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

Percentage Accurate: 88.5% → 97.0%

Time: 15.9s

Alternatives: 22

Speedup: 0.6×

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: 88.5% 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: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

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 (<= (* (- y z) (- t z)) 1e-107)
   (/ (/ x (- y z)) (- 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 - z) * (t - z)) <= 1e-107) {
		tmp = (x / (y - z)) / (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 - z) * (t - z)) <= 1d-107) then
        tmp = (x / (y - z)) / (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 - z) * (t - z)) <= 1e-107) {
		tmp = (x / (y - z)) / (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 - z) * (t - z)) <= 1e-107:
		tmp = (x / (y - z)) / (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 (Float64(Float64(y - z) * Float64(t - z)) <= 1e-107)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(x / 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 - z) * (t - z)) <= 1e-107)
		tmp = (x / (y - z)) / (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[N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], 1e-107], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 1e-107

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0 94.0%

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

      1. associate-/l/ 94.9%

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

   5. Simplified 94.9%

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

   if 1e-107 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 93.4%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

Alternative 2: 81.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;y \leq -7.4:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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))))
   (if (<= y -7.4)
     (/ (/ x y) (- t z))
     (if (<= y -3.3e-46)
       t_1
       (if (<= y -3.8e-71)
         (/ x (* (- y z) t))
         (if (<= y -1.7e-229)
           (* (/ x (- t z)) (/ -1.0 z))
           (if (<= y 5.5e-278)
             (/ x (* z (- z t)))
             (if (<= y 9.5e-154) t_1 (/ (/ 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 - t);
	double tmp;
	if (y <= -7.4) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3.3e-46) {
		tmp = t_1;
	} else if (y <= -3.8e-71) {
		tmp = x / ((y - z) * t);
	} else if (y <= -1.7e-229) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} else if (y <= 5.5e-278) {
		tmp = x / (z * (z - t));
	} else if (y <= 9.5e-154) {
		tmp = t_1;
	} 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 / z) / (z - t)
    if (y <= (-7.4d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-3.3d-46)) then
        tmp = t_1
    else if (y <= (-3.8d-71)) then
        tmp = x / ((y - z) * t)
    else if (y <= (-1.7d-229)) then
        tmp = (x / (t - z)) * ((-1.0d0) / z)
    else if (y <= 5.5d-278) then
        tmp = x / (z * (z - t))
    else if (y <= 9.5d-154) then
        tmp = t_1
    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 - t);
	double tmp;
	if (y <= -7.4) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3.3e-46) {
		tmp = t_1;
	} else if (y <= -3.8e-71) {
		tmp = x / ((y - z) * t);
	} else if (y <= -1.7e-229) {
		tmp = (x / (t - z)) * (-1.0 / z);
	} else if (y <= 5.5e-278) {
		tmp = x / (z * (z - t));
	} else if (y <= 9.5e-154) {
		tmp = t_1;
	} 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)
	tmp = 0
	if y <= -7.4:
		tmp = (x / y) / (t - z)
	elif y <= -3.3e-46:
		tmp = t_1
	elif y <= -3.8e-71:
		tmp = x / ((y - z) * t)
	elif y <= -1.7e-229:
		tmp = (x / (t - z)) * (-1.0 / z)
	elif y <= 5.5e-278:
		tmp = x / (z * (z - t))
	elif y <= 9.5e-154:
		tmp = t_1
	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) / Float64(z - t))
	tmp = 0.0
	if (y <= -7.4)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -3.3e-46)
		tmp = t_1;
	elseif (y <= -3.8e-71)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (y <= -1.7e-229)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(-1.0 / z));
	elseif (y <= 5.5e-278)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	elseif (y <= 9.5e-154)
		tmp = t_1;
	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);
	tmp = 0.0;
	if (y <= -7.4)
		tmp = (x / y) / (t - z);
	elseif (y <= -3.3e-46)
		tmp = t_1;
	elseif (y <= -3.8e-71)
		tmp = x / ((y - z) * t);
	elseif (y <= -1.7e-229)
		tmp = (x / (t - z)) * (-1.0 / z);
	elseif (y <= 5.5e-278)
		tmp = x / (z * (z - t));
	elseif (y <= 9.5e-154)
		tmp = t_1;
	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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-46], t$95$1, If[LessEqual[y, -3.8e-71], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-229], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-278], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-154], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -7.4000000000000004

   1. Initial program 88.6%

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

      1. associate-/l/ 98.3%

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

      2. div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

      1. clear-num 98.2%

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

      2. associate-*l/ 98.4%

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

      3. *-un-lft-identity 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in y around inf 84.4%

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

      1. associate-/r* 89.0%

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

   9. Simplified 89.0%

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

   if -7.4000000000000004 < y < -3.30000000000000013e-46 or 5.49999999999999989e-278 < y < 9.50000000000000057e-154

   1. Initial program 93.2%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. associate-*r/ 82.4%

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

      2. neg-mul-1 82.4%

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

   5. Simplified 82.4%

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

      1. div-inv 82.4%

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

      2. add-sqr-sqrt 36.5%

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

      3. sqrt-unprod 44.1%

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

      4. sqr-neg 44.1%

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

      5. sqrt-unprod 16.5%

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

      6. add-sqr-sqrt 29.5%

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

      7. associate-/r* 29.5%

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

   7. Applied egg-rr 29.5%

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

      1. *-commutative 29.5%

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

      2. associate-*l/ 29.5%

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

      3. associate-*r/ 29.4%

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

      4. associate-*l/ 29.4%

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

      5. *-lft-identity 29.4%

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

   9. Simplified 29.4%

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

       1. frac-2neg 29.4%

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

       2. div-inv 29.4%

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

       3. distribute-neg-frac2 29.4%

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

       4. sub-neg 29.4%

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

       5. distribute-neg-in 29.4%

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

       6. remove-double-neg 29.4%

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

       7. add-sqr-sqrt 13.4%

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

       8. sqrt-unprod 55.9%

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

       9. sqr-neg 55.9%

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

       10. sqrt-unprod 45.4%

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

       11. add-sqr-sqrt 88.2%

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

   11. Applied egg-rr 88.2%

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

       1. associate-*l/ 88.1%

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

       2. associate-*r/ 88.2%

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

       3. *-rgt-identity 88.2%

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

       4. +-commutative 88.2%

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

       5. unsub-neg 88.2%

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

   13. Simplified 88.2%

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

   if -3.30000000000000013e-46 < y < -3.79999999999999992e-71

   1. Initial program 99.5%

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

   3. Taylor expanded in t around inf 83.7%

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

   if -3.79999999999999992e-71 < y < -1.7e-229

   1. Initial program 95.5%

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

      1. associate-/l/ 97.3%

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

      2. div-inv 97.4%

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in y around 0 92.2%

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

   if -1.7e-229 < y < 5.49999999999999989e-278

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 95.8%

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

      1. associate-*r/ 95.8%

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

      2. neg-mul-1 95.8%

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

   5. Simplified 95.8%

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

      1. div-inv 95.7%

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

      2. add-sqr-sqrt 43.3%

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

      3. sqrt-unprod 63.4%

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

      4. sqr-neg 63.4%

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

      5. sqrt-unprod 33.9%

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

      6. add-sqr-sqrt 53.2%

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

      7. associate-/r* 53.2%

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

   7. Applied egg-rr 53.2%

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

      1. *-commutative 53.2%

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

      2. associate-*l/ 53.2%

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

      3. associate-*r/ 53.3%

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

      4. associate-*l/ 53.3%

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

      5. *-lft-identity 53.3%

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

   9. Simplified 53.3%

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

       1. frac-2neg 53.3%

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

       2. div-inv 53.3%

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

       3. distribute-neg-frac2 53.3%

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

       4. sub-neg 53.3%

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

       5. distribute-neg-in 53.3%

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

       6. remove-double-neg 53.3%

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

       7. add-sqr-sqrt 38.5%

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

       8. sqrt-unprod 63.1%

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

       9. sqr-neg 63.1%

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

       10. sqrt-unprod 24.9%

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

       11. add-sqr-sqrt 91.5%

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

   11. Applied egg-rr 91.5%

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

       1. associate-*l/ 86.5%

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

       2. associate-*r/ 86.6%

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

       3. *-rgt-identity 86.6%

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

       4. +-commutative 86.6%

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

       5. unsub-neg 86.6%

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

   13. Simplified 86.6%

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

   14. Taylor expanded in x around 0 95.8%

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

   if 9.50000000000000057e-154 < 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/ 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around inf 60.2%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e+42)
   (/ (/ x z) z)
   (if (<= z -8e-15)
     (/ (/ x y) t)
     (if (<= z -2.8e-15)
       (* (/ x z) (/ 1.0 z))
       (if (<= z 7e-120)
         (/ (/ x t) y)
         (if (<= z 2.15e-16)
           (/ (/ x (- y)) z)
           (if (<= z 7.2e+84) (/ (/ x (- z)) t) (/ 1.0 (* z (/ z x))))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+42) {
		tmp = (x / z) / z;
	} else if (z <= -8e-15) {
		tmp = (x / y) / t;
	} else if (z <= -2.8e-15) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 7e-120) {
		tmp = (x / t) / y;
	} else if (z <= 2.15e-16) {
		tmp = (x / -y) / z;
	} else if (z <= 7.2e+84) {
		tmp = (x / -z) / t;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.5d+42)) then
        tmp = (x / z) / z
    else if (z <= (-8d-15)) then
        tmp = (x / y) / t
    else if (z <= (-2.8d-15)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 7d-120) then
        tmp = (x / t) / y
    else if (z <= 2.15d-16) then
        tmp = (x / -y) / z
    else if (z <= 7.2d+84) then
        tmp = (x / -z) / t
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+42) {
		tmp = (x / z) / z;
	} else if (z <= -8e-15) {
		tmp = (x / y) / t;
	} else if (z <= -2.8e-15) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 7e-120) {
		tmp = (x / t) / y;
	} else if (z <= 2.15e-16) {
		tmp = (x / -y) / z;
	} else if (z <= 7.2e+84) {
		tmp = (x / -z) / t;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e+42:
		tmp = (x / z) / z
	elif z <= -8e-15:
		tmp = (x / y) / t
	elif z <= -2.8e-15:
		tmp = (x / z) * (1.0 / z)
	elif z <= 7e-120:
		tmp = (x / t) / y
	elif z <= 2.15e-16:
		tmp = (x / -y) / z
	elif z <= 7.2e+84:
		tmp = (x / -z) / t
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e+42)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= -8e-15)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= -2.8e-15)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 7e-120)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.15e-16)
		tmp = Float64(Float64(x / Float64(-y)) / z);
	elseif (z <= 7.2e+84)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e+42)
		tmp = (x / z) / z;
	elseif (z <= -8e-15)
		tmp = (x / y) / t;
	elseif (z <= -2.8e-15)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 7e-120)
		tmp = (x / t) / y;
	elseif (z <= 2.15e-16)
		tmp = (x / -y) / z;
	elseif (z <= 7.2e+84)
		tmp = (x / -z) / t;
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e+42], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8e-15], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -2.8e-15], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-120], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.15e-16], N[(N[(x / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 7.2e+84], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -3.50000000000000023e42

   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 87.5%

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

      1. associate-*r/ 87.5%

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

      2. neg-mul-1 87.5%

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

   5. Simplified 87.5%

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

      1. div-inv 87.5%

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

      2. add-sqr-sqrt 43.7%

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

      3. sqrt-unprod 72.8%

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

      4. sqr-neg 72.8%

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

      5. sqrt-unprod 41.7%

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

      6. add-sqr-sqrt 74.8%

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

      7. associate-/r* 74.8%

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

   7. Applied egg-rr 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*l/ 72.7%

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

      3. associate-*r/ 72.7%

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

      4. associate-*l/ 72.7%

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

      5. *-lft-identity 72.7%

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

   9. Simplified 72.7%

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

   10. Taylor expanded in t around 0 68.6%

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

       1. associate-*r/ 92.2%

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

       2. neg-mul-1 92.2%

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

   12. Simplified 68.6%

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

       1. div-inv 68.6%

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

       2. frac-2neg 68.6%

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

       3. add-sqr-sqrt 29.0%

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

       4. sqrt-unprod 64.3%

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

       5. sqr-neg 64.3%

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

       6. sqrt-unprod 41.7%

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

       7. add-sqr-sqrt 81.5%

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

       8. distribute-neg-frac2 81.5%

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

       9. distribute-frac-neg 81.5%

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

       10. remove-double-neg 81.5%

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

   14. Applied egg-rr 81.5%

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

       1. un-div-inv 81.5%

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

   16. Applied egg-rr 81.5%

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

   if -3.50000000000000023e42 < z < -8.0000000000000006e-15

   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/ 100.0%

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

      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. clear-num 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 44.3%

