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

Percentage Accurate: 88.5% → 96.9%

Time: 11.5s

Alternatives: 22

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

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 (- y z)) (- t z)))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 85.9%

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

3. Taylor expanded in x around 0 85.9%

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

   1. associate-/l/ 97.2%

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

5. Simplified 97.2%

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

6. Final simplification 97.2%

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

Alternative 2: 78.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -35000000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -35000000000000.0)
   (/ (/ x y) (- t z))
   (if (<= y -1.02e-44)
     (/ x (* z (- z y)))
     (if (<= y -4.1e-81)
       (/ (/ x (- t z)) y)
       (if (<= y 1.2e-86) (/ 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 <= -35000000000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.02e-44) {
		tmp = x / (z * (z - y));
	} else if (y <= -4.1e-81) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.2e-86) {
		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 <= (-35000000000000.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-1.02d-44)) then
        tmp = x / (z * (z - y))
    else if (y <= (-4.1d-81)) then
        tmp = (x / (t - z)) / y
    else if (y <= 1.2d-86) 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 <= -35000000000000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.02e-44) {
		tmp = x / (z * (z - y));
	} else if (y <= -4.1e-81) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.2e-86) {
		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 <= -35000000000000.0:
		tmp = (x / y) / (t - z)
	elif y <= -1.02e-44:
		tmp = x / (z * (z - y))
	elif y <= -4.1e-81:
		tmp = (x / (t - z)) / y
	elif y <= 1.2e-86:
		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 <= -35000000000000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -1.02e-44)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (y <= -4.1e-81)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 1.2e-86)
		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 <= -35000000000000.0)
		tmp = (x / y) / (t - z);
	elseif (y <= -1.02e-44)
		tmp = x / (z * (z - y));
	elseif (y <= -4.1e-81)
		tmp = (x / (t - z)) / y;
	elseif (y <= 1.2e-86)
		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, -35000000000000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.02e-44], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e-81], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.2e-86], 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 5 regimes

2. if y < -3.5e13

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 84.5%

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

      1. associate-/l/ 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in y around inf 95.8%

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

   if -3.5e13 < y < -1.0199999999999999e-44

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0 91.7%

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

      1. associate-/l/ 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in t around 0 40.2%

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

      1. associate-*r/ 40.2%

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

      2. neg-mul-1 40.2%

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

   8. Simplified 40.2%

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

   if -1.0199999999999999e-44 < y < -4.09999999999999984e-81

   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. clear-num 88.1%

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

      2. associate-/r/ 88.3%

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

   4. Applied egg-rr 88.3%

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

      1. associate-*l/ 88.5%

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

      2. *-commutative 88.5%

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

      3. frac-times 99.6%

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

      4. clear-num 99.8%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 40.7%

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

      1. *-rgt-identity 40.7%

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

      2. times-frac 40.3%

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

      3. associate-*l/ 51.3%

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

      4. associate-*r/ 51.3%

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

      5. *-rgt-identity 51.3%

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

   9. Simplified 51.3%

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

   if -4.09999999999999984e-81 < y < 1.20000000000000007e-86

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

   5. Simplified 74.0%

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

   if 1.20000000000000007e-86 < y

   1. Initial program 83.7%

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

      1. associate-/l/ 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around inf 62.1%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -35000000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+211}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) t)))
   (if (<= t -1.45e-87)
     t_1
     (if (<= t 1.2e-151)
       (/ x (* y (- z)))
       (if (<= t 1.65e+91)
         t_1
         (if (<= t 1.45e+211) (/ x (* z (- t))) (/ (/ x t) y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double tmp;
	if (t <= -1.45e-87) {
		tmp = t_1;
	} else if (t <= 1.2e-151) {
		tmp = x / (y * -z);
	} else if (t <= 1.65e+91) {
		tmp = t_1;
	} else if (t <= 1.45e+211) {
		tmp = x / (z * -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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / t
    if (t <= (-1.45d-87)) then
        tmp = t_1
    else if (t <= 1.2d-151) then
        tmp = x / (y * -z)
    else if (t <= 1.65d+91) then
        tmp = t_1
    else if (t <= 1.45d+211) then
        tmp = x / (z * -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 t_1 = (x / y) / t;
	double tmp;
	if (t <= -1.45e-87) {
		tmp = t_1;
	} else if (t <= 1.2e-151) {
		tmp = x / (y * -z);
	} else if (t <= 1.65e+91) {
		tmp = t_1;
	} else if (t <= 1.45e+211) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / y) / t
	tmp = 0
	if t <= -1.45e-87:
		tmp = t_1
	elif t <= 1.2e-151:
		tmp = x / (y * -z)
	elif t <= 1.65e+91:
		tmp = t_1
	elif t <= 1.45e+211:
		tmp = x / (z * -t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / t)
	tmp = 0.0
	if (t <= -1.45e-87)
		tmp = t_1;
	elseif (t <= 1.2e-151)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (t <= 1.65e+91)
		tmp = t_1;
	elseif (t <= 1.45e+211)
		tmp = Float64(x / Float64(z * Float64(-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)
	t_1 = (x / y) / t;
	tmp = 0.0;
	if (t <= -1.45e-87)
		tmp = t_1;
	elseif (t <= 1.2e-151)
		tmp = x / (y * -z);
	elseif (t <= 1.65e+91)
		tmp = t_1;
	elseif (t <= 1.45e+211)
		tmp = x / (z * -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_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -1.45e-87], t$95$1, If[LessEqual[t, 1.2e-151], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+91], t$95$1, If[LessEqual[t, 1.45e+211], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.45e-87 or 1.2e-151 < t < 1.65000000000000009e91

