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

Percentage Accurate: 88.8% → 96.9%

Time: 16.7s

Alternatives: 22

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = x / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (x / (t - z)) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

   1. associate-/l/ 96.1%

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

3. Simplified 96.1%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 78.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{z \cdot \left(z - t\right)}\\ t_3 := \frac{\frac{x}{t}}{y - z}\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-110}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-206} \lor \neg \left(y \leq -6.2 \cdot 10^{-234}\right) \land y \leq 7.8 \cdot 10^{-120}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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) z))
        (t_2 (/ x (* z (- z t))))
        (t_3 (/ (/ x t) (- y z))))
   (if (<= y -1.52e+190)
     (/ (/ x y) (- t z))
     (if (<= y -3e+17)
       (/ x (* (- t z) y))
       (if (<= y -7.2e-9)
         t_2
         (if (<= y -2.05e-50)
           (/ (/ x (- t z)) y)
           (if (<= y -5.4e-62)
             t_1
             (if (<= y -4.3e-110)
               t_3
               (if (<= y -5.6e-140)
                 t_2
                 (if (<= y -1.7e-174)
                   t_1
                   (if (or (<= y -9.8e-206)
                           (and (not (<= y -6.2e-234)) (<= y 7.8e-120)))
                     t_2
                     t_3)))))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = x / (z * (z - t));
	double t_3 = (x / t) / (y - z);
	double tmp;
	if (y <= -1.52e+190) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3e+17) {
		tmp = x / ((t - z) * y);
	} else if (y <= -7.2e-9) {
		tmp = t_2;
	} else if (y <= -2.05e-50) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -5.4e-62) {
		tmp = t_1;
	} else if (y <= -4.3e-110) {
		tmp = t_3;
	} else if (y <= -5.6e-140) {
		tmp = t_2;
	} else if (y <= -1.7e-174) {
		tmp = t_1;
	} else if ((y <= -9.8e-206) || (!(y <= -6.2e-234) && (y <= 7.8e-120))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (z * (z - t))
    t_3 = (x / t) / (y - z)
    if (y <= (-1.52d+190)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-3d+17)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-7.2d-9)) then
        tmp = t_2
    else if (y <= (-2.05d-50)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-5.4d-62)) then
        tmp = t_1
    else if (y <= (-4.3d-110)) then
        tmp = t_3
    else if (y <= (-5.6d-140)) then
        tmp = t_2
    else if (y <= (-1.7d-174)) then
        tmp = t_1
    else if ((y <= (-9.8d-206)) .or. (.not. (y <= (-6.2d-234))) .and. (y <= 7.8d-120)) then
        tmp = t_2
    else
        tmp = t_3
    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) / z;
	double t_2 = x / (z * (z - t));
	double t_3 = (x / t) / (y - z);
	double tmp;
	if (y <= -1.52e+190) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3e+17) {
		tmp = x / ((t - z) * y);
	} else if (y <= -7.2e-9) {
		tmp = t_2;
	} else if (y <= -2.05e-50) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -5.4e-62) {
		tmp = t_1;
	} else if (y <= -4.3e-110) {
		tmp = t_3;
	} else if (y <= -5.6e-140) {
		tmp = t_2;
	} else if (y <= -1.7e-174) {
		tmp = t_1;
	} else if ((y <= -9.8e-206) || (!(y <= -6.2e-234) && (y <= 7.8e-120))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = x / (z * (z - t))
	t_3 = (x / t) / (y - z)
	tmp = 0
	if y <= -1.52e+190:
		tmp = (x / y) / (t - z)
	elif y <= -3e+17:
		tmp = x / ((t - z) * y)
	elif y <= -7.2e-9:
		tmp = t_2
	elif y <= -2.05e-50:
		tmp = (x / (t - z)) / y
	elif y <= -5.4e-62:
		tmp = t_1
	elif y <= -4.3e-110:
		tmp = t_3
	elif y <= -5.6e-140:
		tmp = t_2
	elif y <= -1.7e-174:
		tmp = t_1
	elif (y <= -9.8e-206) or (not (y <= -6.2e-234) and (y <= 7.8e-120)):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	t_2 = Float64(x / Float64(z * Float64(z - t)))
	t_3 = Float64(Float64(x / t) / Float64(y - z))
	tmp = 0.0
	if (y <= -1.52e+190)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -3e+17)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -7.2e-9)
		tmp = t_2;
	elseif (y <= -2.05e-50)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -5.4e-62)
		tmp = t_1;
	elseif (y <= -4.3e-110)
		tmp = t_3;
	elseif (y <= -5.6e-140)
		tmp = t_2;
	elseif (y <= -1.7e-174)
		tmp = t_1;
	elseif ((y <= -9.8e-206) || (!(y <= -6.2e-234) && (y <= 7.8e-120)))
		tmp = t_2;
	else
		tmp = t_3;
	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) / z;
	t_2 = x / (z * (z - t));
	t_3 = (x / t) / (y - z);
	tmp = 0.0;
	if (y <= -1.52e+190)
		tmp = (x / y) / (t - z);
	elseif (y <= -3e+17)
		tmp = x / ((t - z) * y);
	elseif (y <= -7.2e-9)
		tmp = t_2;
	elseif (y <= -2.05e-50)
		tmp = (x / (t - z)) / y;
	elseif (y <= -5.4e-62)
		tmp = t_1;
	elseif (y <= -4.3e-110)
		tmp = t_3;
	elseif (y <= -5.6e-140)
		tmp = t_2;
	elseif (y <= -1.7e-174)
		tmp = t_1;
	elseif ((y <= -9.8e-206) || (~((y <= -6.2e-234)) && (y <= 7.8e-120)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.52e+190], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+17], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-9], t$95$2, If[LessEqual[y, -2.05e-50], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -5.4e-62], t$95$1, If[LessEqual[y, -4.3e-110], t$95$3, If[LessEqual[y, -5.6e-140], t$95$2, If[LessEqual[y, -1.7e-174], t$95$1, If[Or[LessEqual[y, -9.8e-206], And[N[Not[LessEqual[y, -6.2e-234]], $MachinePrecision], LessEqual[y, 7.8e-120]]], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.5199999999999999e190

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 83.3%

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

      1. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

   if -1.5199999999999999e190 < y < -3e17

   1. Initial program 82.1%

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

   3. Taylor expanded in y around inf 81.4%

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

      1. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   if -3e17 < y < -7.2e-9 or -4.30000000000000025e-110 < y < -5.6000000000000005e-140 or -1.7000000000000001e-174 < y < -9.7999999999999999e-206 or -6.2000000000000003e-234 < y < 7.8000000000000003e-120

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

   5. Simplified 82.3%

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

   if -7.2e-9 < y < -2.04999999999999993e-50

   1. Initial program 98.8%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 99.8%

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

      2. div-inv 99.8%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.5%

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

      6. *-un-lft-identity 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 68.3%

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

      1. associate-/l/ 68.6%

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

   9. Simplified 68.6%

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

   if -2.04999999999999993e-50 < y < -5.40000000000000039e-62 or -5.6000000000000005e-140 < y < -1.7000000000000001e-174

   1. Initial program 75.7%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. associate-*l/ 99.8%

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

      2. div-inv 99.8%

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

      3. div-inv 99.6%

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

      4. clear-num 99.8%

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

      5. associate-*l/ 100.0%

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

      6. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 63.2%

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

      1. associate-*r/ 63.2%

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

      2. times-frac 87.1%

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

      3. associate-*l/ 87.3%

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

      4. mul-1-neg 87.3%

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

   9. Simplified 87.3%

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

   10. Taylor expanded in t around 0 99.8%

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

       1. associate-*r/ 87.3%

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

       2. neg-mul-1 87.3%

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

   12. Simplified 99.8%

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

       1. distribute-neg-frac2 99.8%

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

       2. frac-2neg 99.8%

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

       3. div-inv 99.8%

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

       4. associate-/l* 83.4%

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

   14. Applied egg-rr 83.4%

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

       1. associate-*r/ 99.8%

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

       2. div-inv 99.8%

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

   16. Applied egg-rr 99.8%

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

   if -5.40000000000000039e-62 < y < -4.30000000000000025e-110 or -9.7999999999999999e-206 < y < -6.2000000000000003e-234 or 7.8000000000000003e-120 < y

   1. Initial program 92.6%

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

      1. associate-/l/ 95.6%

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

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 61.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-206} \lor \neg \left(y \leq -6.2 \cdot 10^{-234}\right) \land y \leq 7.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{-z}}{t}\\ t_2 := \frac{\frac{1}{z}}{\frac{z}{x}}\\ t_3 := \frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-221}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \end{array} \]

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 (- z)) t))
        (t_2 (/ (/ 1.0 z) (/ z x)))
        (t_3 (/ x (* (- t z) y))))
   (if (<= z -2.85e+144)
     t_2
     (if (<= z -1.1e+83)
       t_1
       (if (<= z -2.2e+41)
         t_2
         (if (<= z -4.2e-221)
           t_3
           (if (<= z 2e-59)
             (/ x (* t (- y z)))
             (if (<= z 3.1e+18)
               t_3
               (if (<= z 4.8e+45)
                 (/ (/ x z) z)
                 (if (<= z 1.75e+47) t_1 (* x (/ (/ 1.0 z) z))))))))))))

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 / z) / (z / x);
	double t_3 = x / ((t - z) * y);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_2;
	} else if (z <= -1.1e+83) {
		tmp = t_1;
	} else if (z <= -2.2e+41) {
		tmp = t_2;
	} else if (z <= -4.2e-221) {
		tmp = t_3;
	} else if (z <= 2e-59) {
		tmp = x / (t * (y - z));
	} else if (z <= 3.1e+18) {
		tmp = t_3;
	} else if (z <= 4.8e+45) {
		tmp = (x / z) / z;
	} else if (z <= 1.75e+47) {
		tmp = t_1;
	} else {
		tmp = x * ((1.0 / z) / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x / -z) / t
    t_2 = (1.0d0 / z) / (z / x)
    t_3 = x / ((t - z) * y)
    if (z <= (-2.85d+144)) then
        tmp = t_2
    else if (z <= (-1.1d+83)) then
        tmp = t_1
    else if (z <= (-2.2d+41)) then
        tmp = t_2
    else if (z <= (-4.2d-221)) then
        tmp = t_3
    else if (z <= 2d-59) then
        tmp = x / (t * (y - z))
    else if (z <= 3.1d+18) then
        tmp = t_3
    else if (z <= 4.8d+45) then
        tmp = (x / z) / z
    else if (z <= 1.75d+47) then
        tmp = t_1
    else
        tmp = x * ((1.0d0 / z) / 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 / -z) / t;
	double t_2 = (1.0 / z) / (z / x);
	double t_3 = x / ((t - z) * y);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_2;
	} else if (z <= -1.1e+83) {
		tmp = t_1;
	} else if (z <= -2.2e+41) {
		tmp = t_2;
	} else if (z <= -4.2e-221) {
		tmp = t_3;
	} else if (z <= 2e-59) {
		tmp = x / (t * (y - z));
	} else if (z <= 3.1e+18) {
		tmp = t_3;
	} else if (z <= 4.8e+45) {
		tmp = (x / z) / z;
	} else if (z <= 1.75e+47) {
		tmp = t_1;
	} else {
		tmp = x * ((1.0 / z) / z);
	}
	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 / z) / (z / x)
	t_3 = x / ((t - z) * y)
	tmp = 0
	if z <= -2.85e+144:
		tmp = t_2
	elif z <= -1.1e+83:
		tmp = t_1
	elif z <= -2.2e+41:
		tmp = t_2
	elif z <= -4.2e-221:
		tmp = t_3
	elif z <= 2e-59:
		tmp = x / (t * (y - z))
	elif z <= 3.1e+18:
		tmp = t_3
	elif z <= 4.8e+45:
		tmp = (x / z) / z
	elif z <= 1.75e+47:
		tmp = t_1
	else:
		tmp = x * ((1.0 / z) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(-z)) / t)
	t_2 = Float64(Float64(1.0 / z) / Float64(z / x))
	t_3 = Float64(x / Float64(Float64(t - z) * y))
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = t_2;
	elseif (z <= -1.1e+83)
		tmp = t_1;
	elseif (z <= -2.2e+41)
		tmp = t_2;
	elseif (z <= -4.2e-221)
		tmp = t_3;
	elseif (z <= 2e-59)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 3.1e+18)
		tmp = t_3;
	elseif (z <= 4.8e+45)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 1.75e+47)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(1.0 / z) / 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 / -z) / t;
	t_2 = (1.0 / z) / (z / x);
	t_3 = x / ((t - z) * y);
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = t_2;
	elseif (z <= -1.1e+83)
		tmp = t_1;
	elseif (z <= -2.2e+41)
		tmp = t_2;
	elseif (z <= -4.2e-221)
		tmp = t_3;
	elseif (z <= 2e-59)
		tmp = x / (t * (y - z));
	elseif (z <= 3.1e+18)
		tmp = t_3;
	elseif (z <= 4.8e+45)
		tmp = (x / z) / z;
	elseif (z <= 1.75e+47)
		tmp = t_1;
	else
		tmp = x * ((1.0 / z) / 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[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / z), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+144], t$95$2, If[LessEqual[z, -1.1e+83], t$95$1, If[LessEqual[z, -2.2e+41], t$95$2, If[LessEqual[z, -4.2e-221], t$95$3, If[LessEqual[z, 2e-59], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+18], t$95$3, If[LessEqual[z, 4.8e+45], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.75e+47], t$95$1, N[(x * N[(N[(1.0 / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.85000000000000002e144 or -1.09999999999999999e83 < z < -2.1999999999999999e41

   1. Initial program 87.5%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.8%

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

      2. div-inv 99.8%

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

      3. div-inv 99.8%

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

      4. clear-num 99.9%

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

      5. associate-*l/ 99.8%

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

      6. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. times-frac 96.4%

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

      3. associate-*l/ 96.3%

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

      4. mul-1-neg 96.3%

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

   9. Simplified 96.3%

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

   10. Taylor expanded in t around 0 88.2%

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

       1. associate-*r/ 91.7%

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

       2. neg-mul-1 91.7%

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

   12. Simplified 88.2%

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

       1. distribute-neg-frac2 88.2%

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

       2. frac-2neg 88.2%

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

       3. div-inv 88.2%

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

       4. associate-/l* 82.1%

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

   14. Applied egg-rr 82.1%

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

       1. associate-*r/ 88.2%

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

       2. associate-*l/ 88.2%

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

       3. clear-num 88.3%

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

       4. associate-*l/ 88.3%

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

       5. *-un-lft-identity 88.3%

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

   16. Applied egg-rr 88.3%

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

   if -2.85000000000000002e144 < z < -1.09999999999999999e83 or 4.79999999999999979e45 < z < 1.75000000000000008e47