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

      1. associate-/l/ 50.3%

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

   9. Simplified 50.3%

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

   if -8.0000000000000006e-15 < z < -2.80000000000000014e-15

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 98.4%

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

      1. associate-*r/ 98.4%

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

      2. neg-mul-1 98.4%

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

   5. Simplified 98.4%

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

      1. div-inv 98.4%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 0.2%

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

      4. sqr-neg 0.2%

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

      5. sqrt-unprod 0.3%

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

      6. add-sqr-sqrt 0.3%

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

      7. associate-/r* 0.3%

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

   7. Applied egg-rr 0.3%

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

      1. *-commutative 0.3%

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

      2. associate-*l/ 0.3%

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

      3. associate-*r/ 0.3%

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

      4. associate-*l/ 0.3%

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

      5. *-lft-identity 0.3%

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

   9. Simplified 0.3%

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

   10. Taylor expanded in t around 0 0.3%

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

       1. associate-*r/ 80.4%

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

       2. neg-mul-1 80.4%

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

   12. Simplified 0.3%

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

       1. div-inv 0.3%

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

       2. frac-2neg 0.3%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 6.2%

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

       5. sqr-neg 6.2%

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

       6. sqrt-unprod 80.4%

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

       7. add-sqr-sqrt 80.4%

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

       8. distribute-neg-frac2 80.4%

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

       9. distribute-frac-neg 80.4%

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

       10. remove-double-neg 80.4%

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

   14. Applied egg-rr 80.4%

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

   if -2.80000000000000014e-15 < z < 7e-120

   1. Initial program 95.0%

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

      1. associate-/l/ 92.5%

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

      2. div-inv 92.6%

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

   4. Applied egg-rr 92.6%

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

      1. clear-num 92.5%

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

      2. associate-*l/ 94.1%

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

      3. *-un-lft-identity 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in z around 0 69.1%

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

      1. associate-/r* 67.5%

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

   9. Simplified 67.5%

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

   if 7e-120 < z < 2.1499999999999999e-16

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 49.7%

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

      1. mul-1-neg 49.7%

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

      2. associate-/r* 57.0%

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

      3. distribute-neg-frac2 57.0%

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

   8. Simplified 57.0%

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

   if 2.1499999999999999e-16 < z < 7.1999999999999999e84

   1. Initial program 99.7%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 58.7%

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

   6. Taylor expanded in y around 0 45.2%

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

      1. associate-*r/ 45.2%

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

      2. mul-1-neg 45.2%

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

   8. Simplified 45.2%

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

   9. Taylor expanded in x around 0 45.2%

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

       1. mul-1-neg 45.2%

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

       2. associate-/r* 45.2%

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

       3. distribute-neg-frac2 45.2%

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

   11. Simplified 45.2%

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

   12. Taylor expanded in x around 0 45.2%

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

       1. mul-1-neg 45.2%

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

       2. *-lft-identity 45.2%

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

       3. *-commutative 45.2%

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

       4. times-frac 45.2%

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

       5. associate-*r/ 45.2%

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

       6. distribute-neg-frac2 45.2%

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

       7. associate-*l/ 45.2%

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

       8. *-lft-identity 45.2%

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

   14. Simplified 45.2%

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

   if 7.1999999999999999e84 < z

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   5. Simplified 81.3%

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

      1. div-inv 81.3%

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

      2. add-sqr-sqrt 42.3%

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

      3. sqrt-unprod 66.7%

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

      4. sqr-neg 66.7%

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

      5. sqrt-unprod 32.5%

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

      6. add-sqr-sqrt 71.3%

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

      7. associate-/r* 70.0%

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

   7. Applied egg-rr 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-*l/ 68.9%

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

      3. associate-*r/ 68.9%

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

      4. associate-*l/ 68.9%

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

      5. *-lft-identity 68.9%

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

   9. Simplified 68.9%

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

   10. Taylor expanded in t around 0 64.8%

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

       1. associate-*r/ 92.8%

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

       2. neg-mul-1 92.8%

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

   12. Simplified 64.8%

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

       1. div-inv 64.8%

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

       2. frac-2neg 64.8%

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

       3. add-sqr-sqrt 34.1%

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

       4. sqrt-unprod 66.1%

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

       5. sqr-neg 66.1%

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

       6. sqrt-unprod 38.9%

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

       7. add-sqr-sqrt 81.0%

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

       8. distribute-neg-frac2 81.0%

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

       9. distribute-frac-neg 81.0%

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

       10. remove-double-neg 81.0%

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

   14. Applied egg-rr 81.0%

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

       1. clear-num 81.0%

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

       2. frac-times 81.9%

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

       3. metadata-eval 81.9%

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

   16. Applied egg-rr 81.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) z)))
   (if (<= z -1.2e+44)
     t_1
     (if (<= z -5.6e-14)
       (/ (/ x y) t)
       (if (<= z -3e-15)
         (* (/ x z) (/ 1.0 z))
         (if (<= z 8.8e-120)
           (/ (/ x t) y)
           (if (<= z 5.5e-18)
             (/ (/ x (- y)) z)
             (if (<= z 7e+84) (/ (/ x (- z)) t) 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) / z;
	double tmp;
	if (z <= -1.2e+44) {
		tmp = t_1;
	} else if (z <= -5.6e-14) {
		tmp = (x / y) / t;
	} else if (z <= -3e-15) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 8.8e-120) {
		tmp = (x / t) / y;
	} else if (z <= 5.5e-18) {
		tmp = (x / -y) / z;
	} else if (z <= 7e+84) {
		tmp = (x / -z) / t;
	} 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) / z
    if (z <= (-1.2d+44)) then
        tmp = t_1
    else if (z <= (-5.6d-14)) then
        tmp = (x / y) / t
    else if (z <= (-3d-15)) then
        tmp = (x / z) * (1.0d0 / z)
    else if (z <= 8.8d-120) then
        tmp = (x / t) / y
    else if (z <= 5.5d-18) then
        tmp = (x / -y) / z
    else if (z <= 7d+84) then
        tmp = (x / -z) / t
    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) / z;
	double tmp;
	if (z <= -1.2e+44) {
		tmp = t_1;
	} else if (z <= -5.6e-14) {
		tmp = (x / y) / t;
	} else if (z <= -3e-15) {
		tmp = (x / z) * (1.0 / z);
	} else if (z <= 8.8e-120) {
		tmp = (x / t) / y;
	} else if (z <= 5.5e-18) {
		tmp = (x / -y) / z;
	} else if (z <= 7e+84) {
		tmp = (x / -z) / t;
	} 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) / z
	tmp = 0
	if z <= -1.2e+44:
		tmp = t_1
	elif z <= -5.6e-14:
		tmp = (x / y) / t
	elif z <= -3e-15:
		tmp = (x / z) * (1.0 / z)
	elif z <= 8.8e-120:
		tmp = (x / t) / y
	elif z <= 5.5e-18:
		tmp = (x / -y) / z
	elif z <= 7e+84:
		tmp = (x / -z) / t
	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 / z) / z)
	tmp = 0.0
	if (z <= -1.2e+44)
		tmp = t_1;
	elseif (z <= -5.6e-14)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= -3e-15)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	elseif (z <= 8.8e-120)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 5.5e-18)
		tmp = Float64(Float64(x / Float64(-y)) / z);
	elseif (z <= 7e+84)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	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) / z;
	tmp = 0.0;
	if (z <= -1.2e+44)
		tmp = t_1;
	elseif (z <= -5.6e-14)
		tmp = (x / y) / t;
	elseif (z <= -3e-15)
		tmp = (x / z) * (1.0 / z);
	elseif (z <= 8.8e-120)
		tmp = (x / t) / y;
	elseif (z <= 5.5e-18)
		tmp = (x / -y) / z;
	elseif (z <= 7e+84)
		tmp = (x / -z) / t;
	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 / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.2e+44], t$95$1, If[LessEqual[z, -5.6e-14], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -3e-15], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-120], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 5.5e-18], N[(N[(x / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 7e+84], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.20000000000000007e44 or 6.9999999999999998e84 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 84.2%

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

      1. associate-*r/ 84.2%

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

      2. neg-mul-1 84.2%

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

   5. Simplified 84.2%

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

      1. div-inv 84.2%

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

      2. add-sqr-sqrt 43.0%

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

      3. sqrt-unprod 69.5%

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

      4. sqr-neg 69.5%

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

      5. sqrt-unprod 36.8%

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

      6. add-sqr-sqrt 72.9%

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

      7. associate-/r* 72.2%

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

   7. Applied egg-rr 72.2%

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

      1. *-commutative 72.2%

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

      2. associate-*l/ 70.7%

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

      3. associate-*r/ 70.7%

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

      4. associate-*l/ 70.7%

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

      5. *-lft-identity 70.7%

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

   9. Simplified 70.7%

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

   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/ 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 66.6%

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

       1. div-inv 66.6%

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

       2. frac-2neg 66.6%

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

       3. add-sqr-sqrt 31.7%

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

       4. sqrt-unprod 65.2%

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

       5. sqr-neg 65.2%

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

       6. sqrt-unprod 40.2%

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

       7. add-sqr-sqrt 81.2%

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

       8. distribute-neg-frac2 81.2%

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

       9. distribute-frac-neg 81.2%

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

       10. remove-double-neg 81.2%

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

   14. Applied egg-rr 81.2%

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

       1. un-div-inv 81.3%

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

   16. Applied egg-rr 81.3%

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

   if -1.20000000000000007e44 < z < -5.6000000000000001e-14

   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/ 100.0%

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

      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. clear-num 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 44.3%

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

      1. associate-/l/ 50.3%

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

   9. Simplified 50.3%

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

   if -5.6000000000000001e-14 < z < -3e-15

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 98.4%

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

      1. associate-*r/ 98.4%

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

      2. neg-mul-1 98.4%

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

   5. Simplified 98.4%

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

      1. div-inv 98.4%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 0.2%

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

      4. sqr-neg 0.2%

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

      5. sqrt-unprod 0.3%

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

      6. add-sqr-sqrt 0.3%

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

      7. associate-/r* 0.3%

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

   7. Applied egg-rr 0.3%

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

      1. *-commutative 0.3%

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

      2. associate-*l/ 0.3%

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

      3. associate-*r/ 0.3%

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

      4. associate-*l/ 0.3%

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

      5. *-lft-identity 0.3%

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

   9. Simplified 0.3%

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

   10. Taylor expanded in t around 0 0.3%

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

       1. associate-*r/ 80.4%

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

       2. neg-mul-1 80.4%

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

   12. Simplified 0.3%

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

       1. div-inv 0.3%

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

       2. frac-2neg 0.3%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 6.2%

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

       5. sqr-neg 6.2%

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

       6. sqrt-unprod 80.4%

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

       7. add-sqr-sqrt 80.4%

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

       8. distribute-neg-frac2 80.4%

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

       9. distribute-frac-neg 80.4%

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

       10. remove-double-neg 80.4%

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

   14. Applied egg-rr 80.4%

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

   if -3e-15 < z < 8.8000000000000005e-120

   1. Initial program 95.0%

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

      1. associate-/l/ 92.5%

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

      2. div-inv 92.6%

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

   4. Applied egg-rr 92.6%

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

      1. clear-num 92.5%

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

      2. associate-*l/ 94.1%

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

      3. *-un-lft-identity 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in z around 0 69.1%

