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

Percentage Accurate: 88.4% → 97.0%

Time: 13.1s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.4% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

5. Final simplification 96.9%

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

Alternative 2: 82.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{t - z}\\ \mathbf{if}\;y \leq -3.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1 \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- t z))))
   (if (<= y -3.45e+21)
     (/ t_1 y)
     (if (<= y -3.3e-35)
       (/ (/ x z) (- z y))
       (if (<= y -2.5e-59)
         (/ x (* (- t z) y))
         (if (<= y 7.2e-106) (* t_1 (/ -1.0 z)) (/ (/ x t) (- y z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (t - z);
	double tmp;
	if (y <= -3.45e+21) {
		tmp = t_1 / y;
	} else if (y <= -3.3e-35) {
		tmp = (x / z) / (z - y);
	} else if (y <= -2.5e-59) {
		tmp = x / ((t - z) * y);
	} else if (y <= 7.2e-106) {
		tmp = t_1 * (-1.0 / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t - z)
    if (y <= (-3.45d+21)) then
        tmp = t_1 / y
    else if (y <= (-3.3d-35)) then
        tmp = (x / z) / (z - y)
    else if (y <= (-2.5d-59)) then
        tmp = x / ((t - z) * y)
    else if (y <= 7.2d-106) then
        tmp = t_1 * ((-1.0d0) / z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t - z);
	double tmp;
	if (y <= -3.45e+21) {
		tmp = t_1 / y;
	} else if (y <= -3.3e-35) {
		tmp = (x / z) / (z - y);
	} else if (y <= -2.5e-59) {
		tmp = x / ((t - z) * y);
	} else if (y <= 7.2e-106) {
		tmp = t_1 * (-1.0 / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (t - z)
	tmp = 0
	if y <= -3.45e+21:
		tmp = t_1 / y
	elif y <= -3.3e-35:
		tmp = (x / z) / (z - y)
	elif y <= -2.5e-59:
		tmp = x / ((t - z) * y)
	elif y <= 7.2e-106:
		tmp = t_1 * (-1.0 / z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(t - z))
	tmp = 0.0
	if (y <= -3.45e+21)
		tmp = Float64(t_1 / y);
	elseif (y <= -3.3e-35)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (y <= -2.5e-59)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 7.2e-106)
		tmp = Float64(t_1 * Float64(-1.0 / z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (t - z);
	tmp = 0.0;
	if (y <= -3.45e+21)
		tmp = t_1 / y;
	elseif (y <= -3.3e-35)
		tmp = (x / z) / (z - y);
	elseif (y <= -2.5e-59)
		tmp = x / ((t - z) * y);
	elseif (y <= 7.2e-106)
		tmp = t_1 * (-1.0 / z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.45e+21], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[y, -3.3e-35], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-59], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-106], N[(t$95$1 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.45e21

   1. Initial program 90.8%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. un-div-inv 99.9%

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

      2. clear-num 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in y around inf 87.0%

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

      1. associate-/r* 90.5%

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

   9. Simplified 90.5%

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

       1. div-inv 90.4%

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

       2. associate-/l* 86.9%

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

   11. Applied egg-rr 86.9%

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

       1. *-commutative 86.9%

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

       2. associate-*l/ 90.4%

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

       3. associate-*r/ 94.2%

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

       4. associate-*l/ 94.4%

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

       5. *-lft-identity 94.4%

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

   13. Simplified 94.4%

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

   if -3.45e21 < y < -3.3e-35

   1. Initial program 92.0%

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

      1. associate-/l/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 84.0%

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

      1. associate-*r/ 84.0%

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

      2. neg-mul-1 84.0%

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

   7. Simplified 84.0%

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

   if -3.3e-35 < y < -2.5000000000000001e-59

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -2.5000000000000001e-59 < y < 7.20000000000000025e-106

   1. Initial program 90.3%

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

      1. associate-/l/ 95.9%

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

      2. div-inv 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in y around 0 81.9%