   1. Initial program 79.3%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 59.0%

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

   6. Taylor expanded in y around 0 32.0%

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

      1. associate-*r/ 32.0%

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

      2. neg-mul-1 32.0%

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

   8. Simplified 32.0%

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

   9. Taylor expanded in x around 0 32.0%

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

       1. associate-*r/ 32.0%

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

       2. times-frac 45.6%

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

       3. associate-*l/ 45.7%

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

       4. mul-1-neg 45.7%

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

       5. distribute-frac-neg 45.7%

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

   11. Simplified 45.7%

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

   if -2.1999999999999999e41 < z < -4.2e-221 or 2.0000000000000001e-59 < z < 3.1e18

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   if -4.2e-221 < z < 2.0000000000000001e-59

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 79.4%

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

   if 3.1e18 < z < 4.79999999999999979e45

   1. Initial program 88.0%

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

      1. associate-/l/ 99.6%

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

      2. div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. associate-*l/ 99.6%

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

      2. div-inv 99.6%

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

      3. div-inv 99.2%

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

      4. clear-num 99.4%

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

      5. associate-*l/ 99.6%

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

      6. *-un-lft-identity 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. times-frac 63.3%

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

      3. associate-*l/ 63.5%

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

      4. mul-1-neg 63.5%

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

   9. Simplified 63.5%

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

   10. Taylor expanded in t around 0 63.2%

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

       1. associate-*r/ 87.6%

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

       2. neg-mul-1 87.6%

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

   12. Simplified 63.2%

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

       1. distribute-neg-frac2 63.2%

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

       2. frac-2neg 63.2%

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

       3. div-inv 63.2%

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

       4. associate-/l* 63.2%

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

   14. Applied egg-rr 63.2%

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

       1. associate-*r/ 63.2%

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

       2. div-inv 63.2%

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

   16. Applied egg-rr 63.2%

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

   if 1.75000000000000008e47 < z

   1. Initial program 89.3%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 99.8%

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

      2. div-inv 99.8%

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

      3. div-inv 99.8%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.8%

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

      6. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 86.4%

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

      1. associate-*r/ 86.4%

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

      2. times-frac 95.4%

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

      3. associate-*l/ 95.4%

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

      4. mul-1-neg 95.4%

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

   9. Simplified 95.4%

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

   10. Taylor expanded in t around 0 80.8%

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

       1. associate-*r/ 85.8%

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

       2. neg-mul-1 85.8%

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

   12. Simplified 80.8%

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

       1. distribute-neg-frac2 80.8%

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

       2. frac-2neg 80.8%

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

       3. div-inv 80.9%

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

       4. associate-/l* 82.8%

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

   14. Applied egg-rr 82.8%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-221}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{-z}}{t}\\ t_2 := \frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \end{array} \]

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 (- z)) t)) (t_2 (/ x (* (- t z) y))))
   (if (<= z -2.85e+144)
     (* (/ x z) (/ 1.0 z))
     (if (<= z -3.2e+83)
       t_1
       (if (<= z -1.65e+41)
         (/ x (* z z))
         (if (<= z -2.8e-221)
           t_2
           (if (<= z 3.6e-59)
             (/ x (* t (- y z)))
             (if (<= z 2.7e+16)
               t_2
               (if (<= z 1.02e+46)
                 (/ (/ x z) z)
                 (if (<= z 4.5e+47) t_1 (* x (/ (/ 1.0 z) z))))))))))))

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 = x / ((t - z) * y);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -3.2e+83) {
		tmp = t_1;
	} else if (z <= -1.65e+41) {
		tmp = x / (z * z);
	} else if (z <= -2.8e-221) {
		tmp = t_2;
	} else if (z <= 3.6e-59) {
		tmp = x / (t * (y - z));
	} else if (z <= 2.7e+16) {
		tmp = t_2;
	} else if (z <= 1.02e+46) {
		tmp = (x / z) / z;
	} else if (z <= 4.5e+47) {
		tmp = t_1;
	} else {
		tmp = x * ((1.0 / z) / 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) :: t_2
    real(8) :: tmp
    t_1 = (x / -z) / t
    t_2 = x / ((t - z) * y)
    if (z <= (-2.85d+144)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= (-3.2d+83)) then
        tmp = t_1
    else if (z <= (-1.65d+41)) then
        tmp = x / (z * z)
    else if (z <= (-2.8d-221)) then
        tmp = t_2
    else if (z <= 3.6d-59) then
        tmp = x / (t * (y - z))
    else if (z <= 2.7d+16) then
        tmp = t_2
    else if (z <= 1.02d+46) then
        tmp = (x / z) / z
    else if (z <= 4.5d+47) then
        tmp = t_1
    else
        tmp = x * ((1.0d0 / z) / 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 / -z) / t;
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -3.2e+83) {
		tmp = t_1;
	} else if (z <= -1.65e+41) {
		tmp = x / (z * z);
	} else if (z <= -2.8e-221) {
		tmp = t_2;
	} else if (z <= 3.6e-59) {
		tmp = x / (t * (y - z));
	} else if (z <= 2.7e+16) {
		tmp = t_2;
	} else if (z <= 1.02e+46) {
		tmp = (x / z) / z;
	} else if (z <= 4.5e+47) {
		tmp = t_1;
	} else {
		tmp = x * ((1.0 / z) / z);
	}
	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 = x / ((t - z) * y)
	tmp = 0
	if z <= -2.85e+144:
		tmp = (x / z) * (1.0 / z)
	elif z <= -3.2e+83:
		tmp = t_1
	elif z <= -1.65e+41:
		tmp = x / (z * z)
	elif z <= -2.8e-221:
		tmp = t_2
	elif z <= 3.6e-59:
		tmp = x / (t * (y - z))
	elif z <= 2.7e+16:
		tmp = t_2
	elif z <= 1.02e+46:
		tmp = (x / z) / z
	elif z <= 4.5e+47:
		tmp = t_1
	else:
		tmp = x * ((1.0 / z) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(-z)) / t)
	t_2 = Float64(x / Float64(Float64(t - z) * y))
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= -3.2e+83)
		tmp = t_1;
	elseif (z <= -1.65e+41)
		tmp = Float64(x / Float64(z * z));
	elseif (z <= -2.8e-221)
		tmp = t_2;
	elseif (z <= 3.6e-59)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 2.7e+16)
		tmp = t_2;
	elseif (z <= 1.02e+46)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 4.5e+47)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(1.0 / z) / 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 / -z) / t;
	t_2 = x / ((t - z) * y);
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= -3.2e+83)
		tmp = t_1;
	elseif (z <= -1.65e+41)
		tmp = x / (z * z);
	elseif (z <= -2.8e-221)
		tmp = t_2;
	elseif (z <= 3.6e-59)
		tmp = x / (t * (y - z));
	elseif (z <= 2.7e+16)
		tmp = t_2;
	elseif (z <= 1.02e+46)
		tmp = (x / z) / z;
	elseif (z <= 4.5e+47)
		tmp = t_1;
	else
		tmp = x * ((1.0 / z) / 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[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+144], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e+83], t$95$1, If[LessEqual[z, -1.65e+41], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-221], t$95$2, If[LessEqual[z, 3.6e-59], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+16], t$95$2, If[LessEqual[z, 1.02e+46], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.5e+47], t$95$1, N[(x * N[(N[(1.0 / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.85000000000000002e144

   1. Initial program 83.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. associate-*l/ 99.9%

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

      2. div-inv 99.9%

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

      3. div-inv 100.0%

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

      4. clear-num 99.9%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. times-frac 98.4%

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

      3. associate-*l/ 98.4%

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

      4. mul-1-neg 98.4%

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

   9. Simplified 98.4%

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

   10. Taylor expanded in t around 0 94.9%

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

       1. associate-*r/ 96.5%

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

       2. neg-mul-1 96.5%

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

   12. Simplified 94.9%

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

       1. div-inv 95.0%

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

       2. distribute-neg-frac2 95.0%

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

       3. frac-2neg 95.0%

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

   14. Applied egg-rr 95.0%

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

   if -2.85000000000000002e144 < z < -3.1999999999999999e83 or 1.0199999999999999e46 < z < 4.49999999999999979e47

   1. Initial program 79.3%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 59.0%

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

   6. Taylor expanded in y around 0 32.0%

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

      1. associate-*r/ 32.0%

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

      2. neg-mul-1 32.0%

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

   8. Simplified 32.0%

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

   9. Taylor expanded in x around 0 32.0%

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

       1. associate-*r/ 32.0%

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

       2. times-frac 45.6%

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

       3. associate-*l/ 45.7%

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

       4. mul-1-neg 45.7%

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

       5. distribute-frac-neg 45.7%

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

   11. Simplified 45.7%

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

   if -3.1999999999999999e83 < z < -1.65e41

   1. Initial program 99.7%

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

      1. associate-/l/ 99.3%

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

      2. div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. associate-*l/ 99.7%

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

      2. div-inv 99.3%

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

      3. div-inv 99.3%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.5%

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

      6. *-un-lft-identity 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around 0 89.7%

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

      1. associate-*r/ 89.7%

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

      2. times-frac 89.7%

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

      3. associate-*l/ 89.5%

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

      4. mul-1-neg 89.5%

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

   9. Simplified 89.5%

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

   10. Taylor expanded in t around 0 66.4%

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

       1. associate-*r/ 76.2%

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

       2. neg-mul-1 76.2%

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

   12. Simplified 66.4%

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

       1. distribute-neg-frac2 66.4%

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

       2. frac-2neg 66.4%

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

       3. div-inv 66.8%

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

       4. associate-/l* 66.6%

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

   14. Applied egg-rr 66.6%

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

       1. associate-*r/ 66.8%

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

       2. associate-*l/ 66.6%

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

       3. *-commutative 66.6%

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

       4. frac-2neg 66.6%

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

       5. metadata-eval 66.6%

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

       6. frac-2neg 66.6%

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

       7. frac-times 66.8%

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

       8. neg-mul-1 66.8%

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

       9. remove-double-neg 66.8%

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

   16. Applied egg-rr 66.8%

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

   if -1.65e41 < z < -2.80000000000000019e-221 or 3.6e-59 < z < 2.7e16

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   if -2.80000000000000019e-221 < z < 3.6e-59

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 79.4%

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

   if 2.7e16 < z < 1.0199999999999999e46

   1. Initial program 88.0%

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

      1. associate-/l/ 99.6%

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

      2. div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

      1. associate-*l/ 99.6%

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

      2. div-inv 99.6%

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

      3. div-inv 99.2%

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

      4. clear-num 99.4%

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

      5. associate-*l/ 99.6%

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

      6. *-un-lft-identity 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. times-frac 63.3%

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

      3. associate-*l/ 63.5%

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

      4. mul-1-neg 63.5%

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

   9. Simplified 63.5%

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

   10. Taylor expanded in t around 0 63.2%

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

       1. associate-*r/ 87.6%

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

       2. neg-mul-1 87.6%

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

   12. Simplified 63.2%

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

       1. distribute-neg-frac2 63.2%

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

       2. frac-2neg 63.2%

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

       3. div-inv 63.2%

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

       4. associate-/l* 63.2%

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

   14. Applied egg-rr 63.2%

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

       1. associate-*r/ 63.2%

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

       2. div-inv 63.2%

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

   16. Applied egg-rr 63.2%

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

   if 4.49999999999999979e47 < z

   1. Initial program 89.3%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 99.8%

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

      2. div-inv 99.8%

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

      3. div-inv 99.8%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.8%

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

      6. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 86.4%

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

      1. associate-*r/ 86.4%

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

      2. times-frac 95.4%

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

      3. associate-*l/ 95.4%

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

      4. mul-1-neg 95.4%

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

   9. Simplified 95.4%

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

   10. Taylor expanded in t around 0 80.8%

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

       1. associate-*r/ 85.8%

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

       2. neg-mul-1 85.8%

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

   12. Simplified 80.8%

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

       1. distribute-neg-frac2 80.8%

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

       2. frac-2neg 80.8%

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

       3. div-inv 80.9%

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

       4. associate-/l* 82.8%

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

   14. Applied egg-rr 82.8%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-221}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z - t}}{z}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-51}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-106} \lor \neg \left(y \leq 2.75 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) z)))
   (if (<= y -2e+190)
     (/ (/ x y) (- t z))
     (if (<= y -5.5e+21)
       (/ x (* (- t z) y))
       (if (<= y -5.2e-9)
         t_1
         (if (<= y -2.7e-51)
           (/ (/ x (- t z)) y)
           (if (<= y -1.7e-65)
             (/ (/ x z) z)
             (if (or (<= y -1e-106) (not (<= y 2.75e-157)))
               (/ (/ x t) (- y z))
               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)) / z;
	double tmp;
	if (y <= -2e+190) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5.5e+21) {
		tmp = x / ((t - z) * y);
	} else if (y <= -5.2e-9) {
		tmp = t_1;
	} else if (y <= -2.7e-51) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.7e-65) {
		tmp = (x / z) / z;
	} else if ((y <= -1e-106) || !(y <= 2.75e-157)) {
		tmp = (x / t) / (y - z);
	} 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) :: tmp
    t_1 = (x / (z - t)) / z
    if (y <= (-2d+190)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-5.5d+21)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-5.2d-9)) then
        tmp = t_1
    else if (y <= (-2.7d-51)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-1.7d-65)) then
        tmp = (x / z) / z
    else if ((y <= (-1d-106)) .or. (.not. (y <= 2.75d-157))) then
        tmp = (x / t) / (y - z)
    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)) / z;
	double tmp;
	if (y <= -2e+190) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5.5e+21) {
		tmp = x / ((t - z) * y);
	} else if (y <= -5.2e-9) {
		tmp = t_1;
	} else if (y <= -2.7e-51) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.7e-65) {
		tmp = (x / z) / z;
	} else if ((y <= -1e-106) || !(y <= 2.75e-157)) {
		tmp = (x / t) / (y - z);
	} 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)) / z
	tmp = 0
	if y <= -2e+190:
		tmp = (x / y) / (t - z)
	elif y <= -5.5e+21:
		tmp = x / ((t - z) * y)
	elif y <= -5.2e-9:
		tmp = t_1
	elif y <= -2.7e-51:
		tmp = (x / (t - z)) / y
	elif y <= -1.7e-65:
		tmp = (x / z) / z
	elif (y <= -1e-106) or not (y <= 2.75e-157):
		tmp = (x / t) / (y - z)
	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(Float64(x / Float64(z - t)) / z)
	tmp = 0.0
	if (y <= -2e+190)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -5.5e+21)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -5.2e-9)
		tmp = t_1;
	elseif (y <= -2.7e-51)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -1.7e-65)
		tmp = Float64(Float64(x / z) / z);
	elseif ((y <= -1e-106) || !(y <= 2.75e-157))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	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)) / z;
	tmp = 0.0;
	if (y <= -2e+190)
		tmp = (x / y) / (t - z);
	elseif (y <= -5.5e+21)
		tmp = x / ((t - z) * y);
	elseif (y <= -5.2e-9)
		tmp = t_1;
	elseif (y <= -2.7e-51)
		tmp = (x / (t - z)) / y;
	elseif (y <= -1.7e-65)
		tmp = (x / z) / z;
	elseif ((y <= -1e-106) || ~((y <= 2.75e-157)))
		tmp = (x / t) / (y - z);
	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[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -2e+190], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e+21], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-9], t$95$1, If[LessEqual[y, -2.7e-51], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.7e-65], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[y, -1e-106], N[Not[LessEqual[y, 2.75e-157]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.0000000000000001e190