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

      1. associate-/r* 67.5%

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

   9. Simplified 67.5%

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

   if 8.8000000000000005e-120 < z < 5.5e-18

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 49.7%

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

      1. mul-1-neg 49.7%

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

      2. associate-/r* 57.0%

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

      3. distribute-neg-frac2 57.0%

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

   8. Simplified 57.0%

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

   if 5.5e-18 < z < 6.9999999999999998e84

   1. Initial program 99.7%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 58.7%

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

   6. Taylor expanded in y around 0 45.2%

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

      1. associate-*r/ 45.2%

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

      2. mul-1-neg 45.2%

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

   8. Simplified 45.2%

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

   9. Taylor expanded in x around 0 45.2%

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

       1. mul-1-neg 45.2%

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

       2. associate-/r* 45.2%

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

       3. distribute-neg-frac2 45.2%

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

   11. Simplified 45.2%

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

   12. Taylor expanded in x around 0 45.2%

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

       1. mul-1-neg 45.2%

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

       2. *-lft-identity 45.2%

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

       3. *-commutative 45.2%

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

       4. times-frac 45.2%

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

       5. associate-*r/ 45.2%

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

       6. distribute-neg-frac2 45.2%

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

       7. associate-*l/ 45.2%

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

       8. *-lft-identity 45.2%

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

   14. Simplified 45.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) z)))
   (if (<= z -4.5e+46)
     t_1
     (if (<= z -1.26e-11)
       (/ (/ x y) t)
       (if (<= z -7.5e-16)
         t_1
         (if (<= z 8.8e-120)
           (/ (/ x t) y)
           (if (<= z 4.1e-13)
             (/ (/ x (- y)) z)
             (if (<= z 1.18e+85) (/ (/ x (- z)) t) 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) / z;
	double tmp;
	if (z <= -4.5e+46) {
		tmp = t_1;
	} else if (z <= -1.26e-11) {
		tmp = (x / y) / t;
	} else if (z <= -7.5e-16) {
		tmp = t_1;
	} else if (z <= 8.8e-120) {
		tmp = (x / t) / y;
	} else if (z <= 4.1e-13) {
		tmp = (x / -y) / z;
	} else if (z <= 1.18e+85) {
		tmp = (x / -z) / t;
	} 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) / z
    if (z <= (-4.5d+46)) then
        tmp = t_1
    else if (z <= (-1.26d-11)) then
        tmp = (x / y) / t
    else if (z <= (-7.5d-16)) then
        tmp = t_1
    else if (z <= 8.8d-120) then
        tmp = (x / t) / y
    else if (z <= 4.1d-13) then
        tmp = (x / -y) / z
    else if (z <= 1.18d+85) then
        tmp = (x / -z) / t
    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) / z;
	double tmp;
	if (z <= -4.5e+46) {
		tmp = t_1;
	} else if (z <= -1.26e-11) {
		tmp = (x / y) / t;
	} else if (z <= -7.5e-16) {
		tmp = t_1;
	} else if (z <= 8.8e-120) {
		tmp = (x / t) / y;
	} else if (z <= 4.1e-13) {
		tmp = (x / -y) / z;
	} else if (z <= 1.18e+85) {
		tmp = (x / -z) / t;
	} 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) / z
	tmp = 0
	if z <= -4.5e+46:
		tmp = t_1
	elif z <= -1.26e-11:
		tmp = (x / y) / t
	elif z <= -7.5e-16:
		tmp = t_1
	elif z <= 8.8e-120:
		tmp = (x / t) / y
	elif z <= 4.1e-13:
		tmp = (x / -y) / z
	elif z <= 1.18e+85:
		tmp = (x / -z) / t
	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 / z) / z)
	tmp = 0.0
	if (z <= -4.5e+46)
		tmp = t_1;
	elseif (z <= -1.26e-11)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= -7.5e-16)
		tmp = t_1;
	elseif (z <= 8.8e-120)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 4.1e-13)
		tmp = Float64(Float64(x / Float64(-y)) / z);
	elseif (z <= 1.18e+85)
		tmp = Float64(Float64(x / Float64(-z)) / t);
	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) / z;
	tmp = 0.0;
	if (z <= -4.5e+46)
		tmp = t_1;
	elseif (z <= -1.26e-11)
		tmp = (x / y) / t;
	elseif (z <= -7.5e-16)
		tmp = t_1;
	elseif (z <= 8.8e-120)
		tmp = (x / t) / y;
	elseif (z <= 4.1e-13)
		tmp = (x / -y) / z;
	elseif (z <= 1.18e+85)
		tmp = (x / -z) / t;
	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 / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -4.5e+46], t$95$1, If[LessEqual[z, -1.26e-11], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -7.5e-16], t$95$1, If[LessEqual[z, 8.8e-120], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.1e-13], N[(N[(x / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.18e+85], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.5000000000000001e46 or -1.26e-11 < z < -7.5e-16 or 1.17999999999999997e85 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. neg-mul-1 84.3%

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

   5. Simplified 84.3%

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

      1. div-inv 84.3%

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

      2. add-sqr-sqrt 42.5%

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

      3. sqrt-unprod 68.8%

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

      4. sqr-neg 68.8%

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

      5. sqrt-unprod 36.4%

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

      6. add-sqr-sqrt 72.2%

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

      7. associate-/r* 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 70.0%

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

      3. associate-*r/ 70.0%

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

      4. associate-*l/ 70.0%

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

      5. *-lft-identity 70.0%

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

   9. Simplified 70.0%

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

   10. Taylor expanded in t around 0 65.9%

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

       1. associate-*r/ 92.4%

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

       2. neg-mul-1 92.4%

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

   12. Simplified 65.9%

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

       1. div-inv 65.9%

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

       2. frac-2neg 65.9%

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

       3. add-sqr-sqrt 31.4%

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

       4. sqrt-unprod 64.7%

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

       5. sqr-neg 64.7%

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

       6. sqrt-unprod 40.6%

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

       7. add-sqr-sqrt 81.2%

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

       8. distribute-neg-frac2 81.2%

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

       9. distribute-frac-neg 81.2%

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

       10. remove-double-neg 81.2%

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

   14. Applied egg-rr 81.2%

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

       1. un-div-inv 81.2%

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

   16. Applied egg-rr 81.2%

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

   if -4.5000000000000001e46 < z < -1.26e-11

   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/ 100.0%

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

      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. clear-num 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 44.3%

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

      1. associate-/l/ 50.3%

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

   9. Simplified 50.3%

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

   if -7.5e-16 < z < 8.8000000000000005e-120

   1. Initial program 95.0%

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

      1. associate-/l/ 92.5%

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

      2. div-inv 92.6%

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

   4. Applied egg-rr 92.6%

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

      1. clear-num 92.5%

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

      2. associate-*l/ 94.1%

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

      3. *-un-lft-identity 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in z around 0 69.1%

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

      1. associate-/r* 67.5%

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

   9. Simplified 67.5%

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

   if 8.8000000000000005e-120 < z < 4.1000000000000002e-13

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 49.7%

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

      1. mul-1-neg 49.7%

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

      2. associate-/r* 57.0%

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

      3. distribute-neg-frac2 57.0%

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

   8. Simplified 57.0%

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

   if 4.1000000000000002e-13 < z < 1.17999999999999997e85

   1. Initial program 99.7%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 58.7%

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

   6. Taylor expanded in y around 0 45.2%

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

      1. associate-*r/ 45.2%

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

      2. mul-1-neg 45.2%

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

   8. Simplified 45.2%

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

   9. Taylor expanded in x around 0 45.2%

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

       1. mul-1-neg 45.2%

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

       2. associate-/r* 45.2%

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

       3. distribute-neg-frac2 45.2%

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

   11. Simplified 45.2%

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

   12. Taylor expanded in x around 0 45.2%

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

       1. mul-1-neg 45.2%

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

       2. *-lft-identity 45.2%

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

       3. *-commutative 45.2%

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

       4. times-frac 45.2%

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

       5. associate-*r/ 45.2%

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

       6. distribute-neg-frac2 45.2%

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

       7. associate-*l/ 45.2%

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

       8. *-lft-identity 45.2%

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

   14. Simplified 45.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) z)))
   (if (<= z -2.6e+45)
     t_1
     (if (<= z -1.3e-13)
       (/ (/ x y) t)
       (if (<= z -3e-15)
         t_1
         (if (<= z 7e-120)
           (/ (/ x t) y)
           (if (<= z 1.4e-13)
             (/ (/ x (- y)) z)
             (if (<= z 7e+84) (/ x (- (* z t))) 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) / z;
	double tmp;
	if (z <= -2.6e+45) {
		tmp = t_1;
	} else if (z <= -1.3e-13) {
		tmp = (x / y) / t;
	} else if (z <= -3e-15) {
		tmp = t_1;
	} else if (z <= 7e-120) {
		tmp = (x / t) / y;
	} else if (z <= 1.4e-13) {
		tmp = (x / -y) / z;
	} else if (z <= 7e+84) {
		tmp = x / -(z * t);
	} 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) / z
    if (z <= (-2.6d+45)) then
        tmp = t_1
    else if (z <= (-1.3d-13)) then
        tmp = (x / y) / t
    else if (z <= (-3d-15)) then
        tmp = t_1
    else if (z <= 7d-120) then
        tmp = (x / t) / y
    else if (z <= 1.4d-13) then
        tmp = (x / -y) / z
    else if (z <= 7d+84) then
        tmp = x / -(z * t)
    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) / z;
	double tmp;
	if (z <= -2.6e+45) {
		tmp = t_1;
	} else if (z <= -1.3e-13) {
		tmp = (x / y) / t;
	} else if (z <= -3e-15) {
		tmp = t_1;
	} else if (z <= 7e-120) {
		tmp = (x / t) / y;
	} else if (z <= 1.4e-13) {
		tmp = (x / -y) / z;
	} else if (z <= 7e+84) {
		tmp = x / -(z * t);
	} 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) / z
	tmp = 0
	if z <= -2.6e+45:
		tmp = t_1
	elif z <= -1.3e-13:
		tmp = (x / y) / t
	elif z <= -3e-15:
		tmp = t_1
	elif z <= 7e-120:
		tmp = (x / t) / y
	elif z <= 1.4e-13:
		tmp = (x / -y) / z
	elif z <= 7e+84:
		tmp = x / -(z * t)
	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 / z) / z)
	tmp = 0.0
	if (z <= -2.6e+45)
		tmp = t_1;
	elseif (z <= -1.3e-13)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= -3e-15)
		tmp = t_1;
	elseif (z <= 7e-120)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.4e-13)
		tmp = Float64(Float64(x / Float64(-y)) / z);
	elseif (z <= 7e+84)
		tmp = Float64(x / Float64(-Float64(z * t)));
	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) / z;
	tmp = 0.0;
	if (z <= -2.6e+45)
		tmp = t_1;
	elseif (z <= -1.3e-13)
		tmp = (x / y) / t;
	elseif (z <= -3e-15)
		tmp = t_1;
	elseif (z <= 7e-120)
		tmp = (x / t) / y;
	elseif (z <= 1.4e-13)
		tmp = (x / -y) / z;
	elseif (z <= 7e+84)
		tmp = x / -(z * t);
	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 / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2.6e+45], t$95$1, If[LessEqual[z, -1.3e-13], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -3e-15], t$95$1, If[LessEqual[z, 7e-120], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.4e-13], N[(N[(x / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 7e+84], N[(x / (-N[(z * t), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.60000000000000007e45 or -1.3e-13 < z < -3e-15 or 6.9999999999999998e84 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. neg-mul-1 84.3%

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

   5. Simplified 84.3%

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

      1. div-inv 84.3%

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

      2. add-sqr-sqrt 42.5%

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

      3. sqrt-unprod 68.8%

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

      4. sqr-neg 68.8%

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

      5. sqrt-unprod 36.4%

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

      6. add-sqr-sqrt 72.2%

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

      7. associate-/r* 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 70.0%

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

      3. associate-*r/ 70.0%

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

      4. associate-*l/ 70.0%

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

      5. *-lft-identity 70.0%

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

   9. Simplified 70.0%

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

   10. Taylor expanded in t around 0 65.9%

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

       1. associate-*r/ 92.4%

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

       2. neg-mul-1 92.4%

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

   12. Simplified 65.9%

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

       1. div-inv 65.9%

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

       2. frac-2neg 65.9%

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

       3. add-sqr-sqrt 31.4%

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

       4. sqrt-unprod 64.7%

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

       5. sqr-neg 64.7%

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

       6. sqrt-unprod 40.6%

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

       7. add-sqr-sqrt 81.2%

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

       8. distribute-neg-frac2 81.2%

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

       9. distribute-frac-neg 81.2%

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

       10. remove-double-neg 81.2%

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

   14. Applied egg-rr 81.2%

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

       1. un-div-inv 81.2%

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

   16. Applied egg-rr 81.2%

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

   if -2.60000000000000007e45 < z < -1.3e-13

   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/ 100.0%

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

      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. clear-num 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 44.3%

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

      1. associate-/l/ 50.3%

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

   9. Simplified 50.3%

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

   if -3e-15 < z < 7e-120

   1. Initial program 95.0%

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

      1. associate-/l/ 92.5%

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

      2. div-inv 92.6%

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

   4. Applied egg-rr 92.6%

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

      1. clear-num 92.5%

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

      2. associate-*l/ 94.1%

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

      3. *-un-lft-identity 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in z around 0 69.1%

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

      1. associate-/r* 67.5%

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

   9. Simplified 67.5%

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

   if 7e-120 < z < 1.4000000000000001e-13

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around 0 49.7%

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

      1. mul-1-neg 49.7%

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

      2. associate-/r* 57.0%

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

      3. distribute-neg-frac2 57.0%

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

   8. Simplified 57.0%

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

   if 1.4000000000000001e-13 < z < 6.9999999999999998e84

   1. Initial program 99.7%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 58.7%

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

   6. Taylor expanded in y around 0 45.2%

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

      1. associate-*r/ 45.2%

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

      2. mul-1-neg 45.2%

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

   8. Simplified 45.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) z)))
   (if (<= z -6.4e+42)
     t_1
     (if (<= z -1.5e-14)
       (/ (/ x y) t)
       (if (<= z -4e-15)
         t_1
         (if (<= z 3.8e-108)
           (/ (/ x t) y)
           (if (<= z 2.5e-19)
             (/ x (* y (- z)))
             (if (<= z 1.95e+85) (/ x (- (* z t))) 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) / z;
	double tmp;
	if (z <= -6.4e+42) {
		tmp = t_1;
	} else if (z <= -1.5e-14) {
		tmp = (x / y) / t;
	} else if (z <= -4e-15) {
		tmp = t_1;
	} else if (z <= 3.8e-108) {
		tmp = (x / t) / y;
	} else if (z <= 2.5e-19) {
		tmp = x / (y * -z);
	} else if (z <= 1.95e+85) {
		tmp = x / -(z * t);
	} 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) / z
    if (z <= (-6.4d+42)) then
        tmp = t_1
    else if (z <= (-1.5d-14)) then
        tmp = (x / y) / t
    else if (z <= (-4d-15)) then
        tmp = t_1
    else if (z <= 3.8d-108) then
        tmp = (x / t) / y
    else if (z <= 2.5d-19) then
        tmp = x / (y * -z)
    else if (z <= 1.95d+85) then
        tmp = x / -(z * t)
    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) / z;
	double tmp;
	if (z <= -6.4e+42) {
		tmp = t_1;
	} else if (z <= -1.5e-14) {
		tmp = (x / y) / t;
	} else if (z <= -4e-15) {
		tmp = t_1;
	} else if (z <= 3.8e-108) {
		tmp = (x / t) / y;
	} else if (z <= 2.5e-19) {
		tmp = x / (y * -z);
	} else if (z <= 1.95e+85) {
		tmp = x / -(z * t);
	} 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) / z
	tmp = 0
	if z <= -6.4e+42:
		tmp = t_1
	elif z <= -1.5e-14:
		tmp = (x / y) / t
	elif z <= -4e-15:
		tmp = t_1
	elif z <= 3.8e-108:
		tmp = (x / t) / y
	elif z <= 2.5e-19:
		tmp = x / (y * -z)
	elif z <= 1.95e+85:
		tmp = x / -(z * t)
	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 / z) / z)
	tmp = 0.0
	if (z <= -6.4e+42)
		tmp = t_1;
	elseif (z <= -1.5e-14)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= -4e-15)
		tmp = t_1;
	elseif (z <= 3.8e-108)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.5e-19)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (z <= 1.95e+85)
		tmp = Float64(x / Float64(-Float64(z * t)));
	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) / z;
	tmp = 0.0;
	if (z <= -6.4e+42)
		tmp = t_1;
	elseif (z <= -1.5e-14)
		tmp = (x / y) / t;
	elseif (z <= -4e-15)
		tmp = t_1;
	elseif (z <= 3.8e-108)
		tmp = (x / t) / y;
	elseif (z <= 2.5e-19)
		tmp = x / (y * -z);
	elseif (z <= 1.95e+85)
		tmp = x / -(z * t);
	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 / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -6.4e+42], t$95$1, If[LessEqual[z, -1.5e-14], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -4e-15], t$95$1, If[LessEqual[z, 3.8e-108], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.5e-19], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+85], N[(x / (-N[(z * t), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.40000000000000004e42 or -1.4999999999999999e-14 < z < -4.0000000000000003e-15 or 1.95000000000000017e85 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 84.2%