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

   if 7.20000000000000025e-106 < y

   1. Initial program 84.2%

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

      1. associate-/l/ 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around inf 59.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t - z}}{y}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- t z)) y)))
   (if (<= z -2.3e+15)
     (/ (/ x z) (- z y))
     (if (<= z -2e-302)
       t_1
       (if (<= z 2.9e-170)
         (/ (/ x t) (- y z))
         (if (<= z 5e-29) t_1 (/ (/ x z) (- z t))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / (t - z)) / y;
	double tmp;
	if (z <= -2.3e+15) {
		tmp = (x / z) / (z - y);
	} else if (z <= -2e-302) {
		tmp = t_1;
	} else if (z <= 2.9e-170) {
		tmp = (x / t) / (y - z);
	} else if (z <= 5e-29) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / (t - z)) / y
    if (z <= (-2.3d+15)) then
        tmp = (x / z) / (z - y)
    else if (z <= (-2d-302)) then
        tmp = t_1
    else if (z <= 2.9d-170) then
        tmp = (x / t) / (y - z)
    else if (z <= 5d-29) then
        tmp = t_1
    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 t_1 = (x / (t - z)) / y;
	double tmp;
	if (z <= -2.3e+15) {
		tmp = (x / z) / (z - y);
	} else if (z <= -2e-302) {
		tmp = t_1;
	} else if (z <= 2.9e-170) {
		tmp = (x / t) / (y - z);
	} else if (z <= 5e-29) {
		tmp = t_1;
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / (t - z)) / y
	tmp = 0
	if z <= -2.3e+15:
		tmp = (x / z) / (z - y)
	elif z <= -2e-302:
		tmp = t_1
	elif z <= 2.9e-170:
		tmp = (x / t) / (y - z)
	elif z <= 5e-29:
		tmp = t_1
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(t - z)) / y)
	tmp = 0.0
	if (z <= -2.3e+15)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= -2e-302)
		tmp = t_1;
	elseif (z <= 2.9e-170)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 5e-29)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / 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)
	t_1 = (x / (t - z)) / y;
	tmp = 0.0;
	if (z <= -2.3e+15)
		tmp = (x / z) / (z - y);
	elseif (z <= -2e-302)
		tmp = t_1;
	elseif (z <= 2.9e-170)
		tmp = (x / t) / (y - z);
	elseif (z <= 5e-29)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -2.3e+15], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-302], t$95$1, If[LessEqual[z, 2.9e-170], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-29], t$95$1, N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3e15

   1. Initial program 87.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 0 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   7. Simplified 87.6%

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

   if -2.3e15 < z < -1.9999999999999999e-302 or 2.9e-170 < z < 4.99999999999999986e-29

   1. Initial program 93.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 92.4%

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

   4. Applied egg-rr 92.4%

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

      1. un-div-inv 92.5%

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

      2. clear-num 91.6%

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

   6. Applied egg-rr 91.6%

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

   7. Taylor expanded in y around inf 65.7%

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

      1. associate-/r* 69.0%

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

   9. Simplified 69.0%

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

       1. div-inv 69.1%

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

       2. associate-/l* 65.6%

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

   11. Applied egg-rr 65.6%

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

       1. *-commutative 65.6%

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

       2. associate-*l/ 69.1%

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

       3. associate-*r/ 74.0%

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

       4. associate-*l/ 74.0%

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

       5. *-lft-identity 74.0%

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

   13. Simplified 74.0%

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

   if -1.9999999999999999e-302 < z < 2.9e-170

   1. Initial program 93.4%

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

      1. associate-/l/ 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around inf 93.5%

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

   if 4.99999999999999986e-29 < z

   1. Initial program 81.7%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/r* 84.5%

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

      3. distribute-neg-frac2 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in x around 0 70.2%

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

      1. associate-/r* 84.5%

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

   10. Simplified 84.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-302}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-180}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+74} \lor \neg \left(t \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.6e-108)
   (/ (/ x y) t)
   (if (<= t 9.5e-180)
     (/ x (* y (- z)))
     (if (or (<= t 2.5e+74) (not (<= t 3.5e+134)))
       (/ (/ x t) y)
       (/ x (* t (- z)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-108) {
		tmp = (x / y) / t;
	} else if (t <= 9.5e-180) {
		tmp = x / (y * -z);
	} else if ((t <= 2.5e+74) || !(t <= 3.5e+134)) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (t * -z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.6d-108)) then
        tmp = (x / y) / t
    else if (t <= 9.5d-180) then
        tmp = x / (y * -z)
    else if ((t <= 2.5d+74) .or. (.not. (t <= 3.5d+134))) then
        tmp = (x / t) / y
    else
        tmp = x / (t * -z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-108) {
		tmp = (x / y) / t;
	} else if (t <= 9.5e-180) {
		tmp = x / (y * -z);
	} else if ((t <= 2.5e+74) || !(t <= 3.5e+134)) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (t * -z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3.6e-108:
		tmp = (x / y) / t
	elif t <= 9.5e-180:
		tmp = x / (y * -z)
	elif (t <= 2.5e+74) or not (t <= 3.5e+134):
		tmp = (x / t) / y
	else:
		tmp = x / (t * -z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.6e-108)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 9.5e-180)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif ((t <= 2.5e+74) || !(t <= 3.5e+134))
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(t * Float64(-z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.6e-108)
		tmp = (x / y) / t;
	elseif (t <= 9.5e-180)
		tmp = x / (y * -z);
	elseif ((t <= 2.5e+74) || ~((t <= 3.5e+134)))
		tmp = (x / t) / y;
	else
		tmp = x / (t * -z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -3.6e-108], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 9.5e-180], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.5e+74], N[Not[LessEqual[t, 3.5e+134]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.6000000000000001e-108