   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. clear-num 91.4%

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

      2. associate-/r/ 91.4%

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

   4. Applied egg-rr 91.4%

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

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

      3. frac-times 97.1%

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

      4. clear-num 96.8%

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

      5. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in z around 0 48.2%

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

      1. *-rgt-identity 48.2%

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

      2. associate-*r/ 48.1%

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

      3. associate-/l/ 48.8%

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

      4. associate-*r/ 50.9%

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

      5. associate-*r/ 50.9%

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

      6. *-rgt-identity 50.9%

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

   9. Simplified 50.9%

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

   if -1.45e-87 < t < 1.2e-151

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 84.8%

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

      1. associate-/l/ 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in y around inf 62.2%

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

   7. Taylor expanded in t around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. distribute-neg-frac2 52.8%

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

      3. *-commutative 52.8%

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

      4. distribute-rgt-neg-out 52.8%

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

   9. Simplified 52.8%

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

   if 1.65000000000000009e91 < t < 1.45e211

   1. Initial program 66.4%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 82.2%

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

   6. Taylor expanded in y around 0 48.0%

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

      1. associate-*r/ 48.0%

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

      2. neg-mul-1 48.0%

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

   8. Simplified 48.0%

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

   if 1.45e211 < t

   1. Initial program 74.7%

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

      1. clear-num 74.6%

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

      2. associate-/r/ 74.7%

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

   4. Applied egg-rr 74.7%

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

      1. associate-*l/ 74.7%

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

      2. *-commutative 74.7%

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

      3. frac-times 99.6%

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

      4. clear-num 99.5%

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

      5. un-div-inv 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in z around 0 49.0%

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

      1. associate-/r* 73.6%

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

   9. Simplified 73.6%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+211}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+246}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) t)))
   (if (<= t -2.3e-90)
     t_1
     (if (<= t 4.6e-151)
       (/ x (* z (- y)))
       (if (<= t 3e+177)
         t_1
         (if (<= t 3.9e+246) (/ (/ x (- z)) t) (/ (/ x t) y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / t;
	double tmp;
	if (t <= -2.3e-90) {
		tmp = t_1;
	} else if (t <= 4.6e-151) {
		tmp = x / (z * -y);
	} else if (t <= 3e+177) {
		tmp = t_1;
	} else if (t <= 3.9e+246) {
		tmp = (x / -z) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / t
    if (t <= (-2.3d-90)) then
        tmp = t_1
    else if (t <= 4.6d-151) then
        tmp = x / (z * -y)
    else if (t <= 3d+177) then
        tmp = t_1
    else if (t <= 3.9d+246) then
        tmp = (x / -z) / 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 t_1 = (x / y) / t;
	double tmp;
	if (t <= -2.3e-90) {
		tmp = t_1;
	} else if (t <= 4.6e-151) {
		tmp = x / (z * -y);
	} else if (t <= 3e+177) {
		tmp = t_1;
	} else if (t <= 3.9e+246) {
		tmp = (x / -z) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / y) / t
	tmp = 0
	if t <= -2.3e-90:
		tmp = t_1
	elif t <= 4.6e-151:
		tmp = x / (z * -y)
	elif t <= 3e+177:
		tmp = t_1
	elif t <= 3.9e+246:
		tmp = (x / -z) / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / t)
	tmp = 0.0
	if (t <= -2.3e-90)
		tmp = t_1;
	elseif (t <= 4.6e-151)
		tmp = Float64(x / Float64(z * Float64(-y)));
	elseif (t <= 3e+177)
		tmp = t_1;
	elseif (t <= 3.9e+246)
		tmp = Float64(Float64(x / Float64(-z)) / 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)
	t_1 = (x / y) / t;
	tmp = 0.0;
	if (t <= -2.3e-90)
		tmp = t_1;
	elseif (t <= 4.6e-151)
		tmp = x / (z * -y);
	elseif (t <= 3e+177)
		tmp = t_1;
	elseif (t <= 3.9e+246)
		tmp = (x / -z) / 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_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -2.3e-90], t$95$1, If[LessEqual[t, 4.6e-151], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+177], t$95$1, If[LessEqual[t, 3.9e+246], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.2999999999999998e-90 or 4.59999999999999992e-151 < t < 3e177

   1. Initial program 89.2%

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

      1. clear-num 89.0%

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

      2. associate-/r/ 89.1%

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

   4. Applied egg-rr 89.1%

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

      1. associate-*l/ 89.2%

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

      2. *-commutative 89.2%

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

      3. frac-times 97.3%

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

      4. clear-num 97.0%

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

      5. un-div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around 0 48.3%

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

      1. *-rgt-identity 48.3%

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

      2. associate-*r/ 48.2%

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

      3. associate-/l/ 48.8%

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

      4. associate-*r/ 51.5%

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

      5. associate-*r/ 51.5%

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

      6. *-rgt-identity 51.5%

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

   9. Simplified 51.5%

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

   if -2.2999999999999998e-90 < t < 4.59999999999999992e-151

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. associate-/l/ 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in y around inf 62.5%