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

      1. associate-*r/ 84.2%

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

      2. neg-mul-1 84.2%

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

   5. Simplified 84.2%

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

      1. div-inv 84.2%

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

      2. add-sqr-sqrt 42.0%

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

      3. sqrt-unprod 68.5%

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

      4. sqr-neg 68.5%

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

      5. sqrt-unprod 36.8%

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

      6. add-sqr-sqrt 71.9%

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

      7. associate-/r* 71.2%

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

   7. Applied egg-rr 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*l/ 69.7%

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

      3. associate-*r/ 69.7%

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

      4. associate-*l/ 69.7%

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

      5. *-lft-identity 69.7%

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

   9. Simplified 69.7%

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

   10. Taylor expanded in t around 0 65.6%

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

       1. associate-*r/ 92.3%

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

       2. neg-mul-1 92.3%

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

   12. Simplified 65.6%

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

       1. div-inv 65.6%

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

       2. frac-2neg 65.6%

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

       3. add-sqr-sqrt 30.7%

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

       4. sqrt-unprod 64.3%

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

       5. sqr-neg 64.3%

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

       6. sqrt-unprod 41.0%

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

       7. add-sqr-sqrt 81.0%

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

       8. distribute-neg-frac2 81.0%

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

       9. distribute-frac-neg 81.0%

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

       10. remove-double-neg 81.0%

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

   14. Applied egg-rr 81.0%

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

       1. un-div-inv 81.1%

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

   16. Applied egg-rr 81.1%

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

   if -6.40000000000000004e42 < z < -1.4999999999999999e-14

   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/ 100.0%

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

      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. clear-num 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 44.3%

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

      1. associate-/l/ 50.3%

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

   9. Simplified 50.3%

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

   if -4.0000000000000003e-15 < z < 3.79999999999999973e-108

   1. Initial program 95.1%

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

      1. associate-/l/ 92.7%

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

      2. div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

      1. clear-num 92.6%

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

      2. associate-*l/ 94.2%

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

      3. *-un-lft-identity 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in z around 0 69.7%

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

      1. associate-/r* 68.1%

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

   9. Simplified 68.1%

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

   if 3.79999999999999973e-108 < z < 2.5000000000000002e-19

   1. Initial program 94.9%

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

      1. associate-/l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around 0 59.5%

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

      1. associate-*r/ 59.5%

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

      2. neg-mul-1 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in z around 0 54.2%

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

      1. associate-*r/ 54.2%

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

      2. mul-1-neg 54.2%

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

      3. *-commutative 54.2%

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

   10. Simplified 54.2%

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

   if 2.5000000000000002e-19 < z < 1.95000000000000017e85

   1. Initial program 99.7%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 56.6%

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

   6. Taylor expanded in y around 0 43.7%

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

      1. associate-*r/ 43.7%

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

      2. mul-1-neg 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) z)))
   (if (<= z -2.75e+42)
     t_1
     (if (<= z -4.8e-15)
       (/ (/ x y) t)
       (if (<= z -2.8e-15)
         t_1
         (if (<= z 2.5e-65)
           (/ (/ x t) y)
           (if (<= z 7.6e+84) (/ x (- (* z t))) 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) / z;
	double tmp;
	if (z <= -2.75e+42) {
		tmp = t_1;
	} else if (z <= -4.8e-15) {
		tmp = (x / y) / t;
	} else if (z <= -2.8e-15) {
		tmp = t_1;
	} else if (z <= 2.5e-65) {
		tmp = (x / t) / y;
	} else if (z <= 7.6e+84) {
		tmp = x / -(z * t);
	} 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) / z
    if (z <= (-2.75d+42)) then
        tmp = t_1
    else if (z <= (-4.8d-15)) then
        tmp = (x / y) / t
    else if (z <= (-2.8d-15)) then
        tmp = t_1
    else if (z <= 2.5d-65) then
        tmp = (x / t) / y
    else if (z <= 7.6d+84) then
        tmp = x / -(z * t)
    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) / z;
	double tmp;
	if (z <= -2.75e+42) {
		tmp = t_1;
	} else if (z <= -4.8e-15) {
		tmp = (x / y) / t;
	} else if (z <= -2.8e-15) {
		tmp = t_1;
	} else if (z <= 2.5e-65) {
		tmp = (x / t) / y;
	} else if (z <= 7.6e+84) {
		tmp = x / -(z * t);
	} 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) / z
	tmp = 0
	if z <= -2.75e+42:
		tmp = t_1
	elif z <= -4.8e-15:
		tmp = (x / y) / t
	elif z <= -2.8e-15:
		tmp = t_1
	elif z <= 2.5e-65:
		tmp = (x / t) / y
	elif z <= 7.6e+84:
		tmp = x / -(z * t)
	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 / z) / z)
	tmp = 0.0
	if (z <= -2.75e+42)
		tmp = t_1;
	elseif (z <= -4.8e-15)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= -2.8e-15)
		tmp = t_1;
	elseif (z <= 2.5e-65)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 7.6e+84)
		tmp = Float64(x / Float64(-Float64(z * t)));
	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) / z;
	tmp = 0.0;
	if (z <= -2.75e+42)
		tmp = t_1;
	elseif (z <= -4.8e-15)
		tmp = (x / y) / t;
	elseif (z <= -2.8e-15)
		tmp = t_1;
	elseif (z <= 2.5e-65)
		tmp = (x / t) / y;
	elseif (z <= 7.6e+84)
		tmp = x / -(z * t);
	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 / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2.75e+42], t$95$1, If[LessEqual[z, -4.8e-15], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -2.8e-15], t$95$1, If[LessEqual[z, 2.5e-65], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 7.6e+84], N[(x / (-N[(z * t), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.75000000000000001e42 or -4.7999999999999999e-15 < z < -2.80000000000000014e-15 or 7.6000000000000002e84 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. neg-mul-1 84.3%

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

   5. Simplified 84.3%

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

      1. div-inv 84.3%

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

      2. add-sqr-sqrt 42.5%

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

      3. sqrt-unprod 68.8%

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

      4. sqr-neg 68.8%

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

      5. sqrt-unprod 36.4%

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

      6. add-sqr-sqrt 72.2%

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

      7. associate-/r* 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 70.0%

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

      3. associate-*r/ 70.0%

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

      4. associate-*l/ 70.0%

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

      5. *-lft-identity 70.0%

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

   9. Simplified 70.0%

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

   10. Taylor expanded in t around 0 65.9%

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

       1. associate-*r/ 92.4%

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

       2. neg-mul-1 92.4%

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

   12. Simplified 65.9%

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

       1. div-inv 65.9%

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

       2. frac-2neg 65.9%

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

       3. add-sqr-sqrt 31.4%

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

       4. sqrt-unprod 64.7%

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

       5. sqr-neg 64.7%

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

       6. sqrt-unprod 40.6%

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

       7. add-sqr-sqrt 81.2%

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

       8. distribute-neg-frac2 81.2%

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

       9. distribute-frac-neg 81.2%

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

       10. remove-double-neg 81.2%

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

   14. Applied egg-rr 81.2%

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

       1. un-div-inv 81.2%

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

   16. Applied egg-rr 81.2%

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

   if -2.75000000000000001e42 < z < -4.7999999999999999e-15

   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/ 100.0%

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

      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. clear-num 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 44.3%

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

      1. associate-/l/ 50.3%

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

   9. Simplified 50.3%

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

   if -2.80000000000000014e-15 < z < 2.49999999999999991e-65

   1. Initial program 95.5%

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

      1. associate-/l/ 93.3%

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

      2. div-inv 93.4%

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

   4. Applied egg-rr 93.4%

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

      1. clear-num 93.3%

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

      2. associate-*l/ 94.8%

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

      3. *-un-lft-identity 94.8%

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

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in z around 0 68.7%

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

      1. associate-/r* 67.9%

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

   9. Simplified 67.9%

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

   if 2.49999999999999991e-65 < z < 7.6000000000000002e84

   1. Initial program 96.8%

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

      1. associate-/l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around inf 52.2%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r/ 39.4%

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

      2. mul-1-neg 39.4%

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

   8. Simplified 39.4%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{-z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;y \leq -5:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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))))
   (if (<= y -5.0)
     (/ (/ x y) (- t z))
     (if (<= y -5.2e-46)
       t_1
       (if (<= y -8e-72)
         (/ x (* (- y z) t))
         (if (<= y 3.9e-280) t_1 (/ (/ 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 - t);
	double tmp;
	if (y <= -5.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5.2e-46) {
		tmp = t_1;
	} else if (y <= -8e-72) {
		tmp = x / ((y - z) * t);
	} else if (y <= 3.9e-280) {
		tmp = t_1;
	} 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 / z) / (z - t)
    if (y <= (-5.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-5.2d-46)) then
        tmp = t_1
    else if (y <= (-8d-72)) then
        tmp = x / ((y - z) * t)
    else if (y <= 3.9d-280) then
        tmp = t_1
    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 - t);
	double tmp;
	if (y <= -5.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5.2e-46) {
		tmp = t_1;
	} else if (y <= -8e-72) {
		tmp = x / ((y - z) * t);
	} else if (y <= 3.9e-280) {
		tmp = t_1;
	} 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)
	tmp = 0
	if y <= -5.0:
		tmp = (x / y) / (t - z)
	elif y <= -5.2e-46:
		tmp = t_1
	elif y <= -8e-72:
		tmp = x / ((y - z) * t)
	elif y <= 3.9e-280:
		tmp = t_1
	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) / Float64(z - t))
	tmp = 0.0
	if (y <= -5.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -5.2e-46)
		tmp = t_1;
	elseif (y <= -8e-72)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (y <= 3.9e-280)
		tmp = t_1;
	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);
	tmp = 0.0;
	if (y <= -5.0)
		tmp = (x / y) / (t - z);
	elseif (y <= -5.2e-46)
		tmp = t_1;
	elseif (y <= -8e-72)
		tmp = x / ((y - z) * t);
	elseif (y <= 3.9e-280)
		tmp = t_1;
	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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-46], t$95$1, If[LessEqual[y, -8e-72], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-280], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5

   1. Initial program 88.6%

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

      1. associate-/l/ 98.3%

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

      2. div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

      1. clear-num 98.2%

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

      2. associate-*l/ 98.4%

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

      3. *-un-lft-identity 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in y around inf 84.4%

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

      1. associate-/r* 89.0%

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

   9. Simplified 89.0%

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

   if -5 < y < -5.2000000000000004e-46 or -7.9999999999999997e-72 < y < 3.89999999999999998e-280