   1. Initial program 86.4%

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

      1. associate-/l/ 94.7%

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

      2. div-inv 94.7%

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

   4. Applied egg-rr 94.7%

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

      1. associate-*l/ 99.7%

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

      2. div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.6%

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

      5. associate-*l/ 99.7%

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

      6. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 48.3%

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

      1. associate-/l/ 56.8%

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

   9. Simplified 56.8%

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

   if -3.6000000000000001e-108 < t < 9.49999999999999934e-180

   1. Initial program 88.5%

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

      1. associate-/l/ 98.7%

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

      2. div-inv 98.7%

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

   4. Applied egg-rr 98.7%

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

      1. un-div-inv 98.7%

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

      2. clear-num 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around inf 52.0%

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

      1. associate-/r* 49.9%

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

   9. Simplified 49.9%

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

   10. Taylor expanded in t around 0 47.3%

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

       1. associate-*r/ 47.3%

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

       2. neg-mul-1 47.3%

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

       3. *-commutative 47.3%

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

   12. Simplified 47.3%

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

   if 9.49999999999999934e-180 < t < 2.49999999999999982e74 or 3.50000000000000003e134 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 52.5%

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

      1. frac-2neg 52.5%

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

      2. add-cube-cbrt 52.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \sqrt[3]{-x}}}{-t \cdot y} \]

      3. associate-/l* 52.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \frac{\sqrt[3]{-x}}{-t \cdot y}} \]

      4. cbrt-unprod 47.4%

         \[\leadsto \color{blue}{\sqrt[3]{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      5. sqr-neg 47.4%

         \[\leadsto \sqrt[3]{\color{blue}{x \cdot x}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      6. cbrt-unprod 52.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      7. pow2 52.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      8. add-sqr-sqrt 25.4%

         \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}}{-t \cdot y} \]

      9. sqrt-unprod 36.7%

         \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}}{-t \cdot y} \]

      10. sqr-neg 36.7%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\sqrt{\color{blue}{x \cdot x}}}}{-t \cdot y} \]

      11. sqrt-unprod 13.5%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}}{-t \cdot y} \]

      12. add-sqr-sqrt 26.0%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{x}}}{-t \cdot y} \]

      13. distribute-rgt-neg-in 26.0%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{\color{blue}{t \cdot \left(-y\right)}} \]

   5. Applied egg-rr 26.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{t \cdot \left(-y\right)}} \]
   6. Step-by-step derivation

      1. associate-*r/ 26.0%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)}} \]

      2. unpow2 26.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)} \]

      3. rem-3cbrt-lft 26.0%

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

   7. Simplified 26.0%

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

      1. clear-num 27.1%

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

      2. associate-/r/ 26.0%

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

      3. associate-/r* 26.0%

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

      4. add-sqr-sqrt 12.5%

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

      5. sqrt-unprod 34.6%

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

      6. sqr-neg 34.6%

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

      7. sqrt-unprod 29.0%

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

      8. add-sqr-sqrt 52.4%

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

   9. Applied egg-rr 52.4%

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

       1. associate-*l/ 58.6%

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

       2. associate-*l/ 58.6%

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

       3. *-un-lft-identity 58.6%

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

   11. Applied egg-rr 58.6%

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

   if 2.49999999999999982e74 < t < 3.50000000000000003e134

   1. Initial program 79.5%

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

   3. Taylor expanded in y around 0 65.4%

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

      1. associate-*r/ 65.4%

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

      2. neg-mul-1 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in z around 0 50.8%