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 83.3%

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

      1. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

   if -2.0000000000000001e190 < y < -5.5e21

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   if -5.5e21 < y < -5.2000000000000002e-9 or -9.99999999999999941e-107 < y < 2.7499999999999999e-157

   1. Initial program 91.6%

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

      1. associate-/l/ 95.7%

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

      2. div-inv 95.6%

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

   4. Applied egg-rr 95.6%

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

      1. associate-*l/ 95.4%

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

      2. div-inv 95.6%

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

      3. div-inv 95.5%

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

      4. clear-num 95.4%

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

      5. associate-*l/ 95.4%

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

      6. *-un-lft-identity 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in y around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. times-frac 80.8%

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

      3. associate-*l/ 80.9%

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

      4. mul-1-neg 80.9%

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

   9. Simplified 80.9%

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

   if -5.2000000000000002e-9 < y < -2.6999999999999997e-51

   1. Initial program 98.8%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 99.8%

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

      2. div-inv 99.8%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.5%

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

      6. *-un-lft-identity 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 68.3%

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

      1. associate-/l/ 68.6%

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

   9. Simplified 68.6%

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

   if -2.6999999999999997e-51 < y < -1.69999999999999993e-65

   1. Initial program 99.5%

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

      1. associate-/l/ 99.5%

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

      2. div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. associate-*l/ 99.5%

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

      2. div-inv 99.5%

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

      3. div-inv 99.5%

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

      4. clear-num 100.0%

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

      5. associate-*l/ 100.0%

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

      6. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 99.5%

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

      1. associate-*r/ 99.5%

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

      2. times-frac 99.5%

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

      3. associate-*l/ 99.5%

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

      4. mul-1-neg 99.5%

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

   9. Simplified 99.5%

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

   10. Taylor expanded in t around 0 99.5%

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

       1. associate-*r/ 99.5%

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

       2. neg-mul-1 99.5%

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

   12. Simplified 99.5%

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

       1. distribute-neg-frac2 99.5%

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

       2. frac-2neg 99.5%

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

       3. div-inv 99.5%

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

       4. associate-/l* 99.5%

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

   14. Applied egg-rr 99.5%

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

       1. associate-*r/ 99.5%

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

       2. div-inv 99.5%

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

   16. Applied egg-rr 99.5%

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

   if -1.69999999999999993e-65 < y < -9.99999999999999941e-107 or 2.7499999999999999e-157 < y

   1. Initial program 94.8%

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

      1. associate-/l/ 95.7%

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

   3. Simplified 95.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 58.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-51}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-106} \lor \neg \left(y \leq 2.75 \cdot 10^{-157}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+171} \lor \neg \left(z \leq 7.2 \cdot 10^{+213}\right) \land z \leq 3.6 \cdot 10^{+217}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.85e+144)
   (* (/ x z) (/ 1.0 z))
   (if (<= z -1.12e+78)
     (/ (/ x (- z)) t)
     (if (<= z -4.7e-42)
       (/ -1.0 (* y (/ z x)))
       (if (<= z 2.9e-48)
         (/ (/ x t) y)
         (if (or (<= z 3.6e+171) (and (not (<= z 7.2e+213)) (<= z 3.6e+217)))
           (/ (/ x z) z)
           (* x (/ (/ 1.0 z) z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.85e+144) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -1.12e+78) {
		tmp = (x / -z) / t;
	} else if (z <= -4.7e-42) {
		tmp = -1.0 / (y * (z / x));
	} else if (z <= 2.9e-48) {
		tmp = (x / t) / y;
	} else if ((z <= 3.6e+171) || (!(z <= 7.2e+213) && (z <= 3.6e+217))) {
		tmp = (x / z) / z;
	} else {
		tmp = x * ((1.0 / z) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.85d+144)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= (-1.12d+78)) then
        tmp = (x / -z) / t
    else if (z <= (-4.7d-42)) then
        tmp = (-1.0d0) / (y * (z / x))
    else if (z <= 2.9d-48) then
        tmp = (x / t) / y
    else if ((z <= 3.6d+171) .or. (.not. (z <= 7.2d+213)) .and. (z <= 3.6d+217)) then
        tmp = (x / z) / z
    else
        tmp = x * ((1.0d0 / z) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.85e+144) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= -1.12e+78) {
		tmp = (x / -z) / t;
	} else if (z <= -4.7e-42) {
		tmp = -1.0 / (y * (z / x));
	} else if (z <= 2.9e-48) {
		tmp = (x / t) / y;
	} else if ((z <= 3.6e+171) || (!(z <= 7.2e+213) && (z <= 3.6e+217))) {
		tmp = (x / z) / z;
	} else {
		tmp = x * ((1.0 / z) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.85e+144:
		tmp = (x / z) * (1.0 / z)
	elif z <= -1.12e+78:
		tmp = (x / -z) / t
	elif z <= -4.7e-42:
		tmp = -1.0 / (y * (z / x))
	elif z <= 2.9e-48:
		tmp = (x / t) / y
	elif (z <= 3.6e+171) or (not (z <= 7.2e+213) and (z <= 3.6e+217)):
		tmp = (x / z) / z
	else:
		tmp = x * ((1.0 / z) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= -1.12e+78)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif (z <= -4.7e-42)
		tmp = Float64(-1.0 / Float64(y * Float64(z / x)));
	elseif (z <= 2.9e-48)
		tmp = Float64(Float64(x / t) / y);
	elseif ((z <= 3.6e+171) || (!(z <= 7.2e+213) && (z <= 3.6e+217)))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x * Float64(Float64(1.0 / z) / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= -1.12e+78)
		tmp = (x / -z) / t;
	elseif (z <= -4.7e-42)
		tmp = -1.0 / (y * (z / x));
	elseif (z <= 2.9e-48)
		tmp = (x / t) / y;
	elseif ((z <= 3.6e+171) || (~((z <= 7.2e+213)) && (z <= 3.6e+217)))
		tmp = (x / z) / z;
	else
		tmp = x * ((1.0 / z) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.85e+144], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e+78], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -4.7e-42], N[(-1.0 / N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-48], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, 3.6e+171], And[N[Not[LessEqual[z, 7.2e+213]], $MachinePrecision], LessEqual[z, 3.6e+217]]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(1.0 / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.85000000000000002e144

   1. Initial program 83.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. associate-*l/ 99.9%

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

      2. div-inv 99.9%

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

      3. div-inv 100.0%

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

      4. clear-num 99.9%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. times-frac 98.4%

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

      3. associate-*l/ 98.4%

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

      4. mul-1-neg 98.4%

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

   9. Simplified 98.4%

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

   10. Taylor expanded in t around 0 94.9%

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

       1. associate-*r/ 96.5%

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

       2. neg-mul-1 96.5%

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

   12. Simplified 94.9%

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

       1. div-inv 95.0%

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

       2. distribute-neg-frac2 95.0%

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

       3. frac-2neg 95.0%

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

   14. Applied egg-rr 95.0%

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

   if -2.85000000000000002e144 < z < -1.12e78

   1. Initial program 76.0%

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

      1. associate-/l/ 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.3%

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

   6. Taylor expanded in y around 0 28.8%

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

      1. associate-*r/ 28.8%

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

      2. neg-mul-1 28.8%

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

   8. Simplified 28.8%

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

   9. Taylor expanded in x around 0 28.8%

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

       1. associate-*r/ 28.8%

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

       2. times-frac 44.6%

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

       3. associate-*l/ 44.7%

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

       4. mul-1-neg 44.7%

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

       5. distribute-frac-neg 44.7%

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

   11. Simplified 44.7%

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

   if -1.12e78 < z < -4.7000000000000001e-42

   1. Initial program 96.1%

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

      1. associate-/l/ 92.6%

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

      2. div-inv 92.5%

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

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in y around inf 50.4%

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

   6. Taylor expanded in t around 0 35.2%

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

      1. associate-*r/ 65.6%

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

      2. neg-mul-1 65.6%

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

   8. Simplified 35.2%

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

      1. clear-num 38.7%

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

      2. frac-2neg 38.7%

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

      3. metadata-eval 38.7%

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

      4. frac-times 41.9%

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

      5. metadata-eval 41.9%

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

      6. add-sqr-sqrt 22.4%

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

      7. sqrt-unprod 24.7%

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

      8. sqr-neg 24.7%

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

      9. sqrt-unprod 8.2%

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

      10. add-sqr-sqrt 13.8%

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

      11. add-sqr-sqrt 9.2%

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

      12. sqrt-unprod 21.2%

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

      13. sqr-neg 21.2%

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

      14. sqrt-unprod 15.6%

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

      15. add-sqr-sqrt 41.9%

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

   10. Applied egg-rr 41.9%

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

   if -4.7000000000000001e-42 < z < 2.9000000000000003e-48

   1. Initial program 93.6%

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

      1. associate-/l/ 92.4%

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

      2. div-inv 92.4%

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

   4. Applied egg-rr 92.4%

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

      1. associate-*l/ 91.8%

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

      2. div-inv 92.1%

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

      3. div-inv 92.0%

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

      4. clear-num 91.9%

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

      5. associate-*l/ 92.5%

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

      6. *-un-lft-identity 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in z around 0 62.3%

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

      1. associate-/r* 66.0%

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

   9. Simplified 66.0%

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

   if 2.9000000000000003e-48 < z < 3.60000000000000018e171 or 7.2000000000000002e213 < z < 3.6000000000000002e217

   1. Initial program 86.6%

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

      1. associate-/l/ 99.7%

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

      2. div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. associate-*l/ 97.9%

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

      2. div-inv 98.0%

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

      3. div-inv 97.9%

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

      4. clear-num 97.8%

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

      5. associate-*l/ 98.0%

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

      6. *-un-lft-identity 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in y around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. times-frac 80.5%

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

      3. associate-*l/ 80.7%

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

      4. mul-1-neg 80.7%

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

   9. Simplified 80.7%

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

   10. Taylor expanded in t around 0 59.7%

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

       1. associate-*r/ 75.3%

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

       2. neg-mul-1 75.3%

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

   12. Simplified 59.7%

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

       1. distribute-neg-frac2 59.7%

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

       2. frac-2neg 59.7%

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

       3. div-inv 59.7%

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

       4. associate-/l* 57.1%

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

   14. Applied egg-rr 57.1%

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

       1. associate-*r/ 59.7%

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

       2. div-inv 59.7%

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

   16. Applied egg-rr 59.7%

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

   if 3.60000000000000018e171 < z < 7.2000000000000002e213 or 3.6000000000000002e217 < z

   1. Initial program 96.8%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. associate-*l/ 100.0%

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

      2. div-inv 100.0%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. times-frac 97.1%

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

      3. associate-*l/ 97.1%

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

      4. mul-1-neg 97.1%

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

   9. Simplified 97.1%

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

   10. Taylor expanded in t around 0 88.3%

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

       1. associate-*r/ 92.5%

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

       2. neg-mul-1 92.5%

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

   12. Simplified 88.3%

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

       1. distribute-neg-frac2 88.3%

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

       2. frac-2neg 88.3%

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

       3. div-inv 88.3%

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

       4. associate-/l* 96.8%

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

   14. Applied egg-rr 96.8%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+171} \lor \neg \left(z \leq 7.2 \cdot 10^{+213}\right) \land z \leq 3.6 \cdot 10^{+217}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+171} \lor \neg \left(z \leq 2.4 \cdot 10^{+214}\right) \land z \leq 3.6 \cdot 10^{+217}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \end{array} \]