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 86.4%

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

      1. associate-*r/ 86.4%

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

      2. neg-mul-1 86.4%

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

   5. Simplified 86.4%

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

      1. div-inv 85.1%

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

      2. add-sqr-sqrt 42.5%

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

      3. sqrt-unprod 57.5%

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

      4. sqr-neg 57.5%

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

      5. sqrt-unprod 21.1%

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

      6. add-sqr-sqrt 43.7%

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

      7. associate-/r* 43.7%

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

   7. Applied egg-rr 43.7%

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

      1. *-commutative 43.7%

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

      2. associate-*l/ 43.7%

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

      3. associate-*r/ 46.7%

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

      4. associate-*l/ 46.7%

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

      5. *-lft-identity 46.7%

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

   9. Simplified 46.7%

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

       1. frac-2neg 46.7%

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

       2. div-inv 46.7%

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

       3. distribute-neg-frac2 46.7%

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

       4. sub-neg 46.7%

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

       5. distribute-neg-in 46.7%

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

       6. remove-double-neg 46.7%

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

       7. add-sqr-sqrt 19.5%

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

       8. sqrt-unprod 65.8%

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

       9. sqr-neg 65.8%

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

       10. sqrt-unprod 50.4%

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

       11. add-sqr-sqrt 89.6%

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

   11. Applied egg-rr 89.6%

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

       1. associate-*l/ 83.6%

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

       2. associate-*r/ 83.6%

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

       3. *-rgt-identity 83.6%

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

       4. +-commutative 83.6%

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

       5. unsub-neg 83.6%

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

   13. Simplified 83.6%

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

   if -5.2000000000000004e-46 < y < -7.9999999999999997e-72

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf 72.6%

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

   if 3.89999999999999998e-280 < y

   1. Initial program 94.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 60.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-280}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) t))))
   (if (<= z -3.3e+45)
     (/ x (* z (+ z t)))
     (if (<= z 1.95e-101)
       t_1
       (if (<= z 9.5e-30)
         (/ (/ x (- y)) z)
         (if (<= z 1.18e+85) t_1 (/ 1.0 (* z (/ z x)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -3.3e+45) {
		tmp = x / (z * (z + t));
	} else if (z <= 1.95e-101) {
		tmp = t_1;
	} else if (z <= 9.5e-30) {
		tmp = (x / -y) / z;
	} else if (z <= 1.18e+85) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * t)
    if (z <= (-3.3d+45)) then
        tmp = x / (z * (z + t))
    else if (z <= 1.95d-101) then
        tmp = t_1
    else if (z <= 9.5d-30) then
        tmp = (x / -y) / z
    else if (z <= 1.18d+85) then
        tmp = t_1
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -3.3e+45) {
		tmp = x / (z * (z + t));
	} else if (z <= 1.95e-101) {
		tmp = t_1;
	} else if (z <= 9.5e-30) {
		tmp = (x / -y) / z;
	} else if (z <= 1.18e+85) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * t)
	tmp = 0
	if z <= -3.3e+45:
		tmp = x / (z * (z + t))
	elif z <= 1.95e-101:
		tmp = t_1
	elif z <= 9.5e-30:
		tmp = (x / -y) / z
	elif z <= 1.18e+85:
		tmp = t_1
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -3.3e+45)
		tmp = Float64(x / Float64(z * Float64(z + t)));
	elseif (z <= 1.95e-101)
		tmp = t_1;
	elseif (z <= 9.5e-30)
		tmp = Float64(Float64(x / Float64(-y)) / z);
	elseif (z <= 1.18e+85)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * t);
	tmp = 0.0;
	if (z <= -3.3e+45)
		tmp = x / (z * (z + t));
	elseif (z <= 1.95e-101)
		tmp = t_1;
	elseif (z <= 9.5e-30)
		tmp = (x / -y) / z;
	elseif (z <= 1.18e+85)
		tmp = t_1;
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+45], N[(x / N[(z * N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-101], t$95$1, If[LessEqual[z, 9.5e-30], N[(N[(x / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.18e+85], t$95$1, N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3000000000000001e45

   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 87.5%

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

      1. associate-*r/ 87.5%

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

      2. neg-mul-1 87.5%

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

   5. Simplified 87.5%

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

      1. div-inv 87.5%

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

      2. add-sqr-sqrt 43.7%

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

      3. sqrt-unprod 72.8%

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

      4. sqr-neg 72.8%

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

      5. sqrt-unprod 41.7%

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

      6. add-sqr-sqrt 74.8%

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

      7. associate-/r* 74.8%

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

   7. Applied egg-rr 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*l/ 72.7%

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

      3. associate-*r/ 72.7%

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

      4. associate-*l/ 72.7%

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

      5. *-lft-identity 72.7%

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

   9. Simplified 72.7%

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

       1. *-un-lft-identity 72.7%

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

       2. associate-/l/ 74.8%

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

       3. sub-neg 74.8%

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

       4. distribute-rgt-in 63.9%

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

       5. add-sqr-sqrt 63.9%

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

       6. sqrt-unprod 63.9%

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

       7. sqr-neg 63.9%

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

       8. sqrt-unprod 0.0%

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

       9. add-sqr-sqrt 74.5%

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

       10. +-commutative 74.5%

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

       11. distribute-rgt-out 87.5%

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

   11. Applied egg-rr 87.5%

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

       1. *-lft-identity 87.5%

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

   13. Simplified 87.5%

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

   if -3.3000000000000001e45 < z < 1.95000000000000008e-101 or 9.49999999999999939e-30 < z < 1.17999999999999997e85

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf 72.0%

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

   if 1.95000000000000008e-101 < z < 9.49999999999999939e-30

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 69.8%

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

      1. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in t around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-/r* 58.8%

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

      3. distribute-neg-frac2 58.8%

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

   8. Simplified 58.8%

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

   if 1.17999999999999997e85 < z

   1. Initial program 84.0%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   5. Simplified 81.3%

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

      1. div-inv 81.3%

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

      2. add-sqr-sqrt 42.3%

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

      3. sqrt-unprod 66.7%

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

      4. sqr-neg 66.7%

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

      5. sqrt-unprod 32.5%

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

      6. add-sqr-sqrt 71.3%

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

      7. associate-/r* 70.0%

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

   7. Applied egg-rr 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-*l/ 68.9%

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

      3. associate-*r/ 68.9%

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

      4. associate-*l/ 68.9%

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

      5. *-lft-identity 68.9%

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

   9. Simplified 68.9%

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

   10. Taylor expanded in t around 0 64.8%

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

       1. associate-*r/ 92.8%

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

       2. neg-mul-1 92.8%

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

   12. Simplified 64.8%

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

       1. div-inv 64.8%

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

       2. frac-2neg 64.8%

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

       3. add-sqr-sqrt 34.1%

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

       4. sqrt-unprod 66.1%

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

       5. sqr-neg 66.1%

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

       6. sqrt-unprod 38.9%

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

       7. add-sqr-sqrt 81.0%

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

       8. distribute-neg-frac2 81.0%

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

       9. distribute-frac-neg 81.0%

          \[\leadsto \left(-\color{blue}{\left(-\frac{x}{z}\right)}\right) \cdot \frac{1}{z} \]

       10. remove-double-neg 81.0%

           \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{z} \]

   14. Applied egg-rr 81.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
   15. Step-by-step derivation

       1. clear-num 81.0%

          \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{1}{z} \]

       2. frac-times 81.9%

          \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{z}{x} \cdot z}} \]

       3. metadata-eval 81.9%

          \[\leadsto \frac{\color{blue}{1}}{\frac{z}{x} \cdot z} \]

   16. Applied egg-rr 81.9%

       \[\leadsto \color{blue}{\frac{1}{\frac{z}{x} \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{z \cdot \left(z + t\right)}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) t))))
   (if (<= z -4.5e+133)
     (/ (/ x z) z)
     (if (<= z 1.95e-101)
       t_1
       (if (<= z 9.2e-30)
         (/ (/ x (- y)) z)
         (if (<= z 5.6e+55) t_1 (/ 1.0 (* z (/ z x)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -4.5e+133) {
		tmp = (x / z) / z;
	} else if (z <= 1.95e-101) {
		tmp = t_1;
	} else if (z <= 9.2e-30) {
		tmp = (x / -y) / z;
	} else if (z <= 5.6e+55) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * t)
    if (z <= (-4.5d+133)) then
        tmp = (x / z) / z
    else if (z <= 1.95d-101) then
        tmp = t_1
    else if (z <= 9.2d-30) then
        tmp = (x / -y) / z
    else if (z <= 5.6d+55) then
        tmp = t_1
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * t);
	double tmp;
	if (z <= -4.5e+133) {
		tmp = (x / z) / z;
	} else if (z <= 1.95e-101) {
		tmp = t_1;
	} else if (z <= 9.2e-30) {
		tmp = (x / -y) / z;
	} else if (z <= 5.6e+55) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * t)
	tmp = 0
	if z <= -4.5e+133:
		tmp = (x / z) / z
	elif z <= 1.95e-101:
		tmp = t_1
	elif z <= 9.2e-30:
		tmp = (x / -y) / z
	elif z <= 5.6e+55:
		tmp = t_1
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -4.5e+133)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 1.95e-101)
		tmp = t_1;
	elseif (z <= 9.2e-30)
		tmp = Float64(Float64(x / Float64(-y)) / z);
	elseif (z <= 5.6e+55)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * t);
	tmp = 0.0;
	if (z <= -4.5e+133)
		tmp = (x / z) / z;
	elseif (z <= 1.95e-101)
		tmp = t_1;
	elseif (z <= 9.2e-30)
		tmp = (x / -y) / z;
	elseif (z <= 5.6e+55)
		tmp = t_1;
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+133], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.95e-101], t$95$1, If[LessEqual[z, 9.2e-30], N[(N[(x / (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.6e+55], t$95$1, N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.49999999999999985e133

   1. Initial program 99.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. neg-mul-1 99.8%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot \left(t - z\right)} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 99.8%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{z \cdot \left(t - z\right)}} \]

      2. add-sqr-sqrt 44.0%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      3. sqrt-unprod 84.2%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      4. sqr-neg 84.2%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      5. sqrt-unprod 52.1%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      6. add-sqr-sqrt 96.1%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      7. associate-/r* 96.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{z}}{t - z}} \]

   7. Applied egg-rr 96.1%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{t - z}} \]
   8. Step-by-step derivation

      1. *-commutative 96.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{t - z} \cdot x} \]

      2. associate-*l/ 96.0%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot x}{t - z}} \]

      3. associate-*r/ 96.0%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{t - z}} \]

      4. associate-*l/ 96.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{t - z}}{z}} \]

      5. *-lft-identity 96.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{z} \]

   9. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 96.0%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   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 96.0%

       \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. div-inv 96.0%

          \[\leadsto \color{blue}{\frac{-x}{z} \cdot \frac{1}{z}} \]

       2. frac-2neg 96.0%

          \[\leadsto \color{blue}{\frac{-\left(-x\right)}{-z}} \cdot \frac{1}{z} \]

       3. add-sqr-sqrt 44.0%

          \[\leadsto \frac{-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-z} \cdot \frac{1}{z} \]

       4. sqrt-unprod 88.2%

          \[\leadsto \frac{-\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{-z} \cdot \frac{1}{z} \]

       5. sqr-neg 88.2%

          \[\leadsto \frac{-\sqrt{\color{blue}{x \cdot x}}}{-z} \cdot \frac{1}{z} \]

       6. sqrt-unprod 55.9%

          \[\leadsto \frac{-\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-z} \cdot \frac{1}{z} \]

       7. add-sqr-sqrt 100.0%

          \[\leadsto \frac{-\color{blue}{x}}{-z} \cdot \frac{1}{z} \]

       8. distribute-neg-frac2 100.0%

          \[\leadsto \color{blue}{\left(-\frac{-x}{z}\right)} \cdot \frac{1}{z} \]

       9. distribute-frac-neg 100.0%

          \[\leadsto \left(-\color{blue}{\left(-\frac{x}{z}\right)}\right) \cdot \frac{1}{z} \]

       10. remove-double-neg 100.0%

           \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{z} \]

   14. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
   15. Step-by-step derivation

       1. un-div-inv 100.0%

          \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   16. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -4.49999999999999985e133 < z < 1.95000000000000008e-101 or 9.19999999999999937e-30 < z < 5.6000000000000002e55

   1. Initial program 95.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.7%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 1.95000000000000008e-101 < z < 9.19999999999999937e-30

   1. Initial program 93.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 69.8%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   6. Taylor expanded in t around 0 54.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 58.8%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac2 58.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]

   if 5.6000000000000002e55 < z

   1. Initial program 85.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 83.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. neg-mul-1 83.2%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot \left(t - z\right)} \]

   5. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 83.2%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{z \cdot \left(t - z\right)}} \]

      2. add-sqr-sqrt 43.1%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      3. sqrt-unprod 66.7%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      4. sqr-neg 66.7%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      5. sqrt-unprod 32.7%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      6. add-sqr-sqrt 70.9%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      7. associate-/r* 69.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{z}}{t - z}} \]

   7. Applied egg-rr 69.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{t - z}} \]
   8. Step-by-step derivation

      1. *-commutative 69.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{t - z} \cdot x} \]

      2. associate-*l/ 68.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot x}{t - z}} \]

      3. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{t - z}} \]

      4. associate-*l/ 68.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{t - z}}{z}} \]

      5. *-lft-identity 68.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{z} \]

   9. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 60.4%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 85.5%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 85.5%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 60.4%

       \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. div-inv 60.4%

          \[\leadsto \color{blue}{\frac{-x}{z} \cdot \frac{1}{z}} \]

       2. frac-2neg 60.4%

          \[\leadsto \color{blue}{\frac{-\left(-x\right)}{-z}} \cdot \frac{1}{z} \]

       3. add-sqr-sqrt 30.9%

          \[\leadsto \frac{-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-z} \cdot \frac{1}{z} \]

       4. sqrt-unprod 61.4%

          \[\leadsto \frac{-\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{-z} \cdot \frac{1}{z} \]

       5. sqr-neg 61.4%

          \[\leadsto \frac{-\sqrt{\color{blue}{x \cdot x}}}{-z} \cdot \frac{1}{z} \]

       6. sqrt-unprod 36.8%

          \[\leadsto \frac{-\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-z} \cdot \frac{1}{z} \]

       7. add-sqr-sqrt 74.9%

          \[\leadsto \frac{-\color{blue}{x}}{-z} \cdot \frac{1}{z} \]

       8. distribute-neg-frac2 74.9%

          \[\leadsto \color{blue}{\left(-\frac{-x}{z}\right)} \cdot \frac{1}{z} \]

       9. distribute-frac-neg 74.9%

          \[\leadsto \left(-\color{blue}{\left(-\frac{x}{z}\right)}\right) \cdot \frac{1}{z} \]

       10. remove-double-neg 74.9%

           \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{z} \]

   14. Applied egg-rr 74.9%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
   15. Step-by-step derivation

       1. clear-num 74.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{1}{z} \]