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

      1. associate-*r/ 50.8%

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

      2. mul-1-neg 50.8%

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

   8. Simplified 50.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-180}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+74} \lor \neg \left(t \leq 3.5 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e+109)
   (/ (/ x z) (- z y))
   (if (<= z 8e+138) (/ x (* (- t z) (- 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 (z <= -6.5e+109) {
		tmp = (x / z) / (z - y);
	} else if (z <= 8e+138) {
		tmp = x / ((t - z) * (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 (z <= (-6.5d+109)) then
        tmp = (x / z) / (z - y)
    else if (z <= 8d+138) then
        tmp = x / ((t - z) * (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 (z <= -6.5e+109) {
		tmp = (x / z) / (z - y);
	} else if (z <= 8e+138) {
		tmp = x / ((t - z) * (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 z <= -6.5e+109:
		tmp = (x / z) / (z - y)
	elif z <= 8e+138:
		tmp = x / ((t - z) * (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 (z <= -6.5e+109)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 8e+138)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / 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 (z <= -6.5e+109)
		tmp = (x / z) / (z - y);
	elseif (z <= 8e+138)
		tmp = x / ((t - z) * (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[z, -6.5e+109], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+138], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e109

   1. Initial program 86.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 0 95.5%

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

      1. associate-*r/ 95.5%

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

      2. neg-mul-1 95.5%

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

   7. Simplified 95.5%

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

   if -6.5e109 < z < 8.0000000000000003e138

   1. Initial program 92.6%

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

   if 8.0000000000000003e138 < z

   1. Initial program 73.6%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. associate-/r* 99.9%

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

      3. distribute-neg-frac2 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 73.6%

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

      1. associate-/r* 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \end{array} \]

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 -8e+104)
   (/ (/ x z) (- z y))
   (if (<= z 2.3e+151)
     (/ x (* (- t z) (- y z)))
     (/ (/ -1.0 z) (/ (- t z) x)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+104) {
		tmp = (x / z) / (z - y);
	} else if (z <= 2.3e+151) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (-1.0 / z) / ((t - 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 <= (-8d+104)) then
        tmp = (x / z) / (z - y)
    else if (z <= 2.3d+151) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = ((-1.0d0) / z) / ((t - 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 <= -8e+104) {
		tmp = (x / z) / (z - y);
	} else if (z <= 2.3e+151) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (-1.0 / z) / ((t - z) / x);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -8e+104:
		tmp = (x / z) / (z - y)
	elif z <= 2.3e+151:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (-1.0 / z) / ((t - 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 <= -8e+104)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 2.3e+151)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(t - 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 <= -8e+104)
		tmp = (x / z) / (z - y);
	elseif (z <= 2.3e+151)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (-1.0 / z) / ((t - 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, -8e+104], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+151], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e104

   1. Initial program 86.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 0 95.5%

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

      1. associate-*r/ 95.5%

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

      2. neg-mul-1 95.5%

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

   7. Simplified 95.5%

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

   if -8e104 < z < 2.3000000000000001e151

   1. Initial program 92.8%

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

   if 2.3000000000000001e151 < z

   1. Initial program 70.8%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+104}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+14} \lor \neg \left(z \leq 1.5 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e+14) (not (<= z 1.5e-33)))
   (/ 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 ((z <= -1.5e+14) || !(z <= 1.5e-33)) {
		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 ((z <= (-1.5d+14)) .or. (.not. (z <= 1.5d-33))) 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 ((z <= -1.5e+14) || !(z <= 1.5e-33)) {
		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 (z <= -1.5e+14) or not (z <= 1.5e-33):
		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 ((z <= -1.5e+14) || !(z <= 1.5e-33))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(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 ((z <= -1.5e+14) || ~((z <= 1.5e-33)))
		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[Or[LessEqual[z, -1.5e+14], N[Not[LessEqual[z, 1.5e-33]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e14 or 1.5000000000000001e-33 < z

   1. Initial program 84.1%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. associate-/r* 87.9%

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

      3. distribute-neg-frac2 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in x around 0 76.5%

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

   if -1.5e14 < z < 1.5000000000000001e-33

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 77.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+14} \lor \neg \left(z \leq 1.5 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.6e-108)
   (/ (/ x y) t)
   (if (<= t 1.02e-179) (/ x (* y (- z))) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-108) {
		tmp = (x / y) / t;
	} else if (t <= 1.02e-179) {
		tmp = x / (y * -z);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.6d-108)) then
        tmp = (x / y) / t
    else if (t <= 1.02d-179) then
        tmp = x / (y * -z)
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e-108) {
		tmp = (x / y) / t;
	} else if (t <= 1.02e-179) {
		tmp = x / (y * -z);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3.6e-108:
		tmp = (x / y) / t
	elif t <= 1.02e-179:
		tmp = x / (y * -z)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.6e-108)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 1.02e-179)
		tmp = Float64(x / Float64(y * Float64(-z)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.6e-108)
		tmp = (x / y) / t;
	elseif (t <= 1.02e-179)
		tmp = x / (y * -z);
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -3.6e-108], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.02e-179], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6000000000000001e-108