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 z) (/ 1.0 z))))
   (if (<= z -2.85e+144)
     t_1
     (if (<= z -2.15e+84)
       (/ (/ x (- z)) t)
       (if (<= z -7.5e-72)
         t_1
         (if (<= z 5.5e-41)
           (/ (/ x t) y)
           (if (or (<= z 3.6e+171) (and (not (<= z 2.4e+214)) (<= z 3.6e+217)))
             (/ (/ x z) z)
             (* x (/ (/ 1.0 z) z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_1;
	} else if (z <= -2.15e+84) {
		tmp = (x / -z) / t;
	} else if (z <= -7.5e-72) {
		tmp = t_1;
	} else if (z <= 5.5e-41) {
		tmp = (x / t) / y;
	} else if ((z <= 3.6e+171) || (!(z <= 2.4e+214) && (z <= 3.6e+217))) {
		tmp = (x / z) / z;
	} else {
		tmp = x * ((1.0 / z) / 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 / z) * (1.0d0 / z)
    if (z <= (-2.85d+144)) then
        tmp = t_1
    else if (z <= (-2.15d+84)) then
        tmp = (x / -z) / t
    else if (z <= (-7.5d-72)) then
        tmp = t_1
    else if (z <= 5.5d-41) then
        tmp = (x / t) / y
    else if ((z <= 3.6d+171) .or. (.not. (z <= 2.4d+214)) .and. (z <= 3.6d+217)) then
        tmp = (x / z) / z
    else
        tmp = x * ((1.0d0 / z) / 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 / z) * (1.0 / z);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_1;
	} else if (z <= -2.15e+84) {
		tmp = (x / -z) / t;
	} else if (z <= -7.5e-72) {
		tmp = t_1;
	} else if (z <= 5.5e-41) {
		tmp = (x / t) / y;
	} else if ((z <= 3.6e+171) || (!(z <= 2.4e+214) && (z <= 3.6e+217))) {
		tmp = (x / z) / z;
	} else {
		tmp = x * ((1.0 / z) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if z <= -2.85e+144:
		tmp = t_1
	elif z <= -2.15e+84:
		tmp = (x / -z) / t
	elif z <= -7.5e-72:
		tmp = t_1
	elif z <= 5.5e-41:
		tmp = (x / t) / y
	elif (z <= 3.6e+171) or (not (z <= 2.4e+214) and (z <= 3.6e+217)):
		tmp = (x / z) / z
	else:
		tmp = x * ((1.0 / z) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = t_1;
	elseif (z <= -2.15e+84)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif (z <= -7.5e-72)
		tmp = t_1;
	elseif (z <= 5.5e-41)
		tmp = Float64(Float64(x / t) / y);
	elseif ((z <= 3.6e+171) || (!(z <= 2.4e+214) && (z <= 3.6e+217)))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x * Float64(Float64(1.0 / z) / 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 / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = t_1;
	elseif (z <= -2.15e+84)
		tmp = (x / -z) / t;
	elseif (z <= -7.5e-72)
		tmp = t_1;
	elseif (z <= 5.5e-41)
		tmp = (x / t) / y;
	elseif ((z <= 3.6e+171) || (~((z <= 2.4e+214)) && (z <= 3.6e+217)))
		tmp = (x / z) / z;
	else
		tmp = x * ((1.0 / z) / 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[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+144], t$95$1, If[LessEqual[z, -2.15e+84], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -7.5e-72], t$95$1, If[LessEqual[z, 5.5e-41], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, 3.6e+171], And[N[Not[LessEqual[z, 2.4e+214]], $MachinePrecision], LessEqual[z, 3.6e+217]]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(1.0 / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.85000000000000002e144 or -2.1499999999999998e84 < z < -7.5000000000000004e-72

   1. Initial program 90.2%

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

      1. associate-/l/ 96.6%

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

      2. div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

      1. associate-*l/ 99.6%

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

      2. div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 72.2%

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

      1. associate-*r/ 72.2%

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

      2. times-frac 78.0%

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

      3. associate-*l/ 77.9%

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

      4. mul-1-neg 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in t around 0 69.2%

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

       1. associate-*r/ 81.4%

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

       2. neg-mul-1 81.4%

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

   12. Simplified 69.2%

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

       1. div-inv 69.3%

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

       2. distribute-neg-frac2 69.3%

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

       3. frac-2neg 69.3%

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

   14. Applied egg-rr 69.3%

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

   if -2.85000000000000002e144 < z < -2.1499999999999998e84

   1. Initial program 76.0%

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

      1. associate-/l/ 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.3%

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

   6. Taylor expanded in y around 0 28.8%

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

      1. associate-*r/ 28.8%

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

      2. neg-mul-1 28.8%

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

   8. Simplified 28.8%

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

   9. Taylor expanded in x around 0 28.8%

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

       1. associate-*r/ 28.8%

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

       2. times-frac 44.6%

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

       3. associate-*l/ 44.7%

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

       4. mul-1-neg 44.7%

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

       5. distribute-frac-neg 44.7%

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

   11. Simplified 44.7%

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

   if -7.5000000000000004e-72 < z < 5.50000000000000022e-41

   1. Initial program 93.4%

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

      1. associate-/l/ 92.2%

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

      2. div-inv 92.1%

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

   4. Applied egg-rr 92.1%

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

      1. associate-*l/ 91.5%

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

      2. div-inv 91.8%

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

      3. div-inv 91.7%

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

      4. clear-num 91.6%

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

      5. associate-*l/ 92.2%

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

      6. *-un-lft-identity 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in z around 0 63.6%

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

      1. associate-/r* 67.4%

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

   9. Simplified 67.4%

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

   if 5.50000000000000022e-41 < z < 3.60000000000000018e171 or 2.4000000000000001e214 < z < 3.6000000000000002e217

   1. Initial program 86.6%

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

      1. associate-/l/ 99.7%

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

      2. div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. associate-*l/ 97.9%

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

      2. div-inv 98.0%

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

      3. div-inv 97.9%

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

      4. clear-num 97.8%

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

      5. associate-*l/ 98.0%

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

      6. *-un-lft-identity 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in y around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. times-frac 80.5%

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

      3. associate-*l/ 80.7%

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

      4. mul-1-neg 80.7%

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

   9. Simplified 80.7%

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

   10. Taylor expanded in t around 0 59.7%

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

       1. associate-*r/ 75.3%

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

       2. neg-mul-1 75.3%

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

   12. Simplified 59.7%

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

       1. distribute-neg-frac2 59.7%

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

       2. frac-2neg 59.7%

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

       3. div-inv 59.7%

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

       4. associate-/l* 57.1%

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

   14. Applied egg-rr 57.1%

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

       1. associate-*r/ 59.7%

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

       2. div-inv 59.7%

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

   16. Applied egg-rr 59.7%

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

   if 3.60000000000000018e171 < z < 2.4000000000000001e214 or 3.6000000000000002e217 < z

   1. Initial program 96.8%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. associate-*l/ 100.0%

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

      2. div-inv 100.0%

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

      3. div-inv 99.9%

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

      4. clear-num 99.9%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. times-frac 97.1%

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

      3. associate-*l/ 97.1%

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

      4. mul-1-neg 97.1%

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

   9. Simplified 97.1%

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

   10. Taylor expanded in t around 0 88.3%

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

       1. associate-*r/ 92.5%

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

       2. neg-mul-1 92.5%

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

   12. Simplified 88.3%

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

       1. distribute-neg-frac2 88.3%

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

       2. frac-2neg 88.3%

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

       3. div-inv 88.3%

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

       4. associate-/l* 96.8%

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

   14. Applied egg-rr 96.8%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+171} \lor \neg \left(z \leq 2.4 \cdot 10^{+214}\right) \land z \leq 3.6 \cdot 10^{+217}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{1}{z}}{z}\\ t_2 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+171} \lor \neg \left(z \leq 7.2 \cdot 10^{+213}\right) \land z \leq 3.6 \cdot 10^{+217}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (/ (/ 1.0 z) z))) (t_2 (/ (/ x z) z)))
   (if (<= z -2.85e+144)
     t_2
     (if (<= z -3.2e+83)
       (/ (/ x (- z)) t)
       (if (<= z -7.6e-74)
         t_1
         (if (<= z 1.35e-43)
           (/ (/ x t) y)
           (if (or (<= z 3.6e+171) (and (not (<= z 7.2e+213)) (<= z 3.6e+217)))
             t_2
             t_1)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x * ((1.0 / z) / z);
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_2;
	} else if (z <= -3.2e+83) {
		tmp = (x / -z) / t;
	} else if (z <= -7.6e-74) {
		tmp = t_1;
	} else if (z <= 1.35e-43) {
		tmp = (x / t) / y;
	} else if ((z <= 3.6e+171) || (!(z <= 7.2e+213) && (z <= 3.6e+217))) {
		tmp = t_2;
	} 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 * ((1.0d0 / z) / z)
    t_2 = (x / z) / z
    if (z <= (-2.85d+144)) then
        tmp = t_2
    else if (z <= (-3.2d+83)) then
        tmp = (x / -z) / t
    else if (z <= (-7.6d-74)) then
        tmp = t_1
    else if (z <= 1.35d-43) then
        tmp = (x / t) / y
    else if ((z <= 3.6d+171) .or. (.not. (z <= 7.2d+213)) .and. (z <= 3.6d+217)) then
        tmp = t_2
    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 * ((1.0 / z) / z);
	double t_2 = (x / z) / z;
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_2;
	} else if (z <= -3.2e+83) {
		tmp = (x / -z) / t;
	} else if (z <= -7.6e-74) {
		tmp = t_1;
	} else if (z <= 1.35e-43) {
		tmp = (x / t) / y;
	} else if ((z <= 3.6e+171) || (!(z <= 7.2e+213) && (z <= 3.6e+217))) {
		tmp = t_2;
	} 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 * ((1.0 / z) / z)
	t_2 = (x / z) / z
	tmp = 0
	if z <= -2.85e+144:
		tmp = t_2
	elif z <= -3.2e+83:
		tmp = (x / -z) / t
	elif z <= -7.6e-74:
		tmp = t_1
	elif z <= 1.35e-43:
		tmp = (x / t) / y
	elif (z <= 3.6e+171) or (not (z <= 7.2e+213) and (z <= 3.6e+217)):
		tmp = t_2
	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(1.0 / z) / z))
	t_2 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = t_2;
	elseif (z <= -3.2e+83)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif (z <= -7.6e-74)
		tmp = t_1;
	elseif (z <= 1.35e-43)
		tmp = Float64(Float64(x / t) / y);
	elseif ((z <= 3.6e+171) || (!(z <= 7.2e+213) && (z <= 3.6e+217)))
		tmp = t_2;
	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 * ((1.0 / z) / z);
	t_2 = (x / z) / z;
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = t_2;
	elseif (z <= -3.2e+83)
		tmp = (x / -z) / t;
	elseif (z <= -7.6e-74)
		tmp = t_1;
	elseif (z <= 1.35e-43)
		tmp = (x / t) / y;
	elseif ((z <= 3.6e+171) || (~((z <= 7.2e+213)) && (z <= 3.6e+217)))
		tmp = t_2;
	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[(1.0 / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2.85e+144], t$95$2, If[LessEqual[z, -3.2e+83], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -7.6e-74], t$95$1, If[LessEqual[z, 1.35e-43], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, 3.6e+171], And[N[Not[LessEqual[z, 7.2e+213]], $MachinePrecision], LessEqual[z, 3.6e+217]]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.85000000000000002e144 or 1.34999999999999996e-43 < z < 3.60000000000000018e171 or 7.2000000000000002e213 < z < 3.6000000000000002e217

   1. Initial program 85.6%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 98.6%

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

      2. div-inv 98.7%

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

      3. div-inv 98.6%

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

      4. clear-num 98.6%

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

      5. associate-*l/ 98.6%

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

      6. *-un-lft-identity 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in y around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. times-frac 86.7%

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

      3. associate-*l/ 86.8%

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

      4. mul-1-neg 86.8%

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

   9. Simplified 86.8%

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

   10. Taylor expanded in t around 0 71.8%

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

       1. associate-*r/ 82.6%

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

       2. neg-mul-1 82.6%

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

   12. Simplified 71.8%

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

       1. distribute-neg-frac2 71.8%

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

       2. frac-2neg 71.8%

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

       3. div-inv 71.8%

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

       4. associate-/l* 67.4%

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

   14. Applied egg-rr 67.4%

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

       1. associate-*r/ 71.8%

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

       2. div-inv 71.8%

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

   16. Applied egg-rr 71.8%

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

   if -2.85000000000000002e144 < z < -3.1999999999999999e83

   1. Initial program 76.0%

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

      1. associate-/l/ 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.3%

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

   6. Taylor expanded in y around 0 28.8%

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

      1. associate-*r/ 28.8%

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

      2. neg-mul-1 28.8%

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

   8. Simplified 28.8%

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

   9. Taylor expanded in x around 0 28.8%

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

       1. associate-*r/ 28.8%

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

       2. times-frac 44.6%

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

       3. associate-*l/ 44.7%

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

       4. mul-1-neg 44.7%

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

       5. distribute-frac-neg 44.7%

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

   11. Simplified 44.7%

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

   if -3.1999999999999999e83 < z < -7.5999999999999993e-74 or 3.60000000000000018e171 < z < 7.2000000000000002e213 or 3.6000000000000002e217 < z

   1. Initial program 96.7%

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

      1. associate-/l/ 96.8%

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

      2. div-inv 96.7%

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

   4. Applied egg-rr 96.7%

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

      1. associate-*l/ 99.7%

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

      2. div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. times-frac 78.0%

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

      3. associate-*l/ 77.9%

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

      4. mul-1-neg 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in t around 0 66.7%

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

       1. associate-*r/ 79.9%

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

       2. neg-mul-1 79.9%

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

   12. Simplified 66.7%

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

       1. distribute-neg-frac2 66.7%

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

       2. frac-2neg 66.7%

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

       3. div-inv 66.8%

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

       4. associate-/l* 71.0%

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

   14. Applied egg-rr 71.0%

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

   if -7.5999999999999993e-74 < z < 1.34999999999999996e-43

   1. Initial program 93.4%

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

      1. associate-/l/ 92.2%

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

      2. div-inv 92.1%

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

   4. Applied egg-rr 92.1%

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

      1. associate-*l/ 91.5%

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

      2. div-inv 91.8%

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

      3. div-inv 91.7%

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

      4. clear-num 91.6%

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

      5. associate-*l/ 92.2%

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

      6. *-un-lft-identity 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in z around 0 63.6%