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

   7. Taylor expanded in t around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-neg-frac2 53.4%

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

      3. *-commutative 53.4%

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

      4. distribute-rgt-neg-out 53.4%

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

   9. Simplified 53.4%

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

   if 3e177 < t < 3.9e246

   1. Initial program 70.4%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 94.6%

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

   6. Taylor expanded in y around 0 60.1%

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

      1. associate-*r/ 60.1%

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

      2. neg-mul-1 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in x around 0 60.1%

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

       1. mul-1-neg 60.1%

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

       2. associate-/l/ 69.8%

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

       3. distribute-neg-frac2 69.8%

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

   11. Simplified 69.8%

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

   if 3.9e246 < t

   1. Initial program 71.8%

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

      1. clear-num 71.8%

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

      2. associate-/r/ 71.8%

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

   4. Applied egg-rr 71.8%

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

      1. associate-*l/ 71.8%

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

      2. *-commutative 71.8%

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

      3. frac-times 99.5%

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

      4. clear-num 99.4%

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

      5. un-div-inv 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in z around 0 43.3%

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

      1. associate-/r* 70.5%

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

   9. Simplified 70.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-90}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+177}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+246}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{-z}\\ t_2 := \frac{\frac{x}{y}}{t}\\ \mathbf{if}\;t \leq -9 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-153}:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+246}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- z))) (t_2 (/ (/ x y) t)))
   (if (<= t -9e-88)
     t_2
     (if (<= t 4.2e-153)
       (/ t_1 y)
       (if (<= t 3.9e+177)
         t_2
         (if (<= t 4.5e+246) (/ t_1 t) (/ (/ x t) y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / -z;
	double t_2 = (x / y) / t;
	double tmp;
	if (t <= -9e-88) {
		tmp = t_2;
	} else if (t <= 4.2e-153) {
		tmp = t_1 / y;
	} else if (t <= 3.9e+177) {
		tmp = t_2;
	} else if (t <= 4.5e+246) {
		tmp = t_1 / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / -z
    t_2 = (x / y) / t
    if (t <= (-9d-88)) then
        tmp = t_2
    else if (t <= 4.2d-153) then
        tmp = t_1 / y
    else if (t <= 3.9d+177) then
        tmp = t_2
    else if (t <= 4.5d+246) then
        tmp = t_1 / 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 t_1 = x / -z;
	double t_2 = (x / y) / t;
	double tmp;
	if (t <= -9e-88) {
		tmp = t_2;
	} else if (t <= 4.2e-153) {
		tmp = t_1 / y;
	} else if (t <= 3.9e+177) {
		tmp = t_2;
	} else if (t <= 4.5e+246) {
		tmp = t_1 / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / -z
	t_2 = (x / y) / t
	tmp = 0
	if t <= -9e-88:
		tmp = t_2
	elif t <= 4.2e-153:
		tmp = t_1 / y
	elif t <= 3.9e+177:
		tmp = t_2
	elif t <= 4.5e+246:
		tmp = t_1 / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(-z))
	t_2 = Float64(Float64(x / y) / t)
	tmp = 0.0
	if (t <= -9e-88)
		tmp = t_2;
	elseif (t <= 4.2e-153)
		tmp = Float64(t_1 / y);
	elseif (t <= 3.9e+177)
		tmp = t_2;
	elseif (t <= 4.5e+246)
		tmp = Float64(t_1 / 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)
	t_1 = x / -z;
	t_2 = (x / y) / t;
	tmp = 0.0;
	if (t <= -9e-88)
		tmp = t_2;
	elseif (t <= 4.2e-153)
		tmp = t_1 / y;
	elseif (t <= 3.9e+177)
		tmp = t_2;
	elseif (t <= 4.5e+246)
		tmp = t_1 / 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_] := Block[{t$95$1 = N[(x / (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -9e-88], t$95$2, If[LessEqual[t, 4.2e-153], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[t, 3.9e+177], t$95$2, If[LessEqual[t, 4.5e+246], N[(t$95$1 / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.99999999999999982e-88 or 4.20000000000000008e-153 < t < 3.8999999999999999e177

   1. Initial program 89.7%

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

      1. clear-num 89.6%

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

      2. associate-/r/ 89.6%

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

   4. Applied egg-rr 89.6%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

      3. frac-times 97.3%

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

      4. clear-num 97.0%

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

      5. un-div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around 0 48.5%

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

      1. *-rgt-identity 48.5%

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

      2. associate-*r/ 48.5%

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

      3. associate-/l/ 49.1%

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

      4. associate-*r/ 51.6%

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

      5. associate-*r/ 51.5%

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

      6. *-rgt-identity 51.5%

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

   9. Simplified 51.5%

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

   if -8.99999999999999982e-88 < t < 4.20000000000000008e-153

   1. Initial program 84.8%

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

      1. clear-num 84.3%

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

      2. associate-/r/ 84.8%

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

   4. Applied egg-rr 84.8%

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

      1. associate-*l/ 84.8%

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

      2. *-commutative 84.8%

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

      3. frac-times 95.9%

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

      4. clear-num 95.9%

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

      5. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around inf 59.3%

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

      1. *-rgt-identity 59.3%

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

      2. times-frac 62.1%

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

      3. associate-*l/ 64.5%

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

      4. associate-*r/ 64.6%

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

      5. *-rgt-identity 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in t around 0 52.8%