   1. Initial program 86.4%

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

      1. associate-/l/ 94.7%

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

      2. div-inv 94.7%

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

   4. Applied egg-rr 94.7%

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

      1. associate-*l/ 99.7%

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

      2. div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. clear-num 99.6%

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

      5. associate-*l/ 99.7%

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

      6. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 48.3%

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

      1. associate-/l/ 56.8%

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

   9. Simplified 56.8%

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

   if -3.6000000000000001e-108 < t < 1.02e-179

   1. Initial program 88.5%

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

      1. associate-/l/ 98.7%

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

      2. div-inv 98.7%

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

   4. Applied egg-rr 98.7%

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

      1. un-div-inv 98.7%

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

      2. clear-num 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around inf 52.0%

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

      1. associate-/r* 49.9%

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

   9. Simplified 49.9%

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

   10. Taylor expanded in t around 0 47.3%

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

       1. associate-*r/ 47.3%

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

       2. neg-mul-1 47.3%

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

       3. *-commutative 47.3%

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

   12. Simplified 47.3%

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

   if 1.02e-179 < t

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf 71.5%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00043:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.00043)
   (/ x (* (- t z) y))
   (if (<= y 8e-178) (/ 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 <= -0.00043) {
		tmp = x / ((t - z) * y);
	} else if (y <= 8e-178) {
		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 <= (-0.00043d0)) then
        tmp = x / ((t - z) * y)
    else if (y <= 8d-178) 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 <= -0.00043) {
		tmp = x / ((t - z) * y);
	} else if (y <= 8e-178) {
		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 <= -0.00043:
		tmp = x / ((t - z) * y)
	elif y <= 8e-178:
		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 <= -0.00043)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 8e-178)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(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 <= -0.00043)
		tmp = x / ((t - z) * y);
	elseif (y <= 8e-178)
		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, -0.00043], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-178], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.29999999999999989e-4

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 82.0%

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

      1. *-commutative 82.0%

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

   5. Simplified 82.0%

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

   if -4.29999999999999989e-4 < y < 7.9999999999999996e-178

   1. Initial program 91.5%

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

      1. associate-/l/ 96.5%

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

      2. div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in y around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. associate-/r* 83.9%

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

      3. distribute-neg-frac2 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in x around 0 78.7%

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

   if 7.9999999999999996e-178 < y

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf 55.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00043:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00075:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -0.00075)
   (/ x (* (- t z) y))
   (if (<= y 3.4e-112) (/ 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 <= -0.00075) {
		tmp = x / ((t - z) * y);
	} else if (y <= 3.4e-112) {
		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 <= (-0.00075d0)) then
        tmp = x / ((t - z) * y)
    else if (y <= 3.4d-112) 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 <= -0.00075) {
		tmp = x / ((t - z) * y);
	} else if (y <= 3.4e-112) {
		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 <= -0.00075:
		tmp = x / ((t - z) * y)
	elif y <= 3.4e-112:
		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 <= -0.00075)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 3.4e-112)
		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 <= -0.00075)
		tmp = x / ((t - z) * y);
	elseif (y <= 3.4e-112)
		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, -0.00075], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-112], 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 < -7.5000000000000002e-4

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 82.0%

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

      1. *-commutative 82.0%

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

   5. Simplified 82.0%

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

   if -7.5000000000000002e-4 < y < 3.3999999999999998e-112

   1. Initial program 91.7%

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

      1. associate-/l/ 96.1%

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

      2. div-inv 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in y around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. associate-/r* 82.1%