       2. frac-times 75.7%

          \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{z}{x} \cdot z}} \]

       3. metadata-eval 75.7%

          \[\leadsto \frac{\color{blue}{1}}{\frac{z}{x} \cdot z} \]

   16. Applied egg-rr 75.7%

       \[\leadsto \color{blue}{\frac{1}{\frac{z}{x} \cdot z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-15} \lor \neg \left(z \leq 3.1 \cdot 10^{-69}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -4.7e+42)
     t_1
     (if (<= z -1.05e-14)
       (/ (/ x y) t)
       (if (or (<= z -1.15e-15) (not (<= z 3.1e-69))) 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 <= -4.7e+42) {
		tmp = t_1;
	} else if (z <= -1.05e-14) {
		tmp = (x / y) / t;
	} else if ((z <= -1.15e-15) || !(z <= 3.1e-69)) {
		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 <= (-4.7d+42)) then
        tmp = t_1
    else if (z <= (-1.05d-14)) then
        tmp = (x / y) / t
    else if ((z <= (-1.15d-15)) .or. (.not. (z <= 3.1d-69))) 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 <= -4.7e+42) {
		tmp = t_1;
	} else if (z <= -1.05e-14) {
		tmp = (x / y) / t;
	} else if ((z <= -1.15e-15) || !(z <= 3.1e-69)) {
		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 <= -4.7e+42:
		tmp = t_1
	elif z <= -1.05e-14:
		tmp = (x / y) / t
	elif (z <= -1.15e-15) or not (z <= 3.1e-69):
		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 <= -4.7e+42)
		tmp = t_1;
	elseif (z <= -1.05e-14)
		tmp = Float64(Float64(x / y) / t);
	elseif ((z <= -1.15e-15) || !(z <= 3.1e-69))
		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 <= -4.7e+42)
		tmp = t_1;
	elseif (z <= -1.05e-14)
		tmp = (x / y) / t;
	elseif ((z <= -1.15e-15) || ~((z <= 3.1e-69)))
		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, -4.7e+42], t$95$1, If[LessEqual[z, -1.05e-14], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, -1.15e-15], N[Not[LessEqual[z, 3.1e-69]], $MachinePrecision]], t$95$1, N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.69999999999999986e42 or -1.0499999999999999e-14 < z < -1.14999999999999995e-15 or 3.0999999999999999e-69 < z

   1. Initial program 91.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. neg-mul-1 78.2%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot \left(t - z\right)} \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 78.2%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{z \cdot \left(t - z\right)}} \]

      2. add-sqr-sqrt 37.3%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      3. sqrt-unprod 60.0%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      4. sqr-neg 60.0%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      5. sqrt-unprod 29.7%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      6. add-sqr-sqrt 59.7%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      7. associate-/r* 59.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{z}}{t - z}} \]

   7. Applied egg-rr 59.2%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{t - z}} \]
   8. Step-by-step derivation

      1. *-commutative 59.2%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{t - z} \cdot x} \]

      2. associate-*l/ 58.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot x}{t - z}} \]

      3. associate-*r/ 58.1%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{t - z}} \]

      4. associate-*l/ 58.1%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{t - z}}{z}} \]

      5. *-lft-identity 58.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{z} \]

   9. Simplified 58.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{z}} \]

   10. Taylor expanded in t around 0 51.6%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{z} \]
   11. Step-by-step derivation

       1. associate-*r/ 83.8%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

       2. neg-mul-1 83.8%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   12. Simplified 51.6%

       \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{z} \]
   13. Step-by-step derivation

       1. div-inv 51.6%

          \[\leadsto \color{blue}{\frac{-x}{z} \cdot \frac{1}{z}} \]

       2. frac-2neg 51.6%

          \[\leadsto \color{blue}{\frac{-\left(-x\right)}{-z}} \cdot \frac{1}{z} \]

       3. add-sqr-sqrt 24.6%

          \[\leadsto \frac{-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-z} \cdot \frac{1}{z} \]

       4. sqrt-unprod 54.1%

          \[\leadsto \frac{-\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{-z} \cdot \frac{1}{z} \]

       5. sqr-neg 54.1%

          \[\leadsto \frac{-\sqrt{\color{blue}{x \cdot x}}}{-z} \cdot \frac{1}{z} \]

       6. sqrt-unprod 34.0%

          \[\leadsto \frac{-\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-z} \cdot \frac{1}{z} \]

       7. add-sqr-sqrt 67.0%

          \[\leadsto \frac{-\color{blue}{x}}{-z} \cdot \frac{1}{z} \]

       8. distribute-neg-frac2 67.0%

          \[\leadsto \color{blue}{\left(-\frac{-x}{z}\right)} \cdot \frac{1}{z} \]

       9. distribute-frac-neg 67.0%

          \[\leadsto \left(-\color{blue}{\left(-\frac{x}{z}\right)}\right) \cdot \frac{1}{z} \]

       10. remove-double-neg 67.0%

           \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{z} \]

   14. Applied egg-rr 67.0%

       \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
   15. Step-by-step derivation

       1. un-div-inv 67.0%

          \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   16. Applied egg-rr 67.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -4.69999999999999986e42 < z < -1.0499999999999999e-14

   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/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      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. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{x}}} \cdot \frac{1}{y - z} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{y - z}}{\frac{t - z}{x}}} \]

      3. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{y - z}}}{\frac{t - z}{x}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in z around 0 44.3%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/l/ 50.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   9. Simplified 50.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   if -1.14999999999999995e-15 < z < 3.0999999999999999e-69

   1. Initial program 95.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 93.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 93.3%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 93.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{x}}} \cdot \frac{1}{y - z} \]

      2. associate-*l/ 94.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{y - z}}{\frac{t - z}{x}}} \]

      3. *-un-lft-identity 94.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{y - z}}}{\frac{t - z}{x}} \]

   6. Applied egg-rr 94.7%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in z around 0 69.7%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 68.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 68.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-15} \lor \neg \left(z \leq 3.1 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot t}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-32}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+183}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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))))
   (if (<= z -1.2e+59)
     t_1
     (if (<= z -1.12e-32)
       (/ (/ x y) t)
       (if (<= z 3.4e+62)
         (/ (/ x t) y)
         (if (<= z 1.25e+183) (/ x (* 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);
	double tmp;
	if (z <= -1.2e+59) {
		tmp = t_1;
	} else if (z <= -1.12e-32) {
		tmp = (x / y) / t;
	} else if (z <= 3.4e+62) {
		tmp = (x / t) / y;
	} else if (z <= 1.25e+183) {
		tmp = x / (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)
    if (z <= (-1.2d+59)) then
        tmp = t_1
    else if (z <= (-1.12d-32)) then
        tmp = (x / y) / t
    else if (z <= 3.4d+62) then
        tmp = (x / t) / y
    else if (z <= 1.25d+183) then
        tmp = x / (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);
	double tmp;
	if (z <= -1.2e+59) {
		tmp = t_1;
	} else if (z <= -1.12e-32) {
		tmp = (x / y) / t;
	} else if (z <= 3.4e+62) {
		tmp = (x / t) / y;
	} else if (z <= 1.25e+183) {
		tmp = x / (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)
	tmp = 0
	if z <= -1.2e+59:
		tmp = t_1
	elif z <= -1.12e-32:
		tmp = (x / y) / t
	elif z <= 3.4e+62:
		tmp = (x / t) / y
	elif z <= 1.25e+183:
		tmp = x / (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(x / Float64(z * t))
	tmp = 0.0
	if (z <= -1.2e+59)
		tmp = t_1;
	elseif (z <= -1.12e-32)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 3.4e+62)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.25e+183)
		tmp = Float64(x / 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);
	tmp = 0.0;
	if (z <= -1.2e+59)
		tmp = t_1;
	elseif (z <= -1.12e-32)
		tmp = (x / y) / t;
	elseif (z <= 3.4e+62)
		tmp = (x / t) / y;
	elseif (z <= 1.25e+183)
		tmp = x / (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[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+59], t$95$1, If[LessEqual[z, -1.12e-32], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.4e+62], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.25e+183], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2000000000000001e59 or 1.25000000000000002e183 < z

   1. Initial program 90.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 55.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 55.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. mul-1-neg 55.0%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 55.0%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   9. Step-by-step derivation

      1. clear-num 55.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot z}{-x}}} \]

      2. inv-pow 55.4%

         \[\leadsto \color{blue}{{\left(\frac{t \cdot z}{-x}\right)}^{-1}} \]

      3. *-commutative 55.4%

         \[\leadsto {\left(\frac{\color{blue}{z \cdot t}}{-x}\right)}^{-1} \]

      4. associate-/l* 51.3%

         \[\leadsto {\color{blue}{\left(z \cdot \frac{t}{-x}\right)}}^{-1} \]

      5. add-sqr-sqrt 28.5%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}\right)}^{-1} \]

      6. sqrt-unprod 53.7%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}\right)}^{-1} \]

      7. sqr-neg 53.7%

         \[\leadsto {\left(z \cdot \frac{t}{\sqrt{\color{blue}{x \cdot x}}}\right)}^{-1} \]

      8. sqrt-unprod 21.4%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}\right)}^{-1} \]

      9. add-sqr-sqrt 48.5%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{x}}\right)}^{-1} \]

   10. Applied egg-rr 48.5%

       \[\leadsto \color{blue}{{\left(z \cdot \frac{t}{x}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 48.5%

          \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{t}{x}}} \]

   12. Simplified 48.5%

       \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{t}{x}}} \]

   13. Taylor expanded in z around 0 54.9%

       \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]
   14. Step-by-step derivation

       1. *-commutative 54.9%

          \[\leadsto \frac{x}{\color{blue}{z \cdot t}} \]

   15. Simplified 54.9%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t}} \]

   if -1.2000000000000001e59 < z < -1.12e-32

   1. Initial program 99.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 99.5%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{x}}} \cdot \frac{1}{y - z} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{y - z}}{\frac{t - z}{x}}} \]

      3. *-un-lft-identity 99.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{y - z}}}{\frac{t - z}{x}} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in z around 0 38.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/l/ 42.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   if -1.12e-32 < z < 3.40000000000000014e62

   1. Initial program 95.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 93.9%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 93.9%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 93.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{x}}} \cdot \frac{1}{y - z} \]

      2. associate-*l/ 95.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{y - z}}{\frac{t - z}{x}}} \]

      3. *-un-lft-identity 95.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{y - z}}}{\frac{t - z}{x}} \]

   6. Applied egg-rr 95.0%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in z around 0 60.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 60.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 60.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 3.40000000000000014e62 < z < 1.25000000000000002e183

   1. Initial program 87.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 31.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 31.4%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 31.4%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   6. Taylor expanded in t around 0 27.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 33.6%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac2 33.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]

   8. Simplified 33.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]
   9. Step-by-step derivation

      1. div-inv 33.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{-z}} \]

      2. metadata-eval 33.6%

         \[\leadsto \frac{x}{y} \cdot \frac{\color{blue}{--1}}{-z} \]

      3. frac-2neg 33.6%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{-1}{z}} \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\sqrt{\frac{-1}{z}} \cdot \sqrt{\frac{-1}{z}}\right)} \]

      5. sqrt-unprod 28.6%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\sqrt{\frac{-1}{z} \cdot \frac{-1}{z}}} \]

      6. frac-times 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\color{blue}{\frac{-1 \cdot -1}{z \cdot z}}} \]

      7. metadata-eval 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\frac{\color{blue}{1}}{z \cdot z}} \]

      8. metadata-eval 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\frac{\color{blue}{1 \cdot 1}}{z \cdot z}} \]

      9. frac-times 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\color{blue}{\frac{1}{z} \cdot \frac{1}{z}}} \]

      10. sqrt-unprod 25.3%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\sqrt{\frac{1}{z}} \cdot \sqrt{\frac{1}{z}}\right)} \]

      11. add-sqr-sqrt 25.3%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{z}} \]

      12. div-inv 25.3%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z}} \]

      13. *-un-lft-identity 25.3%

          \[\leadsto \color{blue}{1 \cdot \frac{\frac{x}{y}}{z}} \]

      14. associate-/l/ 25.4%

          \[\leadsto 1 \cdot \color{blue}{\frac{x}{z \cdot y}} \]

   10. Applied egg-rr 25.4%

       \[\leadsto \color{blue}{1 \cdot \frac{x}{z \cdot y}} \]
   11. Step-by-step derivation

       1. *-lft-identity 25.4%

          \[\leadsto \color{blue}{\frac{x}{z \cdot y}} \]

   12. Simplified 25.4%

       \[\leadsto \color{blue}{\frac{x}{z \cdot y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-32}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+183}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-77} \lor \neg \left(y \leq 2.6 \cdot 10^{-163}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