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

       1. associate-*r/ 52.8%

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

       2. *-commutative 52.8%

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

       3. associate-/r* 56.5%

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

       4. neg-mul-1 56.5%

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

   12. Simplified 56.5%

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

   if 3.8999999999999999e177 < t < 4.5e246

   1. Initial program 70.4%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 94.6%

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

   6. Taylor expanded in y around 0 60.1%

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

      1. associate-*r/ 60.1%

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

      2. neg-mul-1 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in x around 0 60.1%

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

       1. mul-1-neg 60.1%

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

       2. associate-/l/ 69.8%

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

       3. distribute-neg-frac2 69.8%

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

   11. Simplified 69.8%

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

   if 4.5e246 < t

   1. Initial program 71.8%

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

      1. clear-num 71.8%

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

      2. associate-/r/ 71.8%

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

   4. Applied egg-rr 71.8%

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

      1. associate-*l/ 71.8%

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

      2. *-commutative 71.8%

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

      3. frac-times 99.5%

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

      4. clear-num 99.4%

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

      5. un-div-inv 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in z around 0 43.3%

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

      1. associate-/r* 70.5%

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

   9. Simplified 70.5%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+177}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+246}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{-z}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+177}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+246}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- z))))
   (if (<= t -9.5e-87)
     (* (/ 1.0 y) (/ x t))
     (if (<= t 6.5e-151)
       (/ t_1 y)
       (if (<= t 3.9e+177)
         (/ (/ x y) t)
         (if (<= t 3.9e+246) (/ t_1 t) (/ (/ x t) y)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / -z;
	double tmp;
	if (t <= -9.5e-87) {
		tmp = (1.0 / y) * (x / t);
	} else if (t <= 6.5e-151) {
		tmp = t_1 / y;
	} else if (t <= 3.9e+177) {
		tmp = (x / y) / t;
	} else if (t <= 3.9e+246) {
		tmp = t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = x / -z
    if (t <= (-9.5d-87)) then
        tmp = (1.0d0 / y) * (x / t)
    else if (t <= 6.5d-151) then
        tmp = t_1 / y
    else if (t <= 3.9d+177) then
        tmp = (x / y) / t
    else if (t <= 3.9d+246) then
        tmp = t_1 / 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 t_1 = x / -z;
	double tmp;
	if (t <= -9.5e-87) {
		tmp = (1.0 / y) * (x / t);
	} else if (t <= 6.5e-151) {
		tmp = t_1 / y;
	} else if (t <= 3.9e+177) {
		tmp = (x / y) / t;
	} else if (t <= 3.9e+246) {
		tmp = t_1 / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / -z
	tmp = 0
	if t <= -9.5e-87:
		tmp = (1.0 / y) * (x / t)
	elif t <= 6.5e-151:
		tmp = t_1 / y
	elif t <= 3.9e+177:
		tmp = (x / y) / t
	elif t <= 3.9e+246:
		tmp = t_1 / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(-z))
	tmp = 0.0
	if (t <= -9.5e-87)
		tmp = Float64(Float64(1.0 / y) * Float64(x / t));
	elseif (t <= 6.5e-151)
		tmp = Float64(t_1 / y);
	elseif (t <= 3.9e+177)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 3.9e+246)
		tmp = Float64(t_1 / 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)
	t_1 = x / -z;
	tmp = 0.0;
	if (t <= -9.5e-87)
		tmp = (1.0 / y) * (x / t);
	elseif (t <= 6.5e-151)
		tmp = t_1 / y;
	elseif (t <= 3.9e+177)
		tmp = (x / y) / t;
	elseif (t <= 3.9e+246)
		tmp = t_1 / 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_] := Block[{t$95$1 = N[(x / (-z)), $MachinePrecision]}, If[LessEqual[t, -9.5e-87], N[(N[(1.0 / y), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-151], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[t, 3.9e+177], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 3.9e+246], N[(t$95$1 / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.5e-87

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 48.0%

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

      1. associate-/r* 54.7%

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

      2. div-inv 54.7%

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

   5. Applied egg-rr 54.7%

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

   if -9.5e-87 < t < 6.4999999999999994e-151

   1. Initial program 84.8%

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

      1. clear-num 84.3%

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

      2. associate-/r/ 84.8%

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

   4. Applied egg-rr 84.8%

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

      1. associate-*l/ 84.8%

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

      2. *-commutative 84.8%

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

      3. frac-times 95.9%

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

      4. clear-num 95.9%

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

      5. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around inf 59.3%

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

      1. *-rgt-identity 59.3%

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

      2. times-frac 62.1%

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

      3. associate-*l/ 64.5%

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

      4. associate-*r/ 64.6%

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

      5. *-rgt-identity 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in t around 0 52.8%

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

       1. associate-*r/ 52.8%

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

       2. *-commutative 52.8%

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

       3. associate-/r* 56.5%

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

       4. neg-mul-1 56.5%

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

   12. Simplified 56.5%

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

   if 6.4999999999999994e-151 < t < 3.8999999999999999e177

   1. Initial program 93.1%

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

      1. clear-num 92.9%

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

      2. associate-/r/ 93.0%

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

   4. Applied egg-rr 93.0%

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

      1. associate-*l/ 93.1%

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

      2. *-commutative 93.1%

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

      3. frac-times 98.3%

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

      4. clear-num 97.8%

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

      5. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in z around 0 49.5%

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

      1. *-rgt-identity 49.5%

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

      2. associate-*r/ 49.5%

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

      3. associate-/l/ 49.5%

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

      4. associate-*r/ 52.8%

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

      5. associate-*r/ 52.8%

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

      6. *-rgt-identity 52.8%

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

   9. Simplified 52.8%

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

   if 3.8999999999999999e177 < t < 3.9e246

   1. Initial program 70.4%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 94.6%

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

   6. Taylor expanded in y around 0 60.1%

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

      1. associate-*r/ 60.1%

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

      2. neg-mul-1 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in x around 0 60.1%