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

      1. associate-/r* 67.4%

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

   9. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+171} \lor \neg \left(z \leq 7.2 \cdot 10^{+213}\right) \land z \leq 3.6 \cdot 10^{+217}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) (- t z))))
   (if (<= t -1.55e-193)
     t_1
     (if (<= t 2.4e-236)
       (/ (/ 1.0 z) (/ z x))
       (if (<= t 1.26e-188)
         t_1
         (if (<= t 4.8e-158)
           (/ (/ x z) z)
           (if (<= t 7.8e-78)
             t_1
             (if (<= t 1.25e-16)
               (/ x (* z z))
               (if (<= t 2.15e+86)
                 (/ x (* t (- y z)))
                 (/ (/ x t) (- 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) / (t - z);
	double tmp;
	if (t <= -1.55e-193) {
		tmp = t_1;
	} else if (t <= 2.4e-236) {
		tmp = (1.0 / z) / (z / x);
	} else if (t <= 1.26e-188) {
		tmp = t_1;
	} else if (t <= 4.8e-158) {
		tmp = (x / z) / z;
	} else if (t <= 7.8e-78) {
		tmp = t_1;
	} else if (t <= 1.25e-16) {
		tmp = x / (z * z);
	} else if (t <= 2.15e+86) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / (t - z)
    if (t <= (-1.55d-193)) then
        tmp = t_1
    else if (t <= 2.4d-236) then
        tmp = (1.0d0 / z) / (z / x)
    else if (t <= 1.26d-188) then
        tmp = t_1
    else if (t <= 4.8d-158) then
        tmp = (x / z) / z
    else if (t <= 7.8d-78) then
        tmp = t_1
    else if (t <= 1.25d-16) then
        tmp = x / (z * z)
    else if (t <= 2.15d+86) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / (t - z);
	double tmp;
	if (t <= -1.55e-193) {
		tmp = t_1;
	} else if (t <= 2.4e-236) {
		tmp = (1.0 / z) / (z / x);
	} else if (t <= 1.26e-188) {
		tmp = t_1;
	} else if (t <= 4.8e-158) {
		tmp = (x / z) / z;
	} else if (t <= 7.8e-78) {
		tmp = t_1;
	} else if (t <= 1.25e-16) {
		tmp = x / (z * z);
	} else if (t <= 2.15e+86) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / y) / (t - z)
	tmp = 0
	if t <= -1.55e-193:
		tmp = t_1
	elif t <= 2.4e-236:
		tmp = (1.0 / z) / (z / x)
	elif t <= 1.26e-188:
		tmp = t_1
	elif t <= 4.8e-158:
		tmp = (x / z) / z
	elif t <= 7.8e-78:
		tmp = t_1
	elif t <= 1.25e-16:
		tmp = x / (z * z)
	elif t <= 2.15e+86:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / Float64(t - z))
	tmp = 0.0
	if (t <= -1.55e-193)
		tmp = t_1;
	elseif (t <= 2.4e-236)
		tmp = Float64(Float64(1.0 / z) / Float64(z / x));
	elseif (t <= 1.26e-188)
		tmp = t_1;
	elseif (t <= 4.8e-158)
		tmp = Float64(Float64(x / z) / z);
	elseif (t <= 7.8e-78)
		tmp = t_1;
	elseif (t <= 1.25e-16)
		tmp = Float64(x / Float64(z * z));
	elseif (t <= 2.15e+86)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) / (t - z);
	tmp = 0.0;
	if (t <= -1.55e-193)
		tmp = t_1;
	elseif (t <= 2.4e-236)
		tmp = (1.0 / z) / (z / x);
	elseif (t <= 1.26e-188)
		tmp = t_1;
	elseif (t <= 4.8e-158)
		tmp = (x / z) / z;
	elseif (t <= 7.8e-78)
		tmp = t_1;
	elseif (t <= 1.25e-16)
		tmp = x / (z * z);
	elseif (t <= 2.15e+86)
		tmp = x / (t * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e-193], t$95$1, If[LessEqual[t, 2.4e-236], N[(N[(1.0 / z), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.26e-188], t$95$1, If[LessEqual[t, 4.8e-158], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 7.8e-78], t$95$1, If[LessEqual[t, 1.25e-16], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+86], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.5500000000000001e-193 or 2.4000000000000002e-236 < t < 1.26e-188 or 4.80000000000000015e-158 < t < 7.8000000000000004e-78

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 93.1%

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

      1. associate-/l/ 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around inf 52.7%

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

   if -1.5500000000000001e-193 < t < 2.4000000000000002e-236

   1. Initial program 92.7%

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

      1. associate-/l/ 88.9%

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

      2. div-inv 88.9%

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

   4. Applied egg-rr 88.9%

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

      1. associate-*l/ 96.9%

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

      2. div-inv 97.0%

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

      3. div-inv 97.0%

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

      4. clear-num 97.0%

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

      5. associate-*l/ 97.0%

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

      6. *-un-lft-identity 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in y around 0 48.4%

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

      1. associate-*r/ 48.4%

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

      2. times-frac 52.9%

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

      3. associate-*l/ 52.8%

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

      4. mul-1-neg 52.8%

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

   9. Simplified 52.8%

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

   10. Taylor expanded in t around 0 53.0%

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

       1. associate-*r/ 86.2%

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

       2. neg-mul-1 86.2%

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

   12. Simplified 53.0%

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

       1. distribute-neg-frac2 53.0%

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

       2. frac-2neg 53.0%

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

       3. div-inv 52.9%

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

       4. associate-/l* 47.4%

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

   14. Applied egg-rr 47.4%

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

       1. associate-*r/ 52.9%

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

       2. associate-*l/ 53.0%

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

       3. clear-num 53.0%

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

       4. associate-*l/ 53.0%

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

       5. *-un-lft-identity 53.0%

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

   16. Applied egg-rr 53.0%

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

   if 1.26e-188 < t < 4.80000000000000015e-158

   1. Initial program 81.3%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. associate-*l/ 100.0%

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

      2. div-inv 100.0%

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

      3. div-inv 100.0%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-un-lft-identity 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in y around 0 42.4%

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

      1. associate-*r/ 42.4%

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

      2. times-frac 52.1%

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

      3. associate-*l/ 52.1%

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

      4. mul-1-neg 52.1%

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

   9. Simplified 52.1%

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

   10. Taylor expanded in t around 0 52.1%

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

       1. associate-*r/ 100.0%

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

       2. neg-mul-1 100.0%

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

   12. Simplified 52.1%

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

       1. distribute-neg-frac2 52.1%

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

       2. frac-2neg 52.1%

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

       3. div-inv 52.1%

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

       4. associate-/l* 42.4%

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

   14. Applied egg-rr 42.4%

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

       1. associate-*r/ 52.1%

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

       2. div-inv 52.1%

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

   16. Applied egg-rr 52.1%

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

   if 7.8000000000000004e-78 < t < 1.2500000000000001e-16

   1. Initial program 99.8%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 96.8%

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

      2. div-inv 97.1%

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

      3. div-inv 97.2%

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

      4. clear-num 97.1%

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

      5. associate-*l/ 97.2%

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

      6. *-un-lft-identity 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around 0 76.9%

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

      1. associate-*r/ 76.9%

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

      2. times-frac 76.9%

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

      3. associate-*l/ 76.8%

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

      4. mul-1-neg 76.8%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 76.8%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 71.0%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 77.1%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 77.1%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 71.0%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 71.0%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 71.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 71.1%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 71.0%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 71.0%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
   15. Step-by-step derivation

       1. associate-*r/ 71.1%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{z}} \]

       2. associate-*l/ 71.1%

          \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

       3. *-commutative 71.1%

          \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{z}} \]

       4. frac-2neg 71.1%

          \[\leadsto \color{blue}{\frac{-1}{-z}} \cdot \frac{x}{z} \]

       5. metadata-eval 71.1%

          \[\leadsto \frac{\color{blue}{-1}}{-z} \cdot \frac{x}{z} \]

       6. frac-2neg 71.1%

          \[\leadsto \frac{-1}{-z} \cdot \color{blue}{\frac{-x}{-z}} \]

       7. frac-times 71.1%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(-x\right)}{\left(-z\right) \cdot \left(-z\right)}} \]

       8. neg-mul-1 71.1%

          \[\leadsto \frac{\color{blue}{-\left(-x\right)}}{\left(-z\right) \cdot \left(-z\right)} \]

       9. remove-double-neg 71.1%

          \[\leadsto \frac{\color{blue}{x}}{\left(-z\right) \cdot \left(-z\right)} \]

   16. Applied egg-rr 71.1%

       \[\leadsto \color{blue}{\frac{x}{\left(-z\right) \cdot \left(-z\right)}} \]

   if 1.2500000000000001e-16 < t < 2.1500000000000001e86

   1. Initial program 89.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 60.6%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 2.1500000000000001e86 < t

   1. Initial program 82.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 96.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 93.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-193}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-188}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y - z}\\ t_2 := \frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-269}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \end{array} \]

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 t) (- y z))) (t_2 (/ x (* (- t z) y))))
   (if (<= z -2.85e+144)
     (/ (/ 1.0 z) (/ z x))
     (if (<= z -9.2e+60)
       t_1
       (if (<= z 5.8e-269)
         t_2
         (if (<= z 4.8e-118)
           t_1
           (if (<= z 1.85e-94)
             t_2
             (if (<= z 7.8e-22)
               t_1
               (if (<= z 5000000000.0) t_2 (* x (/ (/ 1.0 z) z)))))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / (y - z);
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = (1.0 / z) / (z / x);
	} else if (z <= -9.2e+60) {
		tmp = t_1;
	} else if (z <= 5.8e-269) {
		tmp = t_2;
	} else if (z <= 4.8e-118) {
		tmp = t_1;
	} else if (z <= 1.85e-94) {
		tmp = t_2;
	} else if (z <= 7.8e-22) {
		tmp = t_1;
	} else if (z <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = x * ((1.0 / z) / 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) :: t_2
    real(8) :: tmp
    t_1 = (x / t) / (y - z)
    t_2 = x / ((t - z) * y)
    if (z <= (-2.85d+144)) then
        tmp = (1.0d0 / z) / (z / x)
    else if (z <= (-9.2d+60)) then
        tmp = t_1
    else if (z <= 5.8d-269) then
        tmp = t_2
    else if (z <= 4.8d-118) then
        tmp = t_1
    else if (z <= 1.85d-94) then
        tmp = t_2
    else if (z <= 7.8d-22) then
        tmp = t_1
    else if (z <= 5000000000.0d0) then
        tmp = t_2
    else
        tmp = x * ((1.0d0 / z) / 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 / t) / (y - z);
	double t_2 = x / ((t - z) * y);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = (1.0 / z) / (z / x);
	} else if (z <= -9.2e+60) {
		tmp = t_1;
	} else if (z <= 5.8e-269) {
		tmp = t_2;
	} else if (z <= 4.8e-118) {
		tmp = t_1;
	} else if (z <= 1.85e-94) {
		tmp = t_2;
	} else if (z <= 7.8e-22) {
		tmp = t_1;
	} else if (z <= 5000000000.0) {
		tmp = t_2;
	} else {
		tmp = x * ((1.0 / z) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / t) / (y - z)
	t_2 = x / ((t - z) * y)
	tmp = 0
	if z <= -2.85e+144:
		tmp = (1.0 / z) / (z / x)
	elif z <= -9.2e+60:
		tmp = t_1
	elif z <= 5.8e-269:
		tmp = t_2
	elif z <= 4.8e-118:
		tmp = t_1
	elif z <= 1.85e-94:
		tmp = t_2
	elif z <= 7.8e-22:
		tmp = t_1
	elif z <= 5000000000.0:
		tmp = t_2
	else:
		tmp = x * ((1.0 / z) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / Float64(y - z))
	t_2 = Float64(x / Float64(Float64(t - z) * y))
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = Float64(Float64(1.0 / z) / Float64(z / x));
	elseif (z <= -9.2e+60)
		tmp = t_1;
	elseif (z <= 5.8e-269)
		tmp = t_2;
	elseif (z <= 4.8e-118)
		tmp = t_1;
	elseif (z <= 1.85e-94)
		tmp = t_2;
	elseif (z <= 7.8e-22)
		tmp = t_1;
	elseif (z <= 5000000000.0)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(1.0 / z) / 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 / t) / (y - z);
	t_2 = x / ((t - z) * y);
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = (1.0 / z) / (z / x);
	elseif (z <= -9.2e+60)
		tmp = t_1;
	elseif (z <= 5.8e-269)
		tmp = t_2;
	elseif (z <= 4.8e-118)
		tmp = t_1;
	elseif (z <= 1.85e-94)
		tmp = t_2;
	elseif (z <= 7.8e-22)
		tmp = t_1;
	elseif (z <= 5000000000.0)
		tmp = t_2;
	else
		tmp = x * ((1.0 / z) / 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[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+144], N[(N[(1.0 / z), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e+60], t$95$1, If[LessEqual[z, 5.8e-269], t$95$2, If[LessEqual[z, 4.8e-118], t$95$1, If[LessEqual[z, 1.85e-94], t$95$2, If[LessEqual[z, 7.8e-22], t$95$1, If[LessEqual[z, 5000000000.0], t$95$2, N[(x * N[(N[(1.0 / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.85000000000000002e144

   1. Initial program 83.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 99.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 99.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 99.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 83.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 83.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 98.4%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 98.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 98.4%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 94.9%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 96.5%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 96.5%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 94.9%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 94.9%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 94.9%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 94.9%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 86.9%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 86.9%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
   15. Step-by-step derivation

       1. associate-*r/ 94.9%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{z}} \]

       2. associate-*l/ 95.0%

          \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

       3. clear-num 95.0%

          \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{1}{z} \]

       4. associate-*l/ 95.0%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{z}}{\frac{z}{x}}} \]

       5. *-un-lft-identity 95.0%

          \[\leadsto \frac{\color{blue}{\frac{1}{z}}}{\frac{z}{x}} \]

   16. Applied egg-rr 95.0%

       \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{z}{x}}} \]

   if -2.85000000000000002e144 < z < -9.20000000000000068e60 or 5.8000000000000002e-269 < z < 4.8000000000000003e-118 or 1.8499999999999999e-94 < z < 7.79999999999999996e-22

   1. Initial program 87.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 97.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   if -9.20000000000000068e60 < z < 5.8000000000000002e-269 or 4.8000000000000003e-118 < z < 1.8499999999999999e-94 or 7.79999999999999996e-22 < z < 5e9

   1. Initial program 95.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 68.4%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 68.4%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if 5e9 < z