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 -2.6e-38)
   (/ (/ x y) (- t z))
   (if (or (<= y -4.4e-77) (not (<= y 2.6e-163)))
     (/ (/ x t) (- y z))
     (/ x (* z (- z t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-38) {
		tmp = (x / y) / (t - z);
	} else if ((y <= -4.4e-77) || !(y <= 2.6e-163)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = x / (z * (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 (y <= (-2.6d-38)) then
        tmp = (x / y) / (t - z)
    else if ((y <= (-4.4d-77)) .or. (.not. (y <= 2.6d-163))) then
        tmp = (x / t) / (y - z)
    else
        tmp = x / (z * (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 (y <= -2.6e-38) {
		tmp = (x / y) / (t - z);
	} else if ((y <= -4.4e-77) || !(y <= 2.6e-163)) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = x / (z * (z - t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e-38:
		tmp = (x / y) / (t - z)
	elif (y <= -4.4e-77) or not (y <= 2.6e-163):
		tmp = (x / t) / (y - z)
	else:
		tmp = x / (z * (z - t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e-38)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif ((y <= -4.4e-77) || !(y <= 2.6e-163))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(x / Float64(z * Float64(z - t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e-38)
		tmp = (x / y) / (t - z);
	elseif ((y <= -4.4e-77) || ~((y <= 2.6e-163)))
		tmp = (x / t) / (y - z);
	else
		tmp = x / (z * (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[y, -2.6e-38], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.4e-77], N[Not[LessEqual[y, 2.6e-163]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.60000000000000011e-38

   1. Initial program 89.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 98.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      2. div-inv 98.4%

         \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]

   4. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. Step-by-step derivation

      1. clear-num 98.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{x}}} \cdot \frac{1}{y - z} \]

      2. associate-*l/ 98.4%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{y - z}}{\frac{t - z}{x}}} \]

      3. *-un-lft-identity 98.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{y - z}}}{\frac{t - z}{x}} \]

   6. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in y around inf 80.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   8. Step-by-step derivation

      1. associate-/r* 84.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   9. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   if -2.60000000000000011e-38 < y < -4.40000000000000014e-77 or 2.60000000000000002e-163 < y

   1. Initial program 93.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 inf 61.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   if -4.40000000000000014e-77 < y < 2.60000000000000002e-163

   1. Initial program 97.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 88.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. neg-mul-1 88.6%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot \left(t - z\right)} \]

   5. Simplified 88.6%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 87.5%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{z \cdot \left(t - z\right)}} \]

      2. add-sqr-sqrt 43.2%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      3. sqrt-unprod 51.8%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      4. sqr-neg 51.8%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      5. sqrt-unprod 17.5%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      6. add-sqr-sqrt 41.5%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      7. associate-/r* 41.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{z}}{t - z}} \]

   7. Applied egg-rr 41.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{t - z}} \]
   8. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{t - z} \cdot x} \]

      2. associate-*l/ 41.4%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot x}{t - z}} \]

      3. associate-*r/ 43.9%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{t - z}} \]

      4. associate-*l/ 43.9%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{t - z}}{z}} \]

      5. *-lft-identity 43.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{z} \]

   9. Simplified 43.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{z}} \]
   10. Step-by-step derivation

       1. frac-2neg 43.9%

          \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{-z}} \]

       2. div-inv 43.9%

          \[\leadsto \color{blue}{\left(-\frac{x}{t - z}\right) \cdot \frac{1}{-z}} \]

       3. distribute-neg-frac2 43.9%

          \[\leadsto \color{blue}{\frac{x}{-\left(t - z\right)}} \cdot \frac{1}{-z} \]

       4. sub-neg 43.9%

          \[\leadsto \frac{x}{-\color{blue}{\left(t + \left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       5. distribute-neg-in 43.9%

          \[\leadsto \frac{x}{\color{blue}{\left(-t\right) + \left(-\left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       6. remove-double-neg 43.9%

          \[\leadsto \frac{x}{\left(-t\right) + \color{blue}{z}} \cdot \frac{1}{-z} \]

       7. add-sqr-sqrt 19.9%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

       8. sqrt-unprod 66.2%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} \]

       9. sqr-neg 66.2%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\sqrt{\color{blue}{z \cdot z}}} \]

       10. sqrt-unprod 51.0%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

       11. add-sqr-sqrt 91.5%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{z}} \]

   11. Applied egg-rr 91.5%

       \[\leadsto \color{blue}{\frac{x}{\left(-t\right) + z} \cdot \frac{1}{z}} \]
   12. Step-by-step derivation

       1. associate-*l/ 86.3%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{\left(-t\right) + z}} \]

       2. associate-*r/ 86.4%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{z}}}{\left(-t\right) + z} \]

       3. *-rgt-identity 86.4%

          \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{\left(-t\right) + z} \]

       4. +-commutative 86.4%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z + \left(-t\right)}} \]

       5. unsub-neg 86.4%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

   13. Simplified 86.4%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - t}} \]

   14. Taylor expanded in x around 0 88.6%

       \[\leadsto \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-77} \lor \neg \left(y \leq 2.6 \cdot 10^{-163}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{if}\;z \leq -2000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- z t)))))
   (if (<= z -2000000.0)
     t_1
     (if (<= z 7.2e-102)
       (/ x (* (- y z) t))
       (if (<= z 1.2e-29) (/ (/ x (- 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 * (z - t));
	double tmp;
	if (z <= -2000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-102) {
		tmp = x / ((y - z) * t);
	} else if (z <= 1.2e-29) {
		tmp = (x / -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 * (z - t))
    if (z <= (-2000000.0d0)) then
        tmp = t_1
    else if (z <= 7.2d-102) then
        tmp = x / ((y - z) * t)
    else if (z <= 1.2d-29) then
        tmp = (x / -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 * (z - t));
	double tmp;
	if (z <= -2000000.0) {
		tmp = t_1;
	} else if (z <= 7.2e-102) {
		tmp = x / ((y - z) * t);
	} else if (z <= 1.2e-29) {
		tmp = (x / -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 * (z - t))
	tmp = 0
	if z <= -2000000.0:
		tmp = t_1
	elif z <= 7.2e-102:
		tmp = x / ((y - z) * t)
	elif z <= 1.2e-29:
		tmp = (x / -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(x / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (z <= -2000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-102)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 1.2e-29)
		tmp = Float64(Float64(x / 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 * (z - t));
	tmp = 0.0;
	if (z <= -2000000.0)
		tmp = t_1;
	elseif (z <= 7.2e-102)
		tmp = x / ((y - z) * t);
	elseif (z <= 1.2e-29)
		tmp = (x / -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[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2000000.0], t$95$1, If[LessEqual[z, 7.2e-102], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-29], N[(N[(x / (-y)), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e6 or 1.19999999999999996e-29 < z

   1. Initial program 92.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 79.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. neg-mul-1 79.8%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot \left(t - z\right)} \]

   5. Simplified 79.8%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 79.8%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{z \cdot \left(t - z\right)}} \]

      2. add-sqr-sqrt 39.6%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      3. sqrt-unprod 63.8%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      4. sqr-neg 63.8%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      5. sqrt-unprod 31.8%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      6. add-sqr-sqrt 61.3%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      7. associate-/r* 60.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{z}}{t - z}} \]

   7. Applied egg-rr 60.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{t - z}} \]
   8. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{t - z} \cdot x} \]

      2. associate-*l/ 59.3%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot x}{t - z}} \]

      3. associate-*r/ 59.3%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{t - z}} \]

      4. associate-*l/ 59.3%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{t - z}}{z}} \]

      5. *-lft-identity 59.3%

         \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{z} \]

   9. Simplified 59.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{z}} \]
   10. Step-by-step derivation

       1. frac-2neg 59.3%

          \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{-z}} \]

       2. div-inv 59.3%

          \[\leadsto \color{blue}{\left(-\frac{x}{t - z}\right) \cdot \frac{1}{-z}} \]

       3. distribute-neg-frac2 59.3%

          \[\leadsto \color{blue}{\frac{x}{-\left(t - z\right)}} \cdot \frac{1}{-z} \]

       4. sub-neg 59.3%

          \[\leadsto \frac{x}{-\color{blue}{\left(t + \left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       5. distribute-neg-in 59.3%

          \[\leadsto \frac{x}{\color{blue}{\left(-t\right) + \left(-\left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       6. remove-double-neg 59.3%

          \[\leadsto \frac{x}{\left(-t\right) + \color{blue}{z}} \cdot \frac{1}{-z} \]

       7. add-sqr-sqrt 27.1%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

       8. sqrt-unprod 71.7%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} \]

       9. sqr-neg 71.7%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\sqrt{\color{blue}{z \cdot z}}} \]

       10. sqrt-unprod 47.2%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

       11. add-sqr-sqrt 82.4%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{z}} \]

   11. Applied egg-rr 82.4%

       \[\leadsto \color{blue}{\frac{x}{\left(-t\right) + z} \cdot \frac{1}{z}} \]
   12. Step-by-step derivation

       1. associate-*l/ 82.4%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{\left(-t\right) + z}} \]

       2. associate-*r/ 82.4%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{z}}}{\left(-t\right) + z} \]

       3. *-rgt-identity 82.4%

          \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{\left(-t\right) + z} \]

       4. +-commutative 82.4%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z + \left(-t\right)}} \]

       5. unsub-neg 82.4%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

   13. Simplified 82.4%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - t}} \]

   14. Taylor expanded in x around 0 79.8%

       \[\leadsto \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]

   if -2e6 < z < 7.2e-102

   1. Initial program 95.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.1%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 7.2e-102 < z < 1.19999999999999996e-29

   1. Initial program 93.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 69.8%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   6. Taylor expanded in t around 0 54.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 58.8%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac2 58.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2000000:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{x}{-y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

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 z) (- t z)))))
   (if (<= t_1 -1e-242) t_1 (/ (/ x (- t z)) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -1e-242) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-1d-242)) then
        tmp = t_1
    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 t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -1e-242) {
		tmp = t_1;
	} 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):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -1e-242:
		tmp = t_1
	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)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -1e-242)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / 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)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -1e-242)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-242], t$95$1, N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -1e-242

   1. Initial program 98.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   if -1e-242 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 92.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 96.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 46.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot t}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+182}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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))))
   (if (<= z -4e+248)
     t_1
     (if (<= z 1.2e+60)
       (/ (/ x t) y)
       (if (<= z 2.6e+182) (/ x (* 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);
	double tmp;
	if (z <= -4e+248) {
		tmp = t_1;
	} else if (z <= 1.2e+60) {
		tmp = (x / t) / y;
	} else if (z <= 2.6e+182) {
		tmp = x / (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)
    if (z <= (-4d+248)) then
        tmp = t_1
    else if (z <= 1.2d+60) then
        tmp = (x / t) / y
    else if (z <= 2.6d+182) then
        tmp = x / (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);
	double tmp;
	if (z <= -4e+248) {
		tmp = t_1;
	} else if (z <= 1.2e+60) {
		tmp = (x / t) / y;
	} else if (z <= 2.6e+182) {
		tmp = x / (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)
	tmp = 0
	if z <= -4e+248:
		tmp = t_1
	elif z <= 1.2e+60:
		tmp = (x / t) / y
	elif z <= 2.6e+182:
		tmp = x / (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(x / Float64(z * t))
	tmp = 0.0
	if (z <= -4e+248)
		tmp = t_1;
	elseif (z <= 1.2e+60)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.6e+182)
		tmp = Float64(x / 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);
	tmp = 0.0;
	if (z <= -4e+248)
		tmp = t_1;
	elseif (z <= 1.2e+60)
		tmp = (x / t) / y;
	elseif (z <= 2.6e+182)
		tmp = x / (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[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+248], t$95$1, If[LessEqual[z, 1.2e+60], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.6e+182], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000018e248 or 2.6e182 < z

   1. Initial program 87.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 51.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 58.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 58.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. mul-1-neg 58.8%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 58.8%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   9. Step-by-step derivation

      1. clear-num 59.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot z}{-x}}} \]

      2. inv-pow 59.6%

         \[\leadsto \color{blue}{{\left(\frac{t \cdot z}{-x}\right)}^{-1}} \]

      3. *-commutative 59.6%

         \[\leadsto {\left(\frac{\color{blue}{z \cdot t}}{-x}\right)}^{-1} \]

      4. associate-/l* 52.1%

         \[\leadsto {\color{blue}{\left(z \cdot \frac{t}{-x}\right)}}^{-1} \]

      5. add-sqr-sqrt 29.9%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}\right)}^{-1} \]

      6. sqrt-unprod 56.6%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}\right)}^{-1} \]

      7. sqr-neg 56.6%

         \[\leadsto {\left(z \cdot \frac{t}{\sqrt{\color{blue}{x \cdot x}}}\right)}^{-1} \]

      8. sqrt-unprod 22.2%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}\right)}^{-1} \]

      9. add-sqr-sqrt 49.6%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{x}}\right)}^{-1} \]

   10. Applied egg-rr 49.6%

       \[\leadsto \color{blue}{{\left(z \cdot \frac{t}{x}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 49.6%

          \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{t}{x}}} \]

   12. Simplified 49.6%

       \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{t}{x}}} \]

   13. Taylor expanded in z around 0 58.8%

       \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]
   14. Step-by-step derivation

       1. *-commutative 58.8%

          \[\leadsto \frac{x}{\color{blue}{z \cdot t}} \]

   15. Simplified 58.8%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t}} \]

   if -4.00000000000000018e248 < z < 1.2e60

   1. Initial program 95.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/l/ 95.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

      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. clear-num 95.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{x}}} \cdot \frac{1}{y - z} \]

      2. associate-*l/ 96.4%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{y - z}}{\frac{t - z}{x}}} \]

      3. *-un-lft-identity 96.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{y - z}}}{\frac{t - z}{x}} \]

   6. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in z around 0 51.9%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   8. Step-by-step derivation

      1. associate-/r* 55.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   9. Simplified 55.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 1.2e60 < z < 2.6e182

   1. Initial program 87.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 31.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 31.4%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 31.4%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   6. Taylor expanded in t around 0 27.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 33.6%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac2 33.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]