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

       1. mul-1-neg 60.1%

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

       2. associate-/l/ 69.8%

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

       3. distribute-neg-frac2 69.8%

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

   11. Simplified 69.8%

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

   if 3.9e246 < t

   1. Initial program 71.8%

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

      1. clear-num 71.8%

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

      2. associate-/r/ 71.8%

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

   4. Applied egg-rr 71.8%

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

      1. associate-*l/ 71.8%

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

      2. *-commutative 71.8%

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

      3. frac-times 99.5%

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

      4. clear-num 99.4%

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

      5. un-div-inv 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in z around 0 43.3%

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

      1. associate-/r* 70.5%

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

   9. Simplified 70.5%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{x}{-z}}{y}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+177}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+246}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

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 -2.4e-46)
   (/ (/ x z) (- z y))
   (if (<= z -5e-97)
     (/ x (* z (- z t)))
     (if (<= z 6.2e+46) (* (/ x (- t z)) (/ 1.0 y)) (/ (/ 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 <= -2.4e-46) {
		tmp = (x / z) / (z - y);
	} else if (z <= -5e-97) {
		tmp = x / (z * (z - t));
	} else if (z <= 6.2e+46) {
		tmp = (x / (t - z)) * (1.0 / y);
	} 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 <= (-2.4d-46)) then
        tmp = (x / z) / (z - y)
    else if (z <= (-5d-97)) then
        tmp = x / (z * (z - t))
    else if (z <= 6.2d+46) then
        tmp = (x / (t - z)) * (1.0d0 / y)
    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 <= -2.4e-46) {
		tmp = (x / z) / (z - y);
	} else if (z <= -5e-97) {
		tmp = x / (z * (z - t));
	} else if (z <= 6.2e+46) {
		tmp = (x / (t - z)) * (1.0 / y);
	} 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 <= -2.4e-46:
		tmp = (x / z) / (z - y)
	elif z <= -5e-97:
		tmp = x / (z * (z - t))
	elif z <= 6.2e+46:
		tmp = (x / (t - z)) * (1.0 / y)
	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 <= -2.4e-46)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= -5e-97)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	elseif (z <= 6.2e+46)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(1.0 / y));
	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 <= -2.4e-46)
		tmp = (x / z) / (z - y);
	elseif (z <= -5e-97)
		tmp = x / (z * (z - t));
	elseif (z <= 6.2e+46)
		tmp = (x / (t - z)) * (1.0 / y);
	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, -2.4e-46], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-97], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+46], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000013e-46

   1. Initial program 84.5%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

   7. Simplified 77.9%

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

   if -2.40000000000000013e-46 < z < -4.9999999999999995e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   if -4.9999999999999995e-97 < z < 6.1999999999999995e46

   1. Initial program 91.2%

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

      1. clear-num 91.1%

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

      2. associate-/r/ 91.1%

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

   4. Applied egg-rr 91.1%

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

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. frac-times 95.6%

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

      4. clear-num 95.5%

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

      5. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around inf 76.5%

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

      1. *-rgt-identity 76.5%

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

      2. times-frac 81.1%

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

      3. associate-*l/ 79.3%

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

      4. associate-*r/ 79.4%

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

      5. *-rgt-identity 79.4%

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

   9. Simplified 79.4%

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

       1. div-inv 79.4%

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

   11. Applied egg-rr 79.4%

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

   if 6.1999999999999995e46 < z

   1. Initial program 73.2%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

   8. Simplified 89.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

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 -3.4e-47)
   (/ (/ x z) (- z y))
   (if (<= z -5e-97)
     (/ x (* z (- z t)))
     (if (<= z 1.52e+47) (/ (/ x (- t z)) y) (/ (/ 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 <= -3.4e-47) {
		tmp = (x / z) / (z - y);
	} else if (z <= -5e-97) {
		tmp = x / (z * (z - t));
	} else if (z <= 1.52e+47) {
		tmp = (x / (t - z)) / y;
	} 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 <= (-3.4d-47)) then
        tmp = (x / z) / (z - y)
    else if (z <= (-5d-97)) then
        tmp = x / (z * (z - t))
    else if (z <= 1.52d+47) then
        tmp = (x / (t - z)) / y
    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 <= -3.4e-47) {
		tmp = (x / z) / (z - y);
	} else if (z <= -5e-97) {
		tmp = x / (z * (z - t));
	} else if (z <= 1.52e+47) {
		tmp = (x / (t - z)) / y;
	} 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 <= -3.4e-47:
		tmp = (x / z) / (z - y)
	elif z <= -5e-97:
		tmp = x / (z * (z - t))
	elif z <= 1.52e+47:
		tmp = (x / (t - z)) / y
	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 <= -3.4e-47)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= -5e-97)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	elseif (z <= 1.52e+47)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	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 <= -3.4e-47)
		tmp = (x / z) / (z - y);
	elseif (z <= -5e-97)
		tmp = x / (z * (z - t));
	elseif (z <= 1.52e+47)
		tmp = (x / (t - z)) / y;
	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, -3.4e-47], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-97], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.52e+47], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4000000000000002e-47