   1. Initial program 89.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 99.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 99.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 81.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 81.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 88.7%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 88.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 88.8%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 74.1%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 84.4%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 84.4%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 74.1%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 74.1%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 74.1%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 74.1%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 75.7%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 75.7%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 72.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{\frac{x}{t - z}}{y}\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)) (t_2 (/ (/ x (- t z)) y)))
   (if (<= t -4.3e-198)
     t_2
     (if (<= t -2.2e-257)
       t_1
       (if (<= t 9.5e-263)
         t_2
         (if (<= t 1.65e-150)
           t_1
           (if (<= t 5e-87)
             (/ (/ x y) (- t z))
             (if (<= t 1.82e-25) (/ x (* z z)) (/ (/ x t) (- y z))))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = (x / (t - z)) / y;
	double tmp;
	if (t <= -4.3e-198) {
		tmp = t_2;
	} else if (t <= -2.2e-257) {
		tmp = t_1;
	} else if (t <= 9.5e-263) {
		tmp = t_2;
	} else if (t <= 1.65e-150) {
		tmp = t_1;
	} else if (t <= 5e-87) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.82e-25) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = (x / (t - z)) / y
    if (t <= (-4.3d-198)) then
        tmp = t_2
    else if (t <= (-2.2d-257)) then
        tmp = t_1
    else if (t <= 9.5d-263) then
        tmp = t_2
    else if (t <= 1.65d-150) then
        tmp = t_1
    else if (t <= 5d-87) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.82d-25) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double t_2 = (x / (t - z)) / y;
	double tmp;
	if (t <= -4.3e-198) {
		tmp = t_2;
	} else if (t <= -2.2e-257) {
		tmp = t_1;
	} else if (t <= 9.5e-263) {
		tmp = t_2;
	} else if (t <= 1.65e-150) {
		tmp = t_1;
	} else if (t <= 5e-87) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.82e-25) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	t_2 = (x / (t - z)) / y
	tmp = 0
	if t <= -4.3e-198:
		tmp = t_2
	elif t <= -2.2e-257:
		tmp = t_1
	elif t <= 9.5e-263:
		tmp = t_2
	elif t <= 1.65e-150:
		tmp = t_1
	elif t <= 5e-87:
		tmp = (x / y) / (t - z)
	elif t <= 1.82e-25:
		tmp = x / (z * z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	t_2 = Float64(Float64(x / Float64(t - z)) / y)
	tmp = 0.0
	if (t <= -4.3e-198)
		tmp = t_2;
	elseif (t <= -2.2e-257)
		tmp = t_1;
	elseif (t <= 9.5e-263)
		tmp = t_2;
	elseif (t <= 1.65e-150)
		tmp = t_1;
	elseif (t <= 5e-87)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.82e-25)
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	t_2 = (x / (t - z)) / y;
	tmp = 0.0;
	if (t <= -4.3e-198)
		tmp = t_2;
	elseif (t <= -2.2e-257)
		tmp = t_1;
	elseif (t <= 9.5e-263)
		tmp = t_2;
	elseif (t <= 1.65e-150)
		tmp = t_1;
	elseif (t <= 5e-87)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.82e-25)
		tmp = x / (z * z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -4.3e-198], t$95$2, If[LessEqual[t, -2.2e-257], t$95$1, If[LessEqual[t, 9.5e-263], t$95$2, If[LessEqual[t, 1.65e-150], t$95$1, If[LessEqual[t, 5e-87], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.82e-25], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.3000000000000003e-198 or -2.19999999999999988e-257 < t < 9.5000000000000005e-263

   1. Initial program 92.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 96.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 96.6%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 96.6%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 96.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 96.6%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 96.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 96.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 96.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around inf 54.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-/l/ 59.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   9. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   if -4.3000000000000003e-198 < t < -2.19999999999999988e-257 or 9.5000000000000005e-263 < t < 1.6500000000000001e-150

   1. Initial program 92.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 91.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 91.0%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 91.0%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 99.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 99.9%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 99.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 99.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 58.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 58.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 65.0%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 65.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 65.0%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 65.2%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 82.0%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 82.0%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 65.2%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 65.2%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 65.2%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 65.1%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 57.6%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 57.6%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
   15. Step-by-step derivation

       1. associate-*r/ 65.1%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{z}} \]

       2. div-inv 65.2%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

   16. Applied egg-rr 65.2%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if 1.6500000000000001e-150 < t < 5.00000000000000042e-87

   1. Initial program 92.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.2%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   6. Taylor expanded in y around inf 61.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{t - z} \]

   if 5.00000000000000042e-87 < t < 1.8199999999999999e-25

   1. Initial program 99.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 99.8%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 96.8%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 96.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 97.0%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 97.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 97.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 97.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 81.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 81.8%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 81.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 81.7%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 81.7%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 75.4%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 81.9%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 81.9%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 75.4%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 75.4%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 75.4%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 75.5%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 75.4%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 75.4%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
   15. Step-by-step derivation

       1. associate-*r/ 75.5%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{z}} \]

       2. associate-*l/ 75.5%

          \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

       3. *-commutative 75.5%

          \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{z}} \]

       4. frac-2neg 75.5%

          \[\leadsto \color{blue}{\frac{-1}{-z}} \cdot \frac{x}{z} \]

       5. metadata-eval 75.5%

          \[\leadsto \frac{\color{blue}{-1}}{-z} \cdot \frac{x}{z} \]

       6. frac-2neg 75.5%

          \[\leadsto \frac{-1}{-z} \cdot \color{blue}{\frac{-x}{-z}} \]

       7. frac-times 75.5%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(-x\right)}{\left(-z\right) \cdot \left(-z\right)}} \]

       8. neg-mul-1 75.5%

          \[\leadsto \frac{\color{blue}{-\left(-x\right)}}{\left(-z\right) \cdot \left(-z\right)} \]

       9. remove-double-neg 75.5%

          \[\leadsto \frac{\color{blue}{x}}{\left(-z\right) \cdot \left(-z\right)} \]

   16. Applied egg-rr 75.5%

       \[\leadsto \color{blue}{\frac{x}{\left(-z\right) \cdot \left(-z\right)}} \]

   if 1.8199999999999999e-25 < t

   1. Initial program 84.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 97.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 82.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-198}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-257}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-263}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \end{array} \]

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 z) (/ 1.0 z))))
   (if (<= z -2.85e+144)
     t_1
     (if (<= z -8.6e+80)
       (/ (/ x (- z)) t)
       (if (<= z -2.6e+41)
         t_1
         (if (<= z 3.6e-66) (/ x (* t (- y z))) (* x (/ (/ 1.0 z) z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_1;
	} else if (z <= -8.6e+80) {
		tmp = (x / -z) / t;
	} else if (z <= -2.6e+41) {
		tmp = t_1;
	} else if (z <= 3.6e-66) {
		tmp = x / (t * (y - z));
	} else {
		tmp = x * ((1.0 / z) / 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 / z) * (1.0d0 / z)
    if (z <= (-2.85d+144)) then
        tmp = t_1
    else if (z <= (-8.6d+80)) then
        tmp = (x / -z) / t
    else if (z <= (-2.6d+41)) then
        tmp = t_1
    else if (z <= 3.6d-66) then
        tmp = x / (t * (y - z))
    else
        tmp = x * ((1.0d0 / z) / 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 / z) * (1.0 / z);
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_1;
	} else if (z <= -8.6e+80) {
		tmp = (x / -z) / t;
	} else if (z <= -2.6e+41) {
		tmp = t_1;
	} else if (z <= 3.6e-66) {
		tmp = x / (t * (y - z));
	} else {
		tmp = x * ((1.0 / z) / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if z <= -2.85e+144:
		tmp = t_1
	elif z <= -8.6e+80:
		tmp = (x / -z) / t
	elif z <= -2.6e+41:
		tmp = t_1
	elif z <= 3.6e-66:
		tmp = x / (t * (y - z))
	else:
		tmp = x * ((1.0 / z) / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = t_1;
	elseif (z <= -8.6e+80)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif (z <= -2.6e+41)
		tmp = t_1;
	elseif (z <= 3.6e-66)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(x * Float64(Float64(1.0 / z) / 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 / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = t_1;
	elseif (z <= -8.6e+80)
		tmp = (x / -z) / t;
	elseif (z <= -2.6e+41)
		tmp = t_1;
	elseif (z <= 3.6e-66)
		tmp = x / (t * (y - z));
	else
		tmp = x * ((1.0 / z) / 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[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+144], t$95$1, If[LessEqual[z, -8.6e+80], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -2.6e+41], t$95$1, If[LessEqual[z, 3.6e-66], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.85000000000000002e144 or -8.60000000000000008e80 < z < -2.6000000000000001e41

   1. Initial program 87.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 99.9%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 99.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 99.9%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 99.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 99.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 84.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 84.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 96.3%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 96.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 96.2%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 96.2%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 87.9%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 91.5%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 91.5%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 87.9%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. div-inv 88.0%

          \[\leadsto \color{blue}{\left(-\frac{-x}{z}\right) \cdot \frac{1}{z}} \]

       2. distribute-neg-frac2 88.0%

          \[\leadsto \color{blue}{\frac{-x}{-z}} \cdot \frac{1}{z} \]

       3. frac-2neg 88.0%

          \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{z} \]

   14. Applied egg-rr 88.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   if -2.85000000000000002e144 < z < -8.60000000000000008e80

   1. Initial program 76.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 99.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 28.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 28.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 28.8%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 28.8%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]

   9. Taylor expanded in x around 0 28.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   10. Step-by-step derivation

       1. associate-*r/ 28.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

       2. times-frac 44.6%

          \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]

       3. associate-*l/ 44.7%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z}}{t}} \]

       4. mul-1-neg 44.7%

          \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{t} \]

       5. distribute-frac-neg 44.7%

          \[\leadsto \color{blue}{-\frac{\frac{x}{z}}{t}} \]

   11. Simplified 44.7%

       \[\leadsto \color{blue}{-\frac{\frac{x}{z}}{t}} \]

   if -2.6000000000000001e41 < z < 3.60000000000000012e-66

   1. Initial program 94.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 69.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 3.60000000000000012e-66 < z

   1. Initial program 89.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 98.7%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 98.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 98.7%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 98.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 98.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 98.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 77.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 83.7%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 83.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 83.8%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 83.8%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 67.7%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 79.9%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 79.9%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 67.7%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 67.7%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 67.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 67.7%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 69.1%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 69.1%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-72} \lor \neg \left(z \leq 1.8 \cdot 10^{-110}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -2.85e+144)
     t_1
     (if (<= z -3.2e+83)
       (/ (/ x (- z)) t)
       (if (or (<= z -2.4e-72) (not (<= z 1.8e-110))) t_1 (/ (/ x t) y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_1;
	} else if (z <= -3.2e+83) {
		tmp = (x / -z) / t;
	} else if ((z <= -2.4e-72) || !(z <= 1.8e-110)) {
		tmp = t_1;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-2.85d+144)) then
        tmp = t_1
    else if (z <= (-3.2d+83)) then
        tmp = (x / -z) / t
    else if ((z <= (-2.4d-72)) .or. (.not. (z <= 1.8d-110))) then
        tmp = t_1
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -2.85e+144) {
		tmp = t_1;
	} else if (z <= -3.2e+83) {
		tmp = (x / -z) / t;
	} else if ((z <= -2.4e-72) || !(z <= 1.8e-110)) {
		tmp = t_1;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -2.85e+144:
		tmp = t_1
	elif z <= -3.2e+83:
		tmp = (x / -z) / t
	elif (z <= -2.4e-72) or not (z <= 1.8e-110):
		tmp = t_1
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -2.85e+144)
		tmp = t_1;
	elseif (z <= -3.2e+83)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	elseif ((z <= -2.4e-72) || !(z <= 1.8e-110))
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -2.85e+144)
		tmp = t_1;
	elseif (z <= -3.2e+83)
		tmp = (x / -z) / t;
	elseif ((z <= -2.4e-72) || ~((z <= 1.8e-110)))
		tmp = t_1;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2.85e+144], t$95$1, If[LessEqual[z, -3.2e+83], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, -2.4e-72], N[Not[LessEqual[z, 1.8e-110]], $MachinePrecision]], t$95$1, N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.85000000000000002e144 or -3.1999999999999999e83 < z < -2.4e-72 or 1.79999999999999997e-110 < z

   1. Initial program 90.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 98.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 97.9%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 99.1%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 99.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 99.1%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 99.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 99.1%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 99.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 73.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 73.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 79.1%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 79.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 79.2%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 79.2%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 66.6%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 79.5%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 79.5%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 66.6%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 66.6%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 66.6%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 66.6%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 65.9%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 65.9%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
   15. Step-by-step derivation

       1. associate-*r/ 66.6%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{z}} \]

       2. div-inv 66.6%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

   16. Applied egg-rr 66.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -2.85000000000000002e144 < z < -3.1999999999999999e83

   1. Initial program 76.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 99.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 28.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 28.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 28.8%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 28.8%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]

   9. Taylor expanded in x around 0 28.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   10. Step-by-step derivation

       1. associate-*r/ 28.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

       2. times-frac 44.6%

          \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]

       3. associate-*l/ 44.7%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z}}{t}} \]

       4. mul-1-neg 44.7%

          \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{t} \]

       5. distribute-frac-neg 44.7%

          \[\leadsto \color{blue}{-\frac{\frac{x}{z}}{t}} \]

   11. Simplified 44.7%

       \[\leadsto \color{blue}{-\frac{\frac{x}{z}}{t}} \]

   if -2.4e-72 < z < 1.79999999999999997e-110

   1. Initial program 93.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 92.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 92.3%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 90.6%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 90.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 90.8%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 90.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 91.4%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 91.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 91.4%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in z around 0 67.2%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 70.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 70.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-72} \lor \neg \left(z \leq 1.8 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e+53)
   (/ (/ x y) (- t z))
   (if (<= t 5.8e+43)
     (/ (/ x z) (- z y))
     (if (<= t 2e+142) (/ x (* t (- y z))) (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+53) {
		tmp = (x / y) / (t - z);
	} else if (t <= 5.8e+43) {
		tmp = (x / z) / (z - y);
	} else if (t <= 2e+142) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d+53)) then
        tmp = (x / y) / (t - z)
    else if (t <= 5.8d+43) then
        tmp = (x / z) / (z - y)
    else if (t <= 2d+142) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+53) {
		tmp = (x / y) / (t - z);
	} else if (t <= 5.8e+43) {
		tmp = (x / z) / (z - y);
	} else if (t <= 2e+142) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e+53:
		tmp = (x / y) / (t - z)
	elif t <= 5.8e+43:
		tmp = (x / z) / (z - y)
	elif t <= 2e+142:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e+53)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 5.8e+43)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (t <= 2e+142)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e+53)
		tmp = (x / y) / (t - z);
	elseif (t <= 5.8e+43)
		tmp = (x / z) / (z - y);
	elseif (t <= 2e+142)
		tmp = x / (t * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e+53], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+43], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+142], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.49999999999999999e53

