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

Percentage Accurate: 99.1% → 99.6%

Time: 10.5s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+70}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+70)
   (+ 1.0 (/ (/ x z) (- y t)))
   (+ 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) {
	double tmp;
	if (z <= -5e+70) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / (y - t)) / (z - y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5d+70)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 + ((x / (y - t)) / (z - y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+70) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / (y - t)) / (z - y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -5e+70:
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 + ((x / (y - t)) / (z - y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+70)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / Float64(y - t)) / Float64(z - y)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e+70)
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 + ((x / (y - t)) / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -5e+70], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e70

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 99.9

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

   5. Simplified 99.9%

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

      1. lift--.f64 N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 99.9

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

   7. Applied egg-rr 99.9%

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

   if -5.0000000000000002e70 < z

   1. Initial program 96.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      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 99.4

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

   4. Applied egg-rr 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+70}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{y - t}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t\_1 \leq 1.1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_1 -5e+17)
     (/ x (* z (- y t)))
     (if (<= t_1 1.1) 1.0 (+ 1.0 (/ x (* (- y z) t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x / (z * (y - t));
	} else if (t_1 <= 1.1) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_1 <= (-5d+17)) then
        tmp = x / (z * (y - t))
    else if (t_1 <= 1.1d0) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x / (z * (y - t));
	} else if (t_1 <= 1.1) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x / (z * (y - t))
	elif t_1 <= 1.1:
		tmp = 1.0
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x / Float64(z * Float64(y - t)));
	elseif (t_1 <= 1.1)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x / (z * (y - t));
	elseif (t_1 <= 1.1)
		tmp = 1.0;
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.1], 1.0, N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e17

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 58.3

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

   5. Simplified 58.3%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 58.3

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

   8. Simplified 58.3%

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

   if -5e17 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 1.1000000000000001

   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. Simplified 99.4%

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

   if 1.1000000000000001 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 93.9%

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

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. distribute-neg-in N/A

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

      18. unsub-neg N/A

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

      19. mul-1-neg N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 58.3

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

   5. Simplified 58.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 1.1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_1 -5e+17)
     (/ x (* z (- y t)))
     (if (<= t_1 2.0) 1.0 (/ x (* (- y z) t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x / (z * (y - t));
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_1 <= (-5d+17)) then
        tmp = x / (z * (y - t))
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x / (z * (y - t));
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x / (z * (y - t))
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x / Float64(z * Float64(y - t)));
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x / (z * (y - t));
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e17

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 58.3

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

   5. Simplified 58.3%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 58.3

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

   8. Simplified 58.3%

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

   if -5e17 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   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. Simplified 98.9%

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

   if 2 < (-.f64 #s(literal 1 binary64) (/.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 t around inf

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

      1. remove-double-neg N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. distribute-neg-in N/A

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

      18. unsub-neg N/A

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

      19. mul-1-neg N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 57.0

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

   5. Simplified 57.0%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 55.9

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

   8. Simplified 55.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - t\right)}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ t_2 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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))) (t_2 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_2 -5e+17) t_1 (if (<= t_2 2.0) 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) * t);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -5e+17) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		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)
    t_2 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_2 <= (-5d+17)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) 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) * t);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -5e+17) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		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)
	t_2 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_2 <= -5e+17:
		tmp = t_1
	elif t_2 <= 2.0:
		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(Float64(y - z) * t))
	t_2 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -5e+17)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		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);
	t_2 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -5e+17)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		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[(N[(y - z), $MachinePrecision] * t), $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+17], t$95$1, If[LessEqual[t$95$2, 2.0], 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)))) < -5e17 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 90.6%