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

      3. distribute-neg-frac2 82.1%

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

   7. Simplified 82.1%

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

   8. Taylor expanded in x around 0 76.7%

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

   if 3.3999999999999998e-112 < y

   1. Initial program 83.8%

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

      1. associate-/l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around inf 59.2%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00075:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00046:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -0.00046)
   (/ (/ x y) (- t z))
   (if (<= y 7e-106) (/ 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 <= -0.00046) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7e-106) {
		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 <= (-0.00046d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= 7d-106) 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 <= -0.00046) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7e-106) {
		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 <= -0.00046:
		tmp = (x / y) / (t - z)
	elif y <= 7e-106:
		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 <= -0.00046)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 7e-106)
		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 <= -0.00046)
		tmp = (x / y) / (t - z);
	elseif (y <= 7e-106)
		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, -0.00046], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-106], 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 < -4.6000000000000001e-4

   1. Initial program 90.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. un-div-inv 99.9%

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

      2. clear-num 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in y around inf 82.0%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   if -4.6000000000000001e-4 < y < 7e-106

   1. Initial program 91.1%

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

      1. associate-/l/ 96.2%

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

      2. div-inv 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. associate-/r* 80.1%

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

      3. distribute-neg-frac2 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in x around 0 74.9%

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

   if 7e-106 < y

   1. Initial program 84.2%

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

      1. associate-/l/ 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around inf 59.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00046:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -170000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -170000000000.0)
   (/ (/ x y) (- t z))
   (if (<= y 2.75e-107) (/ (/ 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 <= -170000000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.75e-107) {
		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 <= (-170000000000.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.75d-107) 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 <= -170000000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.75e-107) {
		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 <= -170000000000.0:
		tmp = (x / y) / (t - z)
	elif y <= 2.75e-107:
		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 <= -170000000000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.75e-107)
		tmp = Float64(Float64(x / 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 <= -170000000000.0)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.75e-107)
		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, -170000000000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e-107], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e11

   1. Initial program 91.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. un-div-inv 99.9%

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

      2. clear-num 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in y around inf 86.0%

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

      1. associate-/r* 89.3%

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

   9. Simplified 89.3%

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

   if -1.7e11 < y < 2.74999999999999993e-107

   1. Initial program 90.5%

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

      1. associate-/l/ 96.3%

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

      2. div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in y around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. associate-/r* 80.6%

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

      3. distribute-neg-frac2 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in x around 0 74.7%

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

      1. associate-/r* 80.6%

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

   10. Simplified 80.6%

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

   if 2.74999999999999993e-107 < y

   1. Initial program 84.3%

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

      1. associate-/l/ 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 60.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -170000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -118000000000:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -118000000000.0)
   (/ (/ x (- t z)) y)
   (if (<= y 4.7e-110) (/ (/ 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 <= -118000000000.0) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 4.7e-110) {
		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 <= (-118000000000.0d0)) then
        tmp = (x / (t - z)) / y
    else if (y <= 4.7d-110) 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 <= -118000000000.0) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 4.7e-110) {
		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 <= -118000000000.0:
		tmp = (x / (t - z)) / y
	elif y <= 4.7e-110:
		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 <= -118000000000.0)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 4.7e-110)
		tmp = Float64(Float64(x / 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 <= -118000000000.0)
		tmp = (x / (t - z)) / y;
	elseif (y <= 4.7e-110)
		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, -118000000000.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 4.7e-110], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.18e11

   1. Initial program 91.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. un-div-inv 99.9%

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

      2. clear-num 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in y around inf 86.0%

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

      1. associate-/r* 89.3%

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

   9. Simplified 89.3%

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

       1. div-inv 89.2%

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

       2. associate-/l* 85.9%

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

   11. Applied egg-rr 85.9%

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

       1. *-commutative 85.9%

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

       2. associate-*l/ 89.2%

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

       3. associate-*r/ 92.8%

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

       4. associate-*l/ 93.0%

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

       5. *-lft-identity 93.0%

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

   13. Simplified 93.0%

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

   if -1.18e11 < y < 4.69999999999999992e-110

   1. Initial program 90.3%

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

      1. associate-/l/ 96.3%

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

      2. div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in y around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/r* 81.2%

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

      3. distribute-neg-frac2 81.2%

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

   7. Simplified 81.2%

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

   8. Taylor expanded in x around 0 75.2%

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

      1. associate-/r* 81.2%

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

   10. Simplified 81.2%

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

   if 4.69999999999999992e-110 < y

   1. Initial program 84.7%

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

      1. associate-/l/ 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 59.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -118000000000:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-110}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e-87)
   (/ (/ x y) t)
   (if (<= y 4e-165) (/ x (* t (- z))) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-87) {
		tmp = (x / y) / t;
	} else if (y <= 4e-165) {
		tmp = x / (t * -z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.25d-87)) then
        tmp = (x / y) / t
    else if (y <= 4d-165) then
        tmp = x / (t * -z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-87) {
		tmp = (x / y) / t;
	} else if (y <= 4e-165) {
		tmp = x / (t * -z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e-87:
		tmp = (x / y) / t
	elif y <= 4e-165:
		tmp = x / (t * -z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-87)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 4e-165)
		tmp = Float64(x / Float64(t * Float64(-z)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-87)
		tmp = (x / y) / t;
	elseif (y <= 4e-165)
		tmp = x / (t * -z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e-87], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 4e-165], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.24999999999999979e-87