   1. Initial program 92.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.1%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-/l/ 94.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   5. Simplified 94.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   6. Taylor expanded in y around inf 45.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{t - z} \]

   if -1.49999999999999999e53 < t < 5.8000000000000004e43

   1. Initial program 93.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 96.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 77.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{y - z} \]
   6. Step-by-step derivation

      1. associate-*r/ 77.9%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

      2. neg-mul-1 77.9%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   7. Simplified 77.9%

      \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{y - z} \]

   if 5.8000000000000004e43 < t < 2.0000000000000001e142

   1. Initial program 94.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 2.0000000000000001e142 < t

   1. Initial program 78.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 95.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 95.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-73} \lor \neg \left(z \leq 1.8 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e-73) (not (<= z 1.8e-110))) (/ (/ x z) z) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-73) || !(z <= 1.8e-110)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d-73)) .or. (.not. (z <= 1.8d-110))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-73) || !(z <= 1.8e-110)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8e-73) or not (z <= 1.8e-110):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e-73) || !(z <= 1.8e-110))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e-73) || ~((z <= 1.8e-110)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e-73], N[Not[LessEqual[z, 1.8e-110]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999998e-73 or 1.79999999999999997e-110 < z

   1. Initial program 89.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 98.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 98.1%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 99.1%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 99.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 99.1%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 99.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 99.2%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 99.2%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in y around 0 71.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-*r/ 71.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. times-frac 77.9%

         \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{t - z}} \]

      3. associate-*l/ 77.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{t - z}}{z}} \]

      4. mul-1-neg 77.9%

         \[\leadsto \frac{\color{blue}{-\frac{x}{t - z}}}{z} \]

   9. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 63.5%

       \[\leadsto \frac{-\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 77.7%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 77.7%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 63.5%

       \[\leadsto \frac{-\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. distribute-neg-frac2 63.5%

          \[\leadsto \frac{\color{blue}{\frac{-x}{-z}}}{z} \]

       2. frac-2neg 63.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

       3. div-inv 63.6%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{z}}}{z} \]

       4. associate-/l* 62.9%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]

   14. Applied egg-rr 62.9%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{z}} \]
   15. Step-by-step derivation

       1. associate-*r/ 63.6%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{z}} \]

       2. div-inv 63.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{z} \]

   16. Applied egg-rr 63.5%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -7.99999999999999998e-73 < z < 1.79999999999999997e-110

   1. Initial program 93.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 92.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 92.3%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 90.6%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 90.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 90.8%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 90.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 91.4%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 91.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 91.4%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in z around 0 67.2%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 70.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 70.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-73} \lor \neg \left(z \leq 1.8 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+174} \lor \neg \left(z \leq 7.8 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+174) (not (<= z 7.8e-7))) (/ x (* z y)) (/ x (* t y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+174) || !(z <= 7.8e-7)) {
		tmp = x / (z * y);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d+174)) .or. (.not. (z <= 7.8d-7))) then
        tmp = x / (z * y)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+174) || !(z <= 7.8e-7)) {
		tmp = x / (z * y);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+174) or not (z <= 7.8e-7):
		tmp = x / (z * y)
	else:
		tmp = x / (t * y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+174) || !(z <= 7.8e-7))
		tmp = Float64(x / Float64(z * y));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+174) || ~((z <= 7.8e-7)))
		tmp = x / (z * y);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+174], N[Not[LessEqual[z, 7.8e-7]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000055e174 or 7.80000000000000049e-7 < z

   1. Initial program 89.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 99.8%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

      3. div-inv 99.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{t - z}\right)} \cdot \frac{1}{y - z} \]

      4. associate-*l* 90.6%

         \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   4. Applied egg-rr 90.6%

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   5. Taylor expanded in t around 0 82.2%

      \[\leadsto x \cdot \color{blue}{\frac{-1}{z \cdot \left(y - z\right)}} \]

   6. Taylor expanded in z around 0 39.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. distribute-neg-frac2 39.6%

         \[\leadsto \color{blue}{\frac{x}{-y \cdot z}} \]

      3. *-commutative 39.6%

         \[\leadsto \frac{x}{-\color{blue}{z \cdot y}} \]

      4. distribute-rgt-neg-out 39.6%

         \[\leadsto \frac{x}{\color{blue}{z \cdot \left(-y\right)}} \]

   8. Simplified 39.6%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(-y\right)}} \]
   9. Step-by-step derivation

      1. frac-2neg 39.6%

         \[\leadsto \color{blue}{\frac{-x}{-z \cdot \left(-y\right)}} \]

      2. div-inv 39.6%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{-z \cdot \left(-y\right)}} \]

      3. add-sqr-sqrt 17.6%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      4. sqrt-unprod 43.4%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      5. sqr-neg 43.4%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      6. sqrt-unprod 17.2%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      7. add-sqr-sqrt 32.9%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      8. distribute-rgt-neg-out 32.9%

         \[\leadsto x \cdot \frac{1}{-\color{blue}{\left(-z \cdot y\right)}} \]

      9. remove-double-neg 32.9%

         \[\leadsto x \cdot \frac{1}{\color{blue}{z \cdot y}} \]

      10. add-sqr-sqrt 12.3%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}} \]

      11. sqrt-unprod 35.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\sqrt{y \cdot y}}} \]

      12. sqr-neg 35.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}} \]

      13. sqrt-unprod 24.6%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}} \]

      14. add-sqr-sqrt 39.6%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(-y\right)}} \]

      15. *-commutative 39.6%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(-y\right) \cdot z}} \]

      16. add-sqr-sqrt 24.6%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot z} \]

      17. sqrt-unprod 35.7%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot z} \]

      18. sqr-neg 35.7%

          \[\leadsto x \cdot \frac{1}{\sqrt{\color{blue}{y \cdot y}} \cdot z} \]

      19. sqrt-unprod 12.3%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot z} \]

      20. add-sqr-sqrt 32.9%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y} \cdot z} \]

   10. Applied egg-rr 32.9%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot z}} \]
   11. Step-by-step derivation

       1. associate-*r/ 32.9%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y \cdot z}} \]

       2. *-rgt-identity 32.9%

          \[\leadsto \frac{\color{blue}{x}}{y \cdot z} \]

   12. Simplified 32.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z}} \]

   if -8.00000000000000055e174 < z < 7.80000000000000049e-7

   1. Initial program 91.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 48.8%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+174} \lor \neg \left(z \leq 7.8 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+178}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 0.16:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

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 -1.55e+178)
   (/ x (* z y))
   (if (<= z 0.16) (/ (/ x t) y) (/ (/ x z) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+178) {
		tmp = x / (z * y);
	} else if (z <= 0.16) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / 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 <= (-1.55d+178)) then
        tmp = x / (z * y)
    else if (z <= 0.16d0) then
        tmp = (x / t) / y
    else
        tmp = (x / 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 <= -1.55e+178) {
		tmp = x / (z * y);
	} else if (z <= 0.16) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e+178:
		tmp = x / (z * y)
	elif z <= 0.16:
		tmp = (x / t) / y
	else:
		tmp = (x / 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 <= -1.55e+178)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 0.16)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / 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 <= -1.55e+178)
		tmp = x / (z * y);
	elseif (z <= 0.16)
		tmp = (x / t) / y;
	else
		tmp = (x / 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, -1.55e+178], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.16], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999996e178

   1. Initial program 90.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

      3. div-inv 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{t - z}\right)} \cdot \frac{1}{y - z} \]

      4. associate-*l* 90.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   4. Applied egg-rr 90.2%

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   5. Taylor expanded in t around 0 90.2%

      \[\leadsto x \cdot \color{blue}{\frac{-1}{z \cdot \left(y - z\right)}} \]

   6. Taylor expanded in z around 0 59.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.9%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. distribute-neg-frac2 59.9%

         \[\leadsto \color{blue}{\frac{x}{-y \cdot z}} \]

      3. *-commutative 59.9%

         \[\leadsto \frac{x}{-\color{blue}{z \cdot y}} \]

      4. distribute-rgt-neg-out 59.9%

         \[\leadsto \frac{x}{\color{blue}{z \cdot \left(-y\right)}} \]

   8. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(-y\right)}} \]
   9. Step-by-step derivation

      1. frac-2neg 59.9%

         \[\leadsto \color{blue}{\frac{-x}{-z \cdot \left(-y\right)}} \]

      2. div-inv 59.9%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{-z \cdot \left(-y\right)}} \]

      3. add-sqr-sqrt 22.4%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      4. sqrt-unprod 59.4%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      5. sqr-neg 59.4%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      6. sqrt-unprod 37.5%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      7. add-sqr-sqrt 59.8%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      8. distribute-rgt-neg-out 59.8%

         \[\leadsto x \cdot \frac{1}{-\color{blue}{\left(-z \cdot y\right)}} \]

      9. remove-double-neg 59.8%

         \[\leadsto x \cdot \frac{1}{\color{blue}{z \cdot y}} \]

      10. add-sqr-sqrt 17.0%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}} \]

      11. sqrt-unprod 59.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\sqrt{y \cdot y}}} \]

      12. sqr-neg 59.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}} \]

      13. sqrt-unprod 42.8%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}} \]

      14. add-sqr-sqrt 59.9%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(-y\right)}} \]

      15. *-commutative 59.9%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(-y\right) \cdot z}} \]

      16. add-sqr-sqrt 42.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot z} \]

      17. sqrt-unprod 59.7%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot z} \]

      18. sqr-neg 59.7%

          \[\leadsto x \cdot \frac{1}{\sqrt{\color{blue}{y \cdot y}} \cdot z} \]

      19. sqrt-unprod 17.0%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot z} \]

      20. add-sqr-sqrt 59.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y} \cdot z} \]

   10. Applied egg-rr 59.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot z}} \]
   11. Step-by-step derivation

       1. associate-*r/ 59.8%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y \cdot z}} \]

       2. *-rgt-identity 59.8%

          \[\leadsto \frac{\color{blue}{x}}{y \cdot z} \]

   12. Simplified 59.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z}} \]

   if -1.54999999999999996e178 < z < 0.160000000000000003

   1. Initial program 91.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 93.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 93.7%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 93.9%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 94.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 94.1%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 94.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 94.4%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 94.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 94.4%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in z around 0 48.3%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 52.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 52.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 0.160000000000000003 < z

   1. Initial program 90.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   5. Taylor expanded in y around inf 46.8%

      \[\leadsto \frac{x}{t - z} \cdot \color{blue}{\frac{1}{y}} \]

   6. Taylor expanded in t around 0 44.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{z}\right)} \cdot \frac{1}{y} \]
   7. Step-by-step derivation

      1. associate-*r/ 83.6%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

      2. neg-mul-1 83.6%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   8. Simplified 44.5%

      \[\leadsto \color{blue}{\frac{-x}{z}} \cdot \frac{1}{y} \]
   9. Step-by-step derivation

      1. un-div-inv 44.5%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y}} \]

      2. distribute-frac-neg 44.5%

         \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{y} \]

      3. distribute-frac-neg 44.5%

         \[\leadsto \color{blue}{-\frac{\frac{x}{z}}{y}} \]

      4. distribute-frac-neg2 44.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{-y}} \]

      5. add-sqr-sqrt 25.3%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

      6. sqrt-unprod 29.0%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

      7. sqr-neg 29.0%

         \[\leadsto \frac{\frac{x}{z}}{\sqrt{\color{blue}{y \cdot y}}} \]

      8. sqrt-unprod 15.7%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

      9. add-sqr-sqrt 34.6%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{y}} \]

   10. Applied egg-rr 34.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+178}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 0.16:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+180)
   (/ x (* z y))
   (if (<= z 5.6e-39) (/ (/ x t) y) (/ (/ x z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+180) {
		tmp = x / (z * y);
	} else if (z <= 5.6e-39) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1d+180)) then
        tmp = x / (z * y)
    else if (z <= 5.6d-39) then
        tmp = (x / t) / y
    else
        tmp = (x / z) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+180) {
		tmp = x / (z * y);
	} else if (z <= 5.6e-39) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1e+180:
		tmp = x / (z * y)
	elif z <= 5.6e-39:
		tmp = (x / t) / y
	else:
		tmp = (x / z) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+180)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 5.6e-39)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / z) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e+180)
		tmp = x / (z * y);
	elseif (z <= 5.6e-39)
		tmp = (x / t) / y;
	else
		tmp = (x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1e+180], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-39], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e180

   1. Initial program 90.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

      3. div-inv 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{t - z}\right)} \cdot \frac{1}{y - z} \]

      4. associate-*l* 90.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   4. Applied egg-rr 90.2%

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   5. Taylor expanded in t around 0 90.2%

      \[\leadsto x \cdot \color{blue}{\frac{-1}{z \cdot \left(y - z\right)}} \]

   6. Taylor expanded in z around 0 59.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.9%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. distribute-neg-frac2 59.9%

         \[\leadsto \color{blue}{\frac{x}{-y \cdot z}} \]

      3. *-commutative 59.9%

         \[\leadsto \frac{x}{-\color{blue}{z \cdot y}} \]

      4. distribute-rgt-neg-out 59.9%

         \[\leadsto \frac{x}{\color{blue}{z \cdot \left(-y\right)}} \]

   8. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(-y\right)}} \]
   9. Step-by-step derivation

      1. frac-2neg 59.9%

         \[\leadsto \color{blue}{\frac{-x}{-z \cdot \left(-y\right)}} \]

      2. div-inv 59.9%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{-z \cdot \left(-y\right)}} \]

      3. add-sqr-sqrt 22.4%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      4. sqrt-unprod 59.4%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      5. sqr-neg 59.4%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      6. sqrt-unprod 37.5%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      7. add-sqr-sqrt 59.8%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      8. distribute-rgt-neg-out 59.8%

         \[\leadsto x \cdot \frac{1}{-\color{blue}{\left(-z \cdot y\right)}} \]

      9. remove-double-neg 59.8%

         \[\leadsto x \cdot \frac{1}{\color{blue}{z \cdot y}} \]

      10. add-sqr-sqrt 17.0%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}} \]

      11. sqrt-unprod 59.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\sqrt{y \cdot y}}} \]

      12. sqr-neg 59.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}} \]

      13. sqrt-unprod 42.8%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}} \]

      14. add-sqr-sqrt 59.9%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(-y\right)}} \]

      15. *-commutative 59.9%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(-y\right) \cdot z}} \]