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

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. distribute-neg-in N/A

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

      18. unsub-neg N/A

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

      19. mul-1-neg N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 56.7

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

   5. Simplified 56.7%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 56.2

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

   8. Simplified 56.2%

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

   if -5e17 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   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. Simplified 98.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t\_1 \leq 1.1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_1 -5e+17)
     (/ x (* z (- t)))
     (if (<= t_1 1.1) 1.0 (- 1.0 (/ x (* z t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x / (z * -t);
	} else if (t_1 <= 1.1) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_1 <= (-5d+17)) then
        tmp = x / (z * -t)
    else if (t_1 <= 1.1d0) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 - (x / (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_1 <= -5e+17) {
		tmp = x / (z * -t);
	} else if (t_1 <= 1.1) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_1 <= -5e+17:
		tmp = x / (z * -t)
	elif t_1 <= 1.1:
		tmp = 1.0
	else:
		tmp = 1.0 - (x / (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_1 <= -5e+17)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t_1 <= 1.1)
		tmp = 1.0;
	else
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_1 <= -5e+17)
		tmp = x / (z * -t);
	elseif (t_1 <= 1.1)
		tmp = 1.0;
	else
		tmp = 1.0 - (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+17], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.1], 1.0, N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -5e17

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 58.3

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

   5. Simplified 58.3%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 58.3

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

   8. Simplified 58.3%

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

   9. Taylor expanded in t around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 44.1

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

   11. Simplified 44.1%

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

   if -5e17 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 1.1000000000000001

   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. Simplified 99.4%

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

   if 1.1000000000000001 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 43.9

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

   5. Simplified 43.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 1.1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-t\right)}\\ t_2 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* z (- t)))) (t_2 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_2 -5e+17) t_1 (if (<= t_2 2.0) 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 / (z * -t);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -5e+17) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		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 / (z * -t)
    t_2 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_2 <= (-5d+17)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) 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 / (z * -t);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -5e+17) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		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 / (z * -t)
	t_2 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_2 <= -5e+17:
		tmp = t_1
	elif t_2 <= 2.0:
		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(z * Float64(-t)))
	t_2 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -5e+17)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		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 / (z * -t);
	t_2 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -5e+17)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		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[(z * (-t)), $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+17], t$95$1, If[LessEqual[t$95$2, 2.0], 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)))) < -5e17 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 56.6

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

   5. Simplified 56.6%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 56.1

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

   8. Simplified 56.1%

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

   9. Taylor expanded in t around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 42.7

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

   11. Simplified 42.7%

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

   if -5e17 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   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. Simplified 98.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -1000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1000000000.0) t_2 (if (<= t_1 5e-7) 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 <= -1000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		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 <= (-1000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d-7) 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 <= -1000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		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 <= -1000000000.0:
		tmp = t_2
	elif t_1 <= 5e-7:
		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 <= -1000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		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 <= -1000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		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, -1000000000.0], t$95$2, If[LessEqual[t$95$1, 5e-7], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e9 or 4.99999999999999977e-7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 90.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   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 90.1

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

   5. Simplified 90.1%

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

   if -1e9 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.99999999999999977e-7

   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. Simplified 98.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1000000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{y \cdot \left(-y\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (- y)))))
   (if (<= t_1 -2e+22) t_2 (if (<= t_1 5e-7) 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 * -y);
	double tmp;
	if (t_1 <= -2e+22) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		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 * -y)
    if (t_1 <= (-2d+22)) then
        tmp = t_2
    else if (t_1 <= 5d-7) 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 * -y);
	double tmp;
	if (t_1 <= -2e+22) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		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 * -y)
	tmp = 0
	if t_1 <= -2e+22:
		tmp = t_2
	elif t_1 <= 5e-7:
		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(y * Float64(-y)))
	tmp = 0.0
	if (t_1 <= -2e+22)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		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 * -y);
	tmp = 0.0;
	if (t_1 <= -2e+22)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		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[(y * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+22], t$95$2, If[LessEqual[t$95$1, 5e-7], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e22 or 4.99999999999999977e-7 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      5. unpow2 N/A

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

      6. lower-*.f64 32.5

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

   5. Simplified 32.5%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{{y}^{2}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{{y}^{2}}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(x\right)}}{{y}^{2}} \]

      4. lower-neg.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(x\right)}}{{y}^{2}} \]

      5. unpow2 N/A

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

      6. lower-*.f64 32.5

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

   8. Simplified 32.5%

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

   if -2e22 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.99999999999999977e-7