   1. Initial program 84.5%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 77.9%

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

      1. associate-*r/ 77.9%

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

      2. neg-mul-1 77.9%

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

   7. Simplified 77.9%

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

   if -3.4000000000000002e-47 < z < -4.9999999999999995e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   if -4.9999999999999995e-97 < z < 1.52e47

   1. Initial program 91.2%

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

      1. clear-num 91.1%

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

      2. associate-/r/ 91.1%

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

   4. Applied egg-rr 91.1%

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

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. frac-times 95.6%

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

      4. clear-num 95.5%

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

      5. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around inf 76.5%

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

      1. *-rgt-identity 76.5%

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

      2. times-frac 81.1%

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

      3. associate-*l/ 79.3%

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

      4. associate-*r/ 79.4%

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

      5. *-rgt-identity 79.4%

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

   9. Simplified 79.4%

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

   if 1.52e47 < z

   1. Initial program 73.2%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

   8. Simplified 89.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 10^{-152}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.2e-86)
   (* (/ 1.0 y) (/ x t))
   (if (<= t 1e-152) (/ (/ x z) (- y)) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e-86) {
		tmp = (1.0 / y) * (x / t);
	} else if (t <= 1e-152) {
		tmp = (x / z) / -y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.2d-86)) then
        tmp = (1.0d0 / y) * (x / t)
    else if (t <= 1d-152) then
        tmp = (x / z) / -y
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.2e-86) {
		tmp = (1.0 / y) * (x / t);
	} else if (t <= 1e-152) {
		tmp = (x / z) / -y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3.2e-86:
		tmp = (1.0 / y) * (x / t)
	elif t <= 1e-152:
		tmp = (x / z) / -y
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.2e-86)
		tmp = Float64(Float64(1.0 / y) * Float64(x / t));
	elseif (t <= 1e-152)
		tmp = Float64(Float64(x / z) / Float64(-y));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.2e-86)
		tmp = (1.0 / y) * (x / t);
	elseif (t <= 1e-152)
		tmp = (x / z) / -y;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -3.2e-86], N[(N[(1.0 / y), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-152], N[(N[(x / z), $MachinePrecision] / (-y)), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000006e-86

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 48.0%

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

      1. associate-/r* 54.7%

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

      2. div-inv 54.7%

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

   5. Applied egg-rr 54.7%

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

   if -3.20000000000000006e-86 < t < 1.00000000000000007e-152

   1. Initial program 84.8%

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

      1. clear-num 84.3%

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

      2. associate-/r/ 84.8%

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

   4. Applied egg-rr 84.8%

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

      1. associate-*l/ 84.8%

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

      2. *-commutative 84.8%

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

      3. frac-times 95.9%

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

      4. clear-num 95.9%

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

      5. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around inf 59.3%

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

      1. *-rgt-identity 59.3%

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

      2. times-frac 62.1%

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

      3. associate-*l/ 64.5%

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

      4. associate-*r/ 64.6%

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

      5. *-rgt-identity 64.6%

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

   9. Simplified 64.6%

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

   10. Taylor expanded in t around 0 52.8%

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

       1. associate-*r/ 52.8%

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

       2. *-commutative 52.8%

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

       3. associate-/r* 56.5%

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

       4. neg-mul-1 56.5%

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

   12. Simplified 56.5%

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

   if 1.00000000000000007e-152 < t

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf 67.1%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 10^{-152}:\\ \;\;\;\;\frac{\frac{x}{z}}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -8.6e-81)
   (/ (/ x y) (- t z))
   (if (<= y 3.2e-87) (/ 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 <= -8.6e-81) {
		tmp = (x / y) / (t - z);
	} else if (y <= 3.2e-87) {
		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 <= (-8.6d-81)) then
        tmp = (x / y) / (t - z)
    else if (y <= 3.2d-87) 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 <= -8.6e-81) {
		tmp = (x / y) / (t - z);
	} else if (y <= 3.2e-87) {
		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 <= -8.6e-81:
		tmp = (x / y) / (t - z)
	elif y <= 3.2e-87:
		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 <= -8.6e-81)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 3.2e-87)
		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 <= -8.6e-81)
		tmp = (x / y) / (t - z);
	elseif (y <= 3.2e-87)
		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, -8.6e-81], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-87], 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 < -8.6000000000000006e-81

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 86.0%

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

      1. associate-/l/ 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in y around inf 83.0%

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

   if -8.6000000000000006e-81 < y < 3.19999999999999979e-87

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

   5. Simplified 74.0%

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

   if 3.19999999999999979e-87 < y

   1. Initial program 83.7%

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

      1. associate-/l/ 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around inf 62.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -0.00047)
   (/ (/ x y) (- t z))
   (if (<= y 2.2e-63) (/ (/ 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 <= -0.00047) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.2e-63) {
		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 <= (-0.00047d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.2d-63) 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 <= -0.00047) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.2e-63) {
		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 <= -0.00047:
		tmp = (x / y) / (t - z)
	elif y <= 2.2e-63:
		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 <= -0.00047)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.2e-63)
		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 <= -0.00047)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.2e-63)
		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, -0.00047], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-63], 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 < -4.69999999999999986e-4