   8. Simplified 33.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{-z}} \]
   9. Step-by-step derivation

      1. div-inv 33.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{-z}} \]

      2. metadata-eval 33.6%

         \[\leadsto \frac{x}{y} \cdot \frac{\color{blue}{--1}}{-z} \]

      3. frac-2neg 33.6%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{-1}{z}} \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\sqrt{\frac{-1}{z}} \cdot \sqrt{\frac{-1}{z}}\right)} \]

      5. sqrt-unprod 28.6%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\sqrt{\frac{-1}{z} \cdot \frac{-1}{z}}} \]

      6. frac-times 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\color{blue}{\frac{-1 \cdot -1}{z \cdot z}}} \]

      7. metadata-eval 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\frac{\color{blue}{1}}{z \cdot z}} \]

      8. metadata-eval 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\frac{\color{blue}{1 \cdot 1}}{z \cdot z}} \]

      9. frac-times 28.6%

         \[\leadsto \frac{x}{y} \cdot \sqrt{\color{blue}{\frac{1}{z} \cdot \frac{1}{z}}} \]

      10. sqrt-unprod 25.3%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\sqrt{\frac{1}{z}} \cdot \sqrt{\frac{1}{z}}\right)} \]

      11. add-sqr-sqrt 25.3%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{1}{z}} \]

      12. div-inv 25.3%

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z}} \]

      13. *-un-lft-identity 25.3%

          \[\leadsto \color{blue}{1 \cdot \frac{\frac{x}{y}}{z}} \]

      14. associate-/l/ 25.4%

          \[\leadsto 1 \cdot \color{blue}{\frac{x}{z \cdot y}} \]

   10. Applied egg-rr 25.4%

       \[\leadsto \color{blue}{1 \cdot \frac{x}{z \cdot y}} \]
   11. Step-by-step derivation

       1. *-lft-identity 25.4%

          \[\leadsto \color{blue}{\frac{x}{z \cdot y}} \]

   12. Simplified 25.4%

       \[\leadsto \color{blue}{\frac{x}{z \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+248}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+182}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 78.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 (<= y -5.2)
   (/ x (* y (- t z)))
   (if (<= y 1.5e-153) (/ x (* z (- z t))) (/ (/ 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 (y <= -5.2) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.5e-153) {
		tmp = x / (z * (z - t));
	} 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 (y <= (-5.2d0)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.5d-153) then
        tmp = x / (z * (z - t))
    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 (y <= -5.2) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.5e-153) {
		tmp = x / (z * (z - t));
	} 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 y <= -5.2:
		tmp = x / (y * (t - z))
	elif y <= 1.5e-153:
		tmp = x / (z * (z - t))
	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 (y <= -5.2)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.5e-153)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	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 (y <= -5.2)
		tmp = x / (y * (t - z));
	elseif (y <= 1.5e-153)
		tmp = x / (z * (z - t));
	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[y, -5.2], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-153], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.20000000000000018

   1. Initial program 88.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 84.4%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if -5.20000000000000018 < y < 1.5e-153

   1. Initial program 95.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 84.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. neg-mul-1 84.0%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot \left(t - z\right)} \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 83.1%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{z \cdot \left(t - z\right)}} \]

      2. add-sqr-sqrt 41.6%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      3. sqrt-unprod 53.8%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      4. sqr-neg 53.8%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      5. sqrt-unprod 19.3%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      6. add-sqr-sqrt 40.7%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      7. associate-/r* 40.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{z}}{t - z}} \]

   7. Applied egg-rr 40.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{t - z}} \]
   8. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{t - z} \cdot x} \]

      2. associate-*l/ 40.6%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot x}{t - z}} \]

      3. associate-*r/ 42.6%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{t - z}} \]

      4. associate-*l/ 42.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{t - z}}{z}} \]

      5. *-lft-identity 42.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{z} \]

   9. Simplified 42.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{z}} \]
   10. Step-by-step derivation

       1. frac-2neg 42.6%

          \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{-z}} \]

       2. div-inv 42.6%

          \[\leadsto \color{blue}{\left(-\frac{x}{t - z}\right) \cdot \frac{1}{-z}} \]

       3. distribute-neg-frac2 42.6%

          \[\leadsto \color{blue}{\frac{x}{-\left(t - z\right)}} \cdot \frac{1}{-z} \]

       4. sub-neg 42.6%

          \[\leadsto \frac{x}{-\color{blue}{\left(t + \left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       5. distribute-neg-in 42.6%

          \[\leadsto \frac{x}{\color{blue}{\left(-t\right) + \left(-\left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       6. remove-double-neg 42.6%

          \[\leadsto \frac{x}{\left(-t\right) + \color{blue}{z}} \cdot \frac{1}{-z} \]

       7. add-sqr-sqrt 20.3%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

       8. sqrt-unprod 62.3%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} \]

       9. sqr-neg 62.3%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\sqrt{\color{blue}{z \cdot z}}} \]

       10. sqrt-unprod 46.8%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

       11. add-sqr-sqrt 88.1%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{z}} \]

   11. Applied egg-rr 88.1%

       \[\leadsto \color{blue}{\frac{x}{\left(-t\right) + z} \cdot \frac{1}{z}} \]
   12. Step-by-step derivation

       1. associate-*l/ 84.1%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{\left(-t\right) + z}} \]

       2. associate-*r/ 84.1%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{z}}}{\left(-t\right) + z} \]

       3. *-rgt-identity 84.1%

          \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{\left(-t\right) + z} \]

       4. +-commutative 84.1%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z + \left(-t\right)}} \]

       5. unsub-neg 84.1%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

   13. Simplified 84.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - t}} \]

   14. Taylor expanded in x around 0 84.0%

       \[\leadsto \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]

   if 1.5e-153 < 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/ 95.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 60.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 77.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -850:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -850.0)
   (/ x (* y (- t z)))
   (if (<= y 1.38e-154) (/ x (* z (- z t))) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -850.0) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.38e-154) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-850.0d0)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.38d-154) then
        tmp = x / (z * (z - t))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -850.0) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.38e-154) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -850.0:
		tmp = x / (y * (t - z))
	elif y <= 1.38e-154:
		tmp = x / (z * (z - t))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -850.0)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.38e-154)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -850.0)
		tmp = x / (y * (t - z));
	elseif (y <= 1.38e-154)
		tmp = x / (z * (z - t));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -850.0], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.38e-154], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -850

   1. Initial program 88.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 84.4%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   5. Simplified 84.4%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if -850 < y < 1.37999999999999995e-154

   1. Initial program 95.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   4. Step-by-step derivation

      1. associate-*r/ 84.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z \cdot \left(t - z\right)}} \]

      2. neg-mul-1 84.0%

         \[\leadsto \frac{\color{blue}{-x}}{z \cdot \left(t - z\right)} \]

   5. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]
   6. Step-by-step derivation

      1. div-inv 83.1%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{z \cdot \left(t - z\right)}} \]

      2. add-sqr-sqrt 41.6%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      3. sqrt-unprod 53.8%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      4. sqr-neg 53.8%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      5. sqrt-unprod 19.3%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      6. add-sqr-sqrt 40.7%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{z \cdot \left(t - z\right)} \]

      7. associate-/r* 40.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{z}}{t - z}} \]

   7. Applied egg-rr 40.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{z}}{t - z}} \]
   8. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{t - z} \cdot x} \]

      2. associate-*l/ 40.6%

         \[\leadsto \color{blue}{\frac{\frac{1}{z} \cdot x}{t - z}} \]

      3. associate-*r/ 42.6%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{x}{t - z}} \]

      4. associate-*l/ 42.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{t - z}}{z}} \]

      5. *-lft-identity 42.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{z} \]

   9. Simplified 42.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{z}} \]
   10. Step-by-step derivation

       1. frac-2neg 42.6%

          \[\leadsto \color{blue}{\frac{-\frac{x}{t - z}}{-z}} \]

       2. div-inv 42.6%

          \[\leadsto \color{blue}{\left(-\frac{x}{t - z}\right) \cdot \frac{1}{-z}} \]

       3. distribute-neg-frac2 42.6%

          \[\leadsto \color{blue}{\frac{x}{-\left(t - z\right)}} \cdot \frac{1}{-z} \]

       4. sub-neg 42.6%

          \[\leadsto \frac{x}{-\color{blue}{\left(t + \left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       5. distribute-neg-in 42.6%

          \[\leadsto \frac{x}{\color{blue}{\left(-t\right) + \left(-\left(-z\right)\right)}} \cdot \frac{1}{-z} \]

       6. remove-double-neg 42.6%

          \[\leadsto \frac{x}{\left(-t\right) + \color{blue}{z}} \cdot \frac{1}{-z} \]

       7. add-sqr-sqrt 20.3%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

       8. sqrt-unprod 62.3%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} \]

       9. sqr-neg 62.3%

          \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\sqrt{\color{blue}{z \cdot z}}} \]

       10. sqrt-unprod 46.8%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

       11. add-sqr-sqrt 88.1%

           \[\leadsto \frac{x}{\left(-t\right) + z} \cdot \frac{1}{\color{blue}{z}} \]

   11. Applied egg-rr 88.1%

       \[\leadsto \color{blue}{\frac{x}{\left(-t\right) + z} \cdot \frac{1}{z}} \]
   12. Step-by-step derivation

       1. associate-*l/ 84.1%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{z}}{\left(-t\right) + z}} \]

       2. associate-*r/ 84.1%

          \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{z}}}{\left(-t\right) + z} \]

       3. *-rgt-identity 84.1%

          \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{\left(-t\right) + z} \]

       4. +-commutative 84.1%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z + \left(-t\right)}} \]

       5. unsub-neg 84.1%

          \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

   13. Simplified 84.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - t}} \]

   14. Taylor expanded in x around 0 84.0%

       \[\leadsto \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]

   if 1.37999999999999995e-154 < y

   1. Initial program 94.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.7%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -850:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+66} \lor \neg \left(z \leq 3.45 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e+66) (not (<= z 3.45e+20))) (/ x (* z t)) (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+66) || !(z <= 3.45e+20)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.5d+66)) .or. (.not. (z <= 3.45d+20))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+66) || !(z <= 3.45e+20)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e+66) or not (z <= 3.45e+20):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e+66) || !(z <= 3.45e+20))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e+66) || ~((z <= 3.45e+20)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e+66], N[Not[LessEqual[z, 3.45e+20]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000024e66 or 3.45e20 < z

   1. Initial program 90.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 99.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 51.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]

   6. Taylor expanded in y around 0 51.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 51.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. mul-1-neg 51.6%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{-x}{t \cdot z}} \]
   9. Step-by-step derivation

      1. clear-num 52.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot z}{-x}}} \]

      2. inv-pow 52.0%

         \[\leadsto \color{blue}{{\left(\frac{t \cdot z}{-x}\right)}^{-1}} \]

      3. *-commutative 52.0%

         \[\leadsto {\left(\frac{\color{blue}{z \cdot t}}{-x}\right)}^{-1} \]

      4. associate-/l* 50.1%

         \[\leadsto {\color{blue}{\left(z \cdot \frac{t}{-x}\right)}}^{-1} \]

      5. add-sqr-sqrt 25.6%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}\right)}^{-1} \]

      6. sqrt-unprod 51.4%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}\right)}^{-1} \]

      7. sqr-neg 51.4%

         \[\leadsto {\left(z \cdot \frac{t}{\sqrt{\color{blue}{x \cdot x}}}\right)}^{-1} \]

      8. sqrt-unprod 21.0%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}\right)}^{-1} \]

      9. add-sqr-sqrt 44.8%

         \[\leadsto {\left(z \cdot \frac{t}{\color{blue}{x}}\right)}^{-1} \]

   10. Applied egg-rr 44.8%

       \[\leadsto \color{blue}{{\left(z \cdot \frac{t}{x}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 44.8%

          \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{t}{x}}} \]

   12. Simplified 44.8%

       \[\leadsto \color{blue}{\frac{1}{z \cdot \frac{t}{x}}} \]

   13. Taylor expanded in z around 0 48.8%

       \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]
   14. Step-by-step derivation

       1. *-commutative 48.8%

          \[\leadsto \frac{x}{\color{blue}{z \cdot t}} \]

   15. Simplified 48.8%

       \[\leadsto \color{blue}{\frac{x}{z \cdot t}} \]

   if -7.50000000000000024e66 < z < 3.45e20

   1. Initial program 96.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 58.2%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+66} \lor \neg \left(z \leq 3.45 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 90.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

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 1.9e+85) (/ x (* (- y z) (- t z))) (/ (/ x z) (- z y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.9e+85) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (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 <= 1.9d+85) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / (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 <= 1.9e+85) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 1.9e+85:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / (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 <= 1.9e+85)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.9e+85)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / (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, 1.9e+85], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.89999999999999996e85

   1. Initial program 96.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   if 1.89999999999999996e85 < z

   1. Initial program 84.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 0 92.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{y - z} \]
   6. Step-by-step derivation

      1. associate-*r/ 92.8%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y - z} \]

      2. neg-mul-1 92.8%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y - z} \]

   7. Simplified 92.8%

      \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{y - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y \cdot t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* y t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / (y * t);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (y * t)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return x / (y * t);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (y * t)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(y * t))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (y * t);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.6%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 43.0%

   \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

4. Final simplification 43.0%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer target: 87.5% 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 2024105 
(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))))