      16. add-sqr-sqrt 42.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot z} \]

      17. sqrt-unprod 59.7%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot z} \]

      18. sqr-neg 59.7%

          \[\leadsto x \cdot \frac{1}{\sqrt{\color{blue}{y \cdot y}} \cdot z} \]

      19. sqrt-unprod 17.0%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot z} \]

      20. add-sqr-sqrt 59.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y} \cdot z} \]

   10. Applied egg-rr 59.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot z}} \]
   11. Step-by-step derivation

       1. associate-*r/ 59.8%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y \cdot z}} \]

       2. *-rgt-identity 59.8%

          \[\leadsto \frac{\color{blue}{x}}{y \cdot z} \]

   12. Simplified 59.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z}} \]

   if -1e180 < z < 5.6000000000000003e-39

   1. Initial program 91.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 93.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 93.5%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 93.5%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 94.3%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 94.4%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 94.4%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 94.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 94.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 94.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in z around 0 50.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 54.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 54.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 5.6000000000000003e-39 < z

   1. Initial program 90.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 40.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 35.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 35.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 35.5%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 35.5%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 16.5%

         \[\leadsto \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t \cdot z} \]

      2. sqrt-unprod 34.6%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t \cdot z} \]

      3. sqr-neg 34.6%

         \[\leadsto \frac{\sqrt{\color{blue}{x \cdot x}}}{t \cdot z} \]

      4. sqrt-unprod 14.2%

         \[\leadsto \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t \cdot z} \]

      5. add-sqr-sqrt 26.1%

         \[\leadsto \frac{\color{blue}{x}}{t \cdot z} \]

      6. *-un-lft-identity 26.1%

         \[\leadsto \color{blue}{1 \cdot \frac{x}{t \cdot z}} \]

      7. associate-/r* 24.9%

         \[\leadsto 1 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   10. Applied egg-rr 24.9%

       \[\leadsto \color{blue}{1 \cdot \frac{\frac{x}{t}}{z}} \]
   11. Step-by-step derivation

       1. *-lft-identity 24.9%

          \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z}} \]

       2. associate-/r* 26.1%

          \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]

       3. *-lft-identity 26.1%

          \[\leadsto \frac{\color{blue}{1 \cdot x}}{t \cdot z} \]

       4. times-frac 32.5%

          \[\leadsto \color{blue}{\frac{1}{t} \cdot \frac{x}{z}} \]

       5. associate-*l/ 32.5%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{z}}{t}} \]

       6. *-lft-identity 32.5%

          \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{t} \]

   12. Simplified 32.5%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+178}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e+178)
   (/ x (* z y))
   (if (<= z 7.2e+44) (/ (/ x t) y) (/ x (* t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+178) {
		tmp = x / (z * y);
	} else if (z <= 7.2e+44) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (t * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.55d+178)) then
        tmp = x / (z * y)
    else if (z <= 7.2d+44) then
        tmp = (x / t) / y
    else
        tmp = x / (t * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+178) {
		tmp = x / (z * y);
	} else if (z <= 7.2e+44) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (t * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e+178:
		tmp = x / (z * y)
	elif z <= 7.2e+44:
		tmp = (x / t) / y
	else:
		tmp = x / (t * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e+178)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 7.2e+44)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(t * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.55e+178)
		tmp = x / (z * y);
	elseif (z <= 7.2e+44)
		tmp = (x / t) / y;
	else
		tmp = x / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.55e+178], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+44], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999996e178

   1. Initial program 90.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

      3. div-inv 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{t - z}\right)} \cdot \frac{1}{y - z} \]

      4. associate-*l* 90.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   4. Applied egg-rr 90.2%

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   5. Taylor expanded in t around 0 90.2%

      \[\leadsto x \cdot \color{blue}{\frac{-1}{z \cdot \left(y - z\right)}} \]

   6. Taylor expanded in z around 0 59.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.9%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. distribute-neg-frac2 59.9%

         \[\leadsto \color{blue}{\frac{x}{-y \cdot z}} \]

      3. *-commutative 59.9%

         \[\leadsto \frac{x}{-\color{blue}{z \cdot y}} \]

      4. distribute-rgt-neg-out 59.9%

         \[\leadsto \frac{x}{\color{blue}{z \cdot \left(-y\right)}} \]

   8. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(-y\right)}} \]
   9. Step-by-step derivation

      1. frac-2neg 59.9%

         \[\leadsto \color{blue}{\frac{-x}{-z \cdot \left(-y\right)}} \]

      2. div-inv 59.9%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{-z \cdot \left(-y\right)}} \]

      3. add-sqr-sqrt 22.4%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      4. sqrt-unprod 59.4%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      5. sqr-neg 59.4%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      6. sqrt-unprod 37.5%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      7. add-sqr-sqrt 59.8%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      8. distribute-rgt-neg-out 59.8%

         \[\leadsto x \cdot \frac{1}{-\color{blue}{\left(-z \cdot y\right)}} \]

      9. remove-double-neg 59.8%

         \[\leadsto x \cdot \frac{1}{\color{blue}{z \cdot y}} \]

      10. add-sqr-sqrt 17.0%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}} \]

      11. sqrt-unprod 59.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\sqrt{y \cdot y}}} \]

      12. sqr-neg 59.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}} \]

      13. sqrt-unprod 42.8%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}} \]

      14. add-sqr-sqrt 59.9%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(-y\right)}} \]

      15. *-commutative 59.9%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(-y\right) \cdot z}} \]

      16. add-sqr-sqrt 42.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot z} \]

      17. sqrt-unprod 59.7%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot z} \]

      18. sqr-neg 59.7%

          \[\leadsto x \cdot \frac{1}{\sqrt{\color{blue}{y \cdot y}} \cdot z} \]

      19. sqrt-unprod 17.0%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot z} \]

      20. add-sqr-sqrt 59.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y} \cdot z} \]

   10. Applied egg-rr 59.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot z}} \]
   11. Step-by-step derivation

       1. associate-*r/ 59.8%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y \cdot z}} \]

       2. *-rgt-identity 59.8%

          \[\leadsto \frac{\color{blue}{x}}{y \cdot z} \]

   12. Simplified 59.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z}} \]

   if -1.54999999999999996e178 < z < 7.2e44

   1. Initial program 91.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 94.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 94.2%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. associate-*l/ 94.3%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{y - z}}{t - z}} \]

      2. div-inv 94.5%

         \[\leadsto \frac{\color{blue}{\frac{x}{y - z}}}{t - z} \]

      3. div-inv 94.4%

         \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

      4. clear-num 94.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{y - z}{x}}} \cdot \frac{1}{t - z} \]

      5. associate-*l/ 94.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{t - z}}{\frac{y - z}{x}}} \]

      6. *-un-lft-identity 94.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{t - z}}}{\frac{y - z}{x}} \]

   6. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{\frac{\frac{1}{t - z}}{\frac{y - z}{x}}} \]

   7. Taylor expanded in z around 0 45.2%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 49.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 49.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 7.2e44 < z

   1. Initial program 89.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 99.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 41.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 38.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 38.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 38.8%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 38.8%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 17.9%

         \[\leadsto \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t \cdot z} \]

      2. sqrt-unprod 42.0%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t \cdot z} \]

      3. sqr-neg 42.0%

         \[\leadsto \frac{\sqrt{\color{blue}{x \cdot x}}}{t \cdot z} \]

      4. sqrt-unprod 17.7%

         \[\leadsto \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t \cdot z} \]

      5. add-sqr-sqrt 32.6%

         \[\leadsto \frac{\color{blue}{x}}{t \cdot z} \]

      6. *-un-lft-identity 32.6%

         \[\leadsto \color{blue}{1 \cdot \frac{x}{t \cdot z}} \]

      7. associate-/r* 31.1%

         \[\leadsto 1 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   10. Applied egg-rr 31.1%

       \[\leadsto \color{blue}{1 \cdot \frac{\frac{x}{t}}{z}} \]
   11. Step-by-step derivation

       1. *-lft-identity 31.1%

          \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z}} \]

       2. associate-/l/ 32.6%

          \[\leadsto \color{blue}{\frac{x}{z \cdot t}} \]

   12. Simplified 32.6%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+178}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-152}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.9e+174)
   (/ x (* z y))
   (if (<= z 1.66e-152) (/ x (* t y)) (/ x (* t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.9e+174) {
		tmp = x / (z * y);
	} else if (z <= 1.66e-152) {
		tmp = x / (t * y);
	} else {
		tmp = x / (t * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.9d+174)) then
        tmp = x / (z * y)
    else if (z <= 1.66d-152) then
        tmp = x / (t * y)
    else
        tmp = x / (t * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.9e+174) {
		tmp = x / (z * y);
	} else if (z <= 1.66e-152) {
		tmp = x / (t * y);
	} else {
		tmp = x / (t * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.9e+174:
		tmp = x / (z * y)
	elif z <= 1.66e-152:
		tmp = x / (t * y)
	else:
		tmp = x / (t * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.9e+174)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 1.66e-152)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = Float64(x / Float64(t * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.9e+174)
		tmp = x / (z * y);
	elseif (z <= 1.66e-152)
		tmp = x / (t * y);
	else
		tmp = x / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -6.9e+174], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.66e-152], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9000000000000002e174

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 100.0%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

      3. div-inv 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{t - z}\right)} \cdot \frac{1}{y - z} \]

      4. associate-*l* 87.3%

         \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   4. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{t - z} \cdot \frac{1}{y - z}\right)} \]

   5. Taylor expanded in t around 0 87.3%

      \[\leadsto x \cdot \color{blue}{\frac{-1}{z \cdot \left(y - z\right)}} \]

   6. Taylor expanded in z around 0 56.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 56.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. distribute-neg-frac2 56.6%

         \[\leadsto \color{blue}{\frac{x}{-y \cdot z}} \]

      3. *-commutative 56.6%

         \[\leadsto \frac{x}{-\color{blue}{z \cdot y}} \]

      4. distribute-rgt-neg-out 56.6%

         \[\leadsto \frac{x}{\color{blue}{z \cdot \left(-y\right)}} \]

   8. Simplified 56.6%

      \[\leadsto \color{blue}{\frac{x}{z \cdot \left(-y\right)}} \]
   9. Step-by-step derivation

      1. frac-2neg 56.6%

         \[\leadsto \color{blue}{\frac{-x}{-z \cdot \left(-y\right)}} \]

      2. div-inv 56.6%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{-z \cdot \left(-y\right)}} \]

      3. add-sqr-sqrt 19.5%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      4. sqrt-unprod 60.5%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      5. sqr-neg 60.5%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      6. sqrt-unprod 37.0%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      7. add-sqr-sqrt 56.5%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{-z \cdot \left(-y\right)} \]

      8. distribute-rgt-neg-out 56.5%

         \[\leadsto x \cdot \frac{1}{-\color{blue}{\left(-z \cdot y\right)}} \]

      9. remove-double-neg 56.5%

         \[\leadsto x \cdot \frac{1}{\color{blue}{z \cdot y}} \]

      10. add-sqr-sqrt 14.7%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}} \]

      11. sqrt-unprod 56.2%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\sqrt{y \cdot y}}} \]

      12. sqr-neg 56.2%

          \[\leadsto x \cdot \frac{1}{z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}} \]

      13. sqrt-unprod 41.8%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}} \]

      14. add-sqr-sqrt 56.6%

          \[\leadsto x \cdot \frac{1}{z \cdot \color{blue}{\left(-y\right)}} \]

      15. *-commutative 56.6%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(-y\right) \cdot z}} \]

      16. add-sqr-sqrt 41.8%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot z} \]

      17. sqrt-unprod 56.2%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot z} \]

      18. sqr-neg 56.2%

          \[\leadsto x \cdot \frac{1}{\sqrt{\color{blue}{y \cdot y}} \cdot z} \]

      19. sqrt-unprod 14.7%

          \[\leadsto x \cdot \frac{1}{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot z} \]

      20. add-sqr-sqrt 56.5%

          \[\leadsto x \cdot \frac{1}{\color{blue}{y} \cdot z} \]

   10. Applied egg-rr 56.5%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot z}} \]
   11. Step-by-step derivation

       1. associate-*r/ 56.5%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y \cdot z}} \]

       2. *-rgt-identity 56.5%

          \[\leadsto \frac{\color{blue}{x}}{y \cdot z} \]

   12. Simplified 56.5%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z}} \]

   if -6.9000000000000002e174 < z < 1.6599999999999999e-152

   1. Initial program 92.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 52.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if 1.6599999999999999e-152 < z

   1. Initial program 89.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 98.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 43.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 35.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 35.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 35.1%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 35.1%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   9. Step-by-step derivation

      1. add-sqr-sqrt 17.0%

         \[\leadsto \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{t \cdot z} \]

      2. sqrt-unprod 32.5%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{t \cdot z} \]

      3. sqr-neg 32.5%

         \[\leadsto \frac{\sqrt{\color{blue}{x \cdot x}}}{t \cdot z} \]

      4. sqrt-unprod 13.1%

         \[\leadsto \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{t \cdot z} \]

      5. add-sqr-sqrt 24.4%

         \[\leadsto \frac{\color{blue}{x}}{t \cdot z} \]

      6. *-un-lft-identity 24.4%

         \[\leadsto \color{blue}{1 \cdot \frac{x}{t \cdot z}} \]

      7. associate-/r* 23.4%

         \[\leadsto 1 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   10. Applied egg-rr 23.4%

       \[\leadsto \color{blue}{1 \cdot \frac{\frac{x}{t}}{z}} \]
   11. Step-by-step derivation

       1. *-lft-identity 23.4%

          \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z}} \]

       2. associate-/l/ 24.4%

          \[\leadsto \color{blue}{\frac{x}{z \cdot t}} \]

   12. Simplified 24.4%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-152}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 90.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e+190) (/ (/ x y) (- t z)) (/ x (* (- t z) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+190) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d+190)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((t - z) * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+190) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e+190:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((t - z) * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e+190)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e+190)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((t - z) * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e+190], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e190

   1. Initial program 83.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.3%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}} \]
   4. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   6. Taylor expanded in y around inf 100.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{t - z} \]

   if -1.65e190 < y

   1. Initial program 91.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{t \cdot y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* t y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (t * y)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (t * y)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(t * y))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (t * y);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.8%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 36.6%

   \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
4. Add Preprocessing

Developer target: 87.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))