   1. Initial program 92.3%

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

      1. associate-/l/ 99.4%

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

      2. div-inv 99.3%

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

   4. Applied egg-rr 99.3%

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

      1. associate-*l/ 97.1%

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

      2. div-inv 97.1%

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

      3. div-inv 97.2%

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

      4. clear-num 97.1%

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

      5. associate-*l/ 97.2%

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

      6. *-un-lft-identity 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in z around 0 50.9%

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

      1. associate-/l/ 55.7%

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

   9. Simplified 55.7%

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

   if -2.24999999999999979e-87 < y < 4e-165

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in z around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. mul-1-neg 55.6%

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

   8. Simplified 55.6%

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

   if 4e-165 < y

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0 43.6%

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

      1. frac-2neg 43.6%

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

      2. add-cube-cbrt 43.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \sqrt[3]{-x}}}{-t \cdot y} \]

      3. associate-/l* 43.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \frac{\sqrt[3]{-x}}{-t \cdot y}} \]

      4. cbrt-unprod 46.6%

         \[\leadsto \color{blue}{\sqrt[3]{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      5. sqr-neg 46.6%

         \[\leadsto \sqrt[3]{\color{blue}{x \cdot x}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      6. cbrt-unprod 43.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      7. pow2 43.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      8. add-sqr-sqrt 22.1%

         \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}}{-t \cdot y} \]

      9. sqrt-unprod 40.6%

         \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}}{-t \cdot y} \]

      10. sqr-neg 40.6%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\sqrt{\color{blue}{x \cdot x}}}}{-t \cdot y} \]

      11. sqrt-unprod 13.6%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}}{-t \cdot y} \]

      12. add-sqr-sqrt 26.6%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{x}}}{-t \cdot y} \]

      13. distribute-rgt-neg-in 26.6%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{\color{blue}{t \cdot \left(-y\right)}} \]

   5. Applied egg-rr 26.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{t \cdot \left(-y\right)}} \]
   6. Step-by-step derivation

      1. associate-*r/ 26.6%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)}} \]

      2. unpow2 26.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)} \]

      3. rem-3cbrt-lft 26.6%

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

   7. Simplified 26.6%

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

      1. clear-num 27.3%

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

      2. associate-/r/ 26.6%

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

      3. associate-/r* 26.6%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 44.0%

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

      6. sqr-neg 44.0%

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

      7. sqrt-unprod 44.4%

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

      8. add-sqr-sqrt 44.5%

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

   9. Applied egg-rr 44.5%

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

       1. associate-*l/ 48.1%

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

       2. associate-*l/ 48.1%

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

       3. *-un-lft-identity 48.1%

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

   11. Applied egg-rr 48.1%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 4 \cdot 10^{-96}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 4e-96) (/ (/ x y) t) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4e-96) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 4d-96) then
        tmp = (x / y) / t
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4e-96) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 4e-96:
		tmp = (x / y) / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4e-96)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 4e-96)
		tmp = (x / y) / t;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 4e-96], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.9999999999999996e-96

   1. Initial program 87.9%

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

      1. associate-/l/ 96.6%

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

      2. div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. associate-*l/ 97.9%

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

      2. div-inv 97.9%

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

      3. div-inv 97.9%

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

      4. clear-num 97.8%

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

      5. associate-*l/ 97.8%

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

      6. *-un-lft-identity 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in z around 0 35.4%

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

      1. associate-/l/ 43.3%

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

   9. Simplified 43.3%

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

   if 3.9999999999999996e-96 < t

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 45.9%

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

      1. frac-2neg 45.9%

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

      2. add-cube-cbrt 45.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \sqrt[3]{-x}}}{-t \cdot y} \]

      3. associate-/l* 45.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \frac{\sqrt[3]{-x}}{-t \cdot y}} \]

