else:
		tmp = t_2
	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)))
	t_2 = Float64(x / Float64(Float64(y - z) * Float64(t - y)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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));
	t_2 = x / ((y - z) * (t - y));
	tmp = 0.0;
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.001], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e15 or 1e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 91.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.5

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

   5. Applied rewrites 91.5%

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

   if -1e15 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e-3

   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 99.6%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot z}\\ t_2 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y z))) (t_2 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_2 -5e+80) t_1 (if (<= t_2 2e+15) 1.0 t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * z);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -5e+80) {
		tmp = t_1;
	} else if (t_2 <= 2e+15) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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 = x / (y * z)
    t_2 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_2 <= (-5d+80)) then
        tmp = t_1
    else if (t_2 <= 2d+15) then
        tmp = 1.0d0
    else
        tmp = t_1
    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);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -5e+80) {
		tmp = t_1;
	} else if (t_2 <= 2e+15) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (y * z)
	t_2 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_2 <= -5e+80:
		tmp = t_1
	elif t_2 <= 2e+15:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * z))
	t_2 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -5e+80)
		tmp = t_1;
	elseif (t_2 <= 2e+15)
		tmp = 1.0;
	else
		tmp = t_1;
	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);
	t_2 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -5e+80)
		tmp = t_1;
	elseif (t_2 <= 2e+15)
		tmp = 1.0;
	else
		tmp = t_1;
	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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+80], t$95$1, If[LessEqual[t$95$2, 2e+15], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -4.99999999999999961e80 or 2e15 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 91.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.3

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

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 64.8%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 33.1%

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

   if -4.99999999999999961e80 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2e15

   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 98.6%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{\left(z - y\right) \cdot \left(-t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)))) (t_2 (/ x (* (- z y) (- t)))))
   (if (<= t_1 -1e+15) t_2 (if (<= t_1 0.001) 1.0 t_2))))

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 t_2 = x / ((z - y) * -t);
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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 = x / ((y - z) * (y - t))
    t_2 = x / ((z - y) * -t)
    if (t_1 <= (-1d+15)) then
        tmp = t_2
    else if (t_1 <= 0.001d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    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 t_2 = x / ((z - y) * -t);
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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))
	t_2 = x / ((z - y) * -t)
	tmp = 0
	if t_1 <= -1e+15:
		tmp = t_2
	elif t_1 <= 0.001:
		tmp = 1.0
	else:
		tmp = t_2
	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)))
	t_2 = Float64(x / Float64(Float64(z - y) * Float64(-t)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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));
	t_2 = x / ((z - y) * -t);
	tmp = 0.0;
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[(N[(z - y), $MachinePrecision] * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.001], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e15 or 1e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 91.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.5

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.7%

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

   if -1e15 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e-3

   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 99.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot \left(-t\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)))) (t_2 (/ x (* z (- y t)))))
   (if (<= t_1 -1e+15) t_2 (if (<= t_1 0.001) 1.0 t_2))))

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 t_2 = x / (z * (y - t));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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 = x / ((y - z) * (y - t))
    t_2 = x / (z * (y - t))
    if (t_1 <= (-1d+15)) then
        tmp = t_2
    else if (t_1 <= 0.001d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    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 t_2 = x / (z * (y - t));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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))
	t_2 = x / (z * (y - t))
	tmp = 0
	if t_1 <= -1e+15:
		tmp = t_2
	elif t_1 <= 0.001:
		tmp = 1.0
	else:
		tmp = t_2
	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)))
	t_2 = Float64(x / Float64(z * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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));
	t_2 = x / (z * (y - t));
	tmp = 0.0;
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.001], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e15 or 1e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 91.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.5

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 64.8%

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

   if -1e15 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e-3

   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 99.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{z \cdot \left(-t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)))) (t_2 (/ x (* z (- t)))))
   (if (<= t_1 -1e+15) t_2 (if (<= t_1 0.001) 1.0 t_2))))

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 t_2 = x / (z * -t);
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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 = x / ((y - z) * (y - t))
    t_2 = x / (z * -t)
    if (t_1 <= (-1d+15)) then
        tmp = t_2
    else if (t_1 <= 0.001d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    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 t_2 = x / (z * -t);
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.001) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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))
	t_2 = x / (z * -t)
	tmp = 0
	if t_1 <= -1e+15:
		tmp = t_2
	elif t_1 <= 0.001:
		tmp = 1.0
	else:
		tmp = t_2
	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)))
	t_2 = Float64(x / Float64(z * Float64(-t)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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));
	t_2 = x / (z * -t);
	tmp = 0.0;
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.001)
		tmp = 1.0;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.001], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e15 or 1e-3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 91.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 91.5

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 45.0%

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

   if -1e15 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e-3

   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 99.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 0.001:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.1%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
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. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 99.2

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

4. Applied rewrites 99.2%

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

5. Final simplification 99.2%

   \[\leadsto 1 + \frac{\frac{x}{y - t}}{z - y} \]
6. 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 98.1%

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

3. Final simplification 98.1%

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

Alternative 10: 75.5% 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 98.1%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 77.6%

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

Reproduce

herbie shell --seed 2024220 
(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)))))