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 85.5%

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

      1. associate-/l/ 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in y around inf 93.4%

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

   if -4.69999999999999986e-4 < y < 2.2e-63

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0 86.9%

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

      1. associate-/l/ 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around 0 81.2%

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

      1. associate-*r/ 81.2%

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

      2. neg-mul-1 81.2%

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

   8. Simplified 81.2%

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

   if 2.2e-63 < y

   1. Initial program 84.5%

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

      1. associate-/l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf 63.3%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= t -1.05e-88)
   (/ (/ x y) t)
   (if (<= t 1.25e-107) (/ x (* y (- 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 (t <= -1.05e-88) {
		tmp = (x / y) / t;
	} else if (t <= 1.25e-107) {
		tmp = x / (y * -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 (t <= (-1.05d-88)) then
        tmp = (x / y) / t
    else if (t <= 1.25d-107) then
        tmp = x / (y * -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 (t <= -1.05e-88) {
		tmp = (x / y) / t;
	} else if (t <= 1.25e-107) {
		tmp = x / (y * -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 t <= -1.05e-88:
		tmp = (x / y) / t
	elif t <= 1.25e-107:
		tmp = x / (y * -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 (t <= -1.05e-88)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 1.25e-107)
		tmp = Float64(x / Float64(y * 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 (t <= -1.05e-88)
		tmp = (x / y) / t;
	elseif (t <= 1.25e-107)
		tmp = x / (y * -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[t, -1.05e-88], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.25e-107], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e-88

   1. Initial program 87.8%

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

      1. clear-num 87.7%

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

      2. associate-/r/ 87.7%

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

   4. Applied egg-rr 87.7%

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

      1. associate-*l/ 87.8%

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

      2. *-commutative 87.8%

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

      3. frac-times 96.6%

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

      4. clear-num 96.5%

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

      5. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in z around 0 48.0%

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

      1. *-rgt-identity 48.0%

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

      2. associate-*r/ 47.9%

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

      3. associate-/l/ 48.8%

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

      4. associate-*r/ 50.8%

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

      5. associate-*r/ 50.9%

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

      6. *-rgt-identity 50.9%

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

   9. Simplified 50.9%

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

   if -1.05e-88 < t < 1.24999999999999993e-107

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 85.5%

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

      1. associate-/l/ 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in y around inf 61.6%

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

   7. Taylor expanded in t around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-neg-frac2 51.1%

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

      3. *-commutative 51.1%

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

      4. distribute-rgt-neg-out 51.1%

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

   9. Simplified 51.1%

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

   if 1.24999999999999993e-107 < t

   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. clear-num 84.0%

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

      2. associate-/r/ 84.1%

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

   4. Applied egg-rr 84.1%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

      3. frac-times 98.7%

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

      4. clear-num 98.4%

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

      5. un-div-inv 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in z around 0 46.0%

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

      1. associate-/r* 54.7%

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

   9. Simplified 54.7%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-88}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 6.5 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e+55) (not (<= z 6.5e+81))) (/ x (* z t)) (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 6.5e+81)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.4d+55)) .or. (.not. (z <= 6.5d+81))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 6.5e+81)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e+55) or not (z <= 6.5e+81):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+55) || !(z <= 6.5e+81))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e+55) || ~((z <= 6.5e+81)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e+55], N[Not[LessEqual[z, 6.5e+81]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e55 or 6.4999999999999996e81 < z

   1. Initial program 76.8%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 46.5%

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

   6. Taylor expanded in y around 0 39.6%

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

      1. associate-*r/ 39.6%

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

      2. neg-mul-1 39.6%

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

   8. Simplified 39.6%

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

      1. add-sqr-sqrt 28.5%

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

      2. sqrt-unprod 44.5%

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

      3. sqr-neg 44.5%

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

      4. sqrt-unprod 10.0%

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

      5. add-sqr-sqrt 35.3%

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

      6. *-un-lft-identity 35.3%

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

      7. *-commutative 35.3%

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

      8. associate-/r* 43.3%

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

   10. Applied egg-rr 43.3%

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

       1. *-lft-identity 43.3%

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

       2. associate-/l/ 35.3%

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

       3. *-commutative 35.3%

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

   12. Simplified 35.3%

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

   if -1.4e55 < z < 6.4999999999999996e81

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 46.8%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 6.5 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 90.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+151) (/ (/ x y) (- t z)) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+151) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (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 (y <= (-1.7d+151)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * (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 (y <= -1.7e+151) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+151:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+151)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+151)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * (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[y, -1.7e+151], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e151

   1. Initial program 83.2%

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

   3. Taylor expanded in x around 0 83.2%

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

      1. associate-/l/ 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 99.7%

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

   if -1.7e151 < y

   1. Initial program 86.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-89}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1e-89) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-89) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1d-89) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-89) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1e-89:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1e-89)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1e-89)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1e-89], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000004e-89

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   if 1.00000000000000004e-89 < t

   1. Initial program 83.1%

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

   3. Taylor expanded in t around inf 69.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-89}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.6e-90) (/ x (* y (- t 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-90) {
		tmp = x / (y * (t - 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-90) then
        tmp = x / (y * (t - 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-90) {
		tmp = x / (y * (t - 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-90:
		tmp = x / (y * (t - 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-90)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.6e-90)
		tmp = x / (y * (t - 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-90], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.59999999999999981e-90