   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. Simplified 98.5%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -2 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{y \cdot \left(-y\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -1e+59) (/ x (* y t)) (if (<= t_1 5e+18) 1.0 (/ x (* y z))))))

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 <= -1e+59) {
		tmp = x / (y * t);
	} else if (t_1 <= 5e+18) {
		tmp = 1.0;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if (t_1 <= (-1d+59)) then
        tmp = x / (y * t)
    else if (t_1 <= 5d+18) then
        tmp = 1.0d0
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+59) {
		tmp = x / (y * t);
	} else if (t_1 <= 5e+18) {
		tmp = 1.0;
	} else {
		tmp = x / (y * z);
	}
	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 <= -1e+59:
		tmp = x / (y * t)
	elif t_1 <= 5e+18:
		tmp = 1.0
	else:
		tmp = x / (y * z)
	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 <= -1e+59)
		tmp = Float64(x / Float64(y * t));
	elseif (t_1 <= 5e+18)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -1e+59)
		tmp = x / (y * t);
	elseif (t_1 <= 5e+18)
		tmp = 1.0;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+59], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+18], 1.0, N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.99999999999999972e58

   1. Initial program 93.2%

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

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. distribute-neg-in N/A

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

      18. unsub-neg N/A

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

      19. mul-1-neg N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 56.0

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

   5. Simplified 56.0%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 26.1

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

   8. Simplified 26.1%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 26.1

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

   11. Simplified 26.1%

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

   if -9.99999999999999972e58 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5e18

   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. Simplified 96.5%

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

   if 5e18 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. unsub-neg N/A

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

      15. mul-1-neg N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 56.1

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

   5. Simplified 56.1%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 56.1

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

   8. Simplified 56.1%

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

   9. Taylor expanded in t around 0

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

       1. lower-/.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 24.1

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

   11. Simplified 24.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{y \cdot t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 t))))
   (if (<= t_1 -1e+59) t_2 (if (<= t_1 1e+18) 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 * t);
	double tmp;
	if (t_1 <= -1e+59) {
		tmp = t_2;
	} else if (t_1 <= 1e+18) {
		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 * t)
    if (t_1 <= (-1d+59)) then
        tmp = t_2
    else if (t_1 <= 1d+18) 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 * t);
	double tmp;
	if (t_1 <= -1e+59) {
		tmp = t_2;
	} else if (t_1 <= 1e+18) {
		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 * t)
	tmp = 0
	if t_1 <= -1e+59:
		tmp = t_2
	elif t_1 <= 1e+18:
		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(y * t))
	tmp = 0.0
	if (t_1 <= -1e+59)
		tmp = t_2;
	elseif (t_1 <= 1e+18)
		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 * t);
	tmp = 0.0;
	if (t_1 <= -1e+59)
		tmp = t_2;
	elseif (t_1 <= 1e+18)
		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[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+59], t$95$2, If[LessEqual[t$95$1, 1e+18], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.99999999999999972e58 or 1e18 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 90.0%

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

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. lower--.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. lower-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. distribute-neg-in N/A

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

      18. unsub-neg N/A

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

      19. mul-1-neg N/A

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

      20. remove-double-neg N/A

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

      21. lower--.f64 55.7

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

   5. Simplified 55.7%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 25.4

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

   8. Simplified 25.4%

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

   9. Taylor expanded in x around inf

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 25.4

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

   11. Simplified 25.4%

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

   if -9.99999999999999972e58 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 1e18

   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. Simplified 97.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 97.4%

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

   1. lift--.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. remove-double-neg N/A

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

   5. remove-double-neg N/A

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

   6. lift-*.f64 N/A

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

   7. associate-/r* N/A

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

   8. lower-/.f64 N/A

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

   9. lower-/.f64 98.1

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

4. Applied egg-rr 98.1%

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

5. Final simplification 98.1%

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

Alternative 12: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + (x / ((y - z) * (t - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

3. Final simplification 97.4%

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

Alternative 13: 74.8% 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 97.4%

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

3. Taylor expanded in x around 0

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

5. Simplified 72.3%

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

Reproduce

herbie shell --seed 2024207 
(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)))))