      4. cbrt-unprod 41.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      5. sqr-neg 41.8%

         \[\leadsto \sqrt[3]{\color{blue}{x \cdot x}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      6. cbrt-unprod 45.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      7. pow2 45.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

      8. add-sqr-sqrt 19.2%

         \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}}{-t \cdot y} \]

      9. sqrt-unprod 31.8%

         \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}}{-t \cdot y} \]

      10. sqr-neg 31.8%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\sqrt{\color{blue}{x \cdot x}}}}{-t \cdot y} \]

      11. sqrt-unprod 14.1%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}}{-t \cdot y} \]

      12. add-sqr-sqrt 25.8%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{x}}}{-t \cdot y} \]

      13. distribute-rgt-neg-in 25.8%

          \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{\color{blue}{t \cdot \left(-y\right)}} \]

   5. Applied egg-rr 25.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{t \cdot \left(-y\right)}} \]
   6. Step-by-step derivation

      1. associate-*r/ 25.8%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)}} \]

      2. unpow2 25.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)} \]

      3. rem-3cbrt-lft 25.8%

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

   7. Simplified 25.8%

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

      1. clear-num 26.8%

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

      2. associate-/r/ 25.8%

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

      3. associate-/r* 25.8%

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

      4. add-sqr-sqrt 13.2%

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

      5. sqrt-unprod 29.3%

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

      6. sqr-neg 29.3%

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

      7. sqrt-unprod 22.5%

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

      8. add-sqr-sqrt 45.9%

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

   9. Applied egg-rr 45.9%

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

       1. associate-*l/ 51.7%

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

       2. associate-*l/ 51.7%

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

       3. *-un-lft-identity 51.7%

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

   11. Applied egg-rr 51.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4 \cdot 10^{-96}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

3. Taylor expanded in z around 0 38.5%

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

4. Final simplification 38.5%

   \[\leadsto \frac{x}{t \cdot y} \]
5. Add Preprocessing

Alternative 17: 43.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

3. Taylor expanded in z around 0 38.5%

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

   1. frac-2neg 38.5%

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

   2. add-cube-cbrt 38.3%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \sqrt[3]{-x}}}{-t \cdot y} \]

   3. associate-/l* 38.3%

      \[\leadsto \color{blue}{\left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \frac{\sqrt[3]{-x}}{-t \cdot y}} \]

   4. cbrt-unprod 41.7%

      \[\leadsto \color{blue}{\sqrt[3]{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

   5. sqr-neg 41.7%

      \[\leadsto \sqrt[3]{\color{blue}{x \cdot x}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

   6. cbrt-unprod 38.3%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

   7. pow2 38.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot \frac{\sqrt[3]{-x}}{-t \cdot y} \]

   8. add-sqr-sqrt 18.8%

      \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}}{-t \cdot y} \]

   9. sqrt-unprod 34.9%

      \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}}{-t \cdot y} \]

   10. sqr-neg 34.9%

       \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\sqrt{\color{blue}{x \cdot x}}}}{-t \cdot y} \]

   11. sqrt-unprod 10.9%

       \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}}{-t \cdot y} \]

   12. add-sqr-sqrt 21.1%

       \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{\color{blue}{x}}}{-t \cdot y} \]

   13. distribute-rgt-neg-in 21.1%

       \[\leadsto {\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{\color{blue}{t \cdot \left(-y\right)}} \]

5. Applied egg-rr 21.1%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2} \cdot \frac{\sqrt[3]{x}}{t \cdot \left(-y\right)}} \]
6. Step-by-step derivation

   1. associate-*r/ 21.1%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)}} \]

   2. unpow2 21.1%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{t \cdot \left(-y\right)} \]

   3. rem-3cbrt-lft 21.1%

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

7. Simplified 21.1%

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

   1. clear-num 21.5%

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

   2. associate-/r/ 21.1%

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

   3. associate-/r* 21.1%

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

   4. add-sqr-sqrt 10.2%

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

   5. sqrt-unprod 31.9%

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

   6. sqr-neg 31.9%

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

   7. sqrt-unprod 20.7%

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

   8. add-sqr-sqrt 38.8%

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

9. Applied egg-rr 38.8%

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

    1. associate-*l/ 45.5%

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

    2. associate-*l/ 45.6%

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

    3. *-un-lft-identity 45.6%

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

11. Applied egg-rr 45.6%

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

12. Final simplification 45.6%

    \[\leadsto \frac{\frac{x}{t}}{y} \]
13. Add Preprocessing

Developer target: 87.6% 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 2024079 
(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))))