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   if 3.59999999999999981e-90 < t

   1. Initial program 83.1%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf 80.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-89}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1e-89) (/ (/ x y) (- t 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 <= 1e-89) {
		tmp = (x / y) / (t - 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 <= 1d-89) then
        tmp = (x / y) / (t - 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 <= 1e-89) {
		tmp = (x / y) / (t - 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 <= 1e-89:
		tmp = (x / y) / (t - 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 <= 1e-89)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1e-89)
		tmp = (x / y) / (t - 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, 1e-89], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000004e-89

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 87.1%

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

      1. associate-/l/ 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in y around inf 59.7%

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

   if 1.00000000000000004e-89 < t

   1. Initial program 83.1%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf 80.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-89}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{-89}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.1e-89) (/ (/ x (- t z)) y) (/ (/ 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 <= 3.1e-89) {
		tmp = (x / (t - z)) / y;
	} 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 <= 3.1d-89) then
        tmp = (x / (t - z)) / y
    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 <= 3.1e-89) {
		tmp = (x / (t - z)) / y;
	} 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 <= 3.1e-89:
		tmp = (x / (t - z)) / y
	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 <= 3.1e-89)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.1e-89)
		tmp = (x / (t - z)) / y;
	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, 3.1e-89], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.09999999999999996e-89

   1. Initial program 87.2%

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

      1. clear-num 86.9%

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

      2. associate-/r/ 87.1%

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

   4. Applied egg-rr 87.1%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

      3. frac-times 96.5%

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

      4. clear-num 96.4%

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

      5. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in y around inf 56.7%

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

      1. *-rgt-identity 56.7%

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

      2. times-frac 59.4%

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

      3. associate-*l/ 62.4%

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

      4. associate-*r/ 62.5%

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

      5. *-rgt-identity 62.5%

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

   9. Simplified 62.5%

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

   if 3.09999999999999996e-89 < t

   1. Initial program 82.9%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around inf 80.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{-89}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 46.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= z -2.5e+57) (/ x (* z 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 (z <= -2.5e+57) {
		tmp = x / (z * 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 (z <= (-2.5d+57)) then
        tmp = x / (z * 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 (z <= -2.5e+57) {
		tmp = x / (z * 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 z <= -2.5e+57:
		tmp = x / (z * 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 (z <= -2.5e+57)
		tmp = Float64(x / Float64(z * 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 (z <= -2.5e+57)
		tmp = x / (z * 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[z, -2.5e+57], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999986e57

   1. Initial program 84.8%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 47.5%

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

   6. Taylor expanded in y around 0 41.8%

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

      1. associate-*r/ 41.8%

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

      2. neg-mul-1 41.8%

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

   8. Simplified 41.8%

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

      1. add-sqr-sqrt 34.2%

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

      2. sqrt-unprod 44.7%

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

      3. sqr-neg 44.7%

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

      4. sqrt-unprod 5.4%

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

      5. add-sqr-sqrt 35.7%

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

      6. *-un-lft-identity 35.7%

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

      7. *-commutative 35.7%

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

      8. associate-/r* 43.3%

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

   10. Applied egg-rr 43.3%

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

       1. *-lft-identity 43.3%

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

       2. associate-/l/ 35.7%

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

       3. *-commutative 35.7%

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

   12. Simplified 35.7%

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

   if -2.49999999999999986e57 < z

   1. Initial program 86.2%

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

      1. clear-num 86.1%

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

      2. associate-/r/ 86.1%

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

   4. Applied egg-rr 86.1%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

      3. frac-times 96.5%

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

      4. clear-num 96.3%

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

      5. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in z around 0 40.2%

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

      1. associate-/r* 45.6%

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

   9. Simplified 45.6%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 2.5e-74) (/ (/ 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 <= 2.5e-74) {
		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 <= 2.5d-74) 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 <= 2.5e-74) {
		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 <= 2.5e-74:
		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 <= 2.5e-74)
		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 <= 2.5e-74)
		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, 2.5e-74], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.49999999999999999e-74

   1. Initial program 87.5%

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

      1. clear-num 87.3%

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

      2. associate-/r/ 87.5%

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

   4. Applied egg-rr 87.5%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

      3. frac-times 96.6%

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

      4. clear-num 96.5%

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

      5. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around 0 33.2%

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

      1. *-rgt-identity 33.2%

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

      2. associate-*r/ 33.1%

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

      3. associate-/l/ 33.6%

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

      4. associate-*r/ 39.9%

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

      5. associate-*r/ 39.9%

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

      6. *-rgt-identity 39.9%

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

   9. Simplified 39.9%

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

   if 2.49999999999999999e-74 < t

   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. clear-num 81.6%

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

      2. associate-/r/ 81.6%

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

   4. Applied egg-rr 81.6%

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

      1. associate-*l/ 81.7%

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

      2. *-commutative 81.7%

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

      3. frac-times 98.6%

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

      4. clear-num 98.2%

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

      5. un-div-inv 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in z around 0 43.1%

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

      1. associate-/r* 54.5%

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

   9. Simplified 54.5%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 97.2% 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 85.9%

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

   1. associate-/l/ 97.4%

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

3. Simplified 97.4%

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

5. Final simplification 97.4%

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

Alternative 22: 39.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

3. Taylor expanded in z around 0 35.9%

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

4. Final simplification 35.9%

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

Developer target: 87.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024082 